Managerial Economics

CyryxCollege, Maldvies

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Managerial Economics Syllabus Lecture 1 Notes Lecture 2 Notes

Problem Set 1 Problem Set 1Key

Lecture 3 Notes

Problem Set 2 Problem Set 2 Key

Lecture 4 Notes Lecture 5 Notes Lecture 6 Notes Lecture 7 Notes

Problem Set 3 Problem Set 3 Key

Lecture 8 Notes Lecture 9 Notes Lecture 10 Notes Problem Set 4 Problem Set 4 Key Lecture 11 Notes Lecture 12 Notes Lecture 13 Notes Problem Set 5 Problem Set 5 Key Lecture 14 Notes Lecture 15 Notes Problem Set 6 Problem Set 6 Key Lecture 16 Notes Test 1 Review Outline Lecture 17 Notes Problem Set 7 Problem 7 Key Lecture 18 Notes

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Lecture 19 Notes Problem Set 8 Problem 8 Key Lecture 20 Notes Lecture 21 Notes Problem Set 9 Problem 9 Key Lecture 22 Notes Problem Set 10 Problem 10 Key Lecture 23 Notes Problem Set 11 Problem 11 Key Lecture 24 Notes Lecture 25 Notes Lecture 26 Notes Lecture 27 Notes Problem 12 Lecture 28 Notes Lecture 29 Notes Lecture 30 Notes Problem 13 NEW Problem 13 Key Test 2 Review Outline Lecture 31 Notes Lecture 32 Notes Lecture 33 Notes Problem 14 Problem 14 Key Lecture 34 Notes Lecture 35 Notes Lecture 36 Problem 15 Problem 15 Key (CORRECTED) Lecture 37 Lecture 38 Review Outline for Final Examination

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Review Outline for Final Examination I. Chapter 1. The Fundamentals of Managerial Economics A. Definition of Topic. 1. Economics 2. Managerial Decisions B. Components of Effective Decision Making 1. Identify Goals and Constraints: 2. Recognize the Nature and Importance of Profits: Economic profits differ from Accounting profits. . Good decision-making involves the maximization of economic profits. 3. Understanding Incentives. .Compensation and the structure of organizations affects importantly organizations. a. Organizational Incentives b. Incentives for Motivating Individuals 4. Understand Markets. Market forces represent a series of rivalries. In any problem, you must appreciate your position relative to other agents. 5. Recognize the Time Value of Money 6. Appreciate Marginal Analysis. Marginal decisions are an easy way to optimize totals. Calculus is just a formal expression of marginal analysis. a. Discrete Decisions. b. Continuous Decisions and the calculus c. Incremental Analysis 1. Pay attention to incremental costs and incremental benefits. 2. Ignore sunk costs. . II. Chapter Market Forces: Demand and Supply A. Introduction and Overview. 1. Overview 2. The structure of the supply and demand model. B. The Demand Side. 1. Motivation: Diminishing marginal utility: 2. Definition of Demand Curve 3. Determinants of Demand. 4. Changes in demand vs. changes in qty demanded. 5. The Notion of Consumer Surplus 6. An Analytical Example C. The Supply Side. 1. Driving Force. The Law of Diminishing Returns 2. Definition of Supply Curve 3. Determinants of supply:

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4. Changes in supply vs. changes in quantity supplied. 5. Producer Surplus. 6. An Analytical Example. D. Equilibrium. Putting Supply and Demand Together 1. Definition. 2. Binding the market. Price floors Price Ceilings E. Comparative Statics. 1. Supply or Demand Shifts 2. Supply and Demand Shifts III. Quantitative Demand Analysis A. Price Elasticity of Demand 1. Motivation 2. Calculations a. Arc price elasticity of demand b. Point price elasticity of demand c. Percentage Changes 3. A Graphical Interpretation of Price Elasticity. 4. Some Observations about Price Elasticity of Demand a. Most Demand curves have elastic and inelastic segments b. Exceptions c. Elasticity and the Slope of Demand Curves 5. Price Elasticity, MR and TR. 6. Determinants of price elasticity of demand B. Other Demand Elasticities 1. Cross Price Elasticities 2. Income Elasticities 3.Other Elasticites. C. Elasticities and demand functions 1. Linear Demand functions. 2. Logrithmic Demand. D. Estimating Demand: Regression Analysis. 1. Interpreting the significance of individual parameter estimates 2. Forecasting

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IV. Chapter 5. The Production Process and Costs A. Introduction B. The Production Function 1. Short Run Production. a. Diminishing Marginal Productivity and Marginal Product b. Relationships between Productivity Measures. c. Optimal Use of a single input. 2. Long Run Production (Optimal use of multiple inputs) 3. Returns to scale: Given a production function of the form α F(K,L) = KL The function exhibits increasing returns to scale if α>.5 constant returns to scale if α=.5 decreasing returns to scale if α.5 constant returns to scale if α=.5 decreasing returns to scale if α 0, terms get smaller as we get further into the future. It is well known that the present value of such a perpetuity can be expressed simply as PV

=

CF/i

Similarly, for a firm generating a constant profit PV

=

π/i

Notice that the above PV formula excludes a payment received now (e.g., at time 0).The PV of a stream of returns starting today is PV

=

π/i + π =

[(1+i) π]/i

You must always be careful to stipulate the timing of the first payment when doing PV calculations. Note: Your text discusses extensions of this model. In this class you will be responsible only for the material covered above. 6. Using Marginal Analysis. A final principle in intelligent decision-making pertains to the unit of analysis used. One can often cut through a very difficult optimization process by confining attention to incremental changes. a. Discrete Decisions. Example. Suppose you were faced with the problem of trying to allocate study time between two courses for a test on the same day. If you had a total of 6 hours to study, you might have the following possibilities.

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Econ Hours score 0 0 1 30 2 55 3 75 4 93 5 98 6 100

Math Hours 0 1 2 3 4 5 6

score 0 40 65 77 86 94 100

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One way to approach this problem would be to consider all combinations of all totals that were available:

Scores Econ 0 1 2 3 4 5 6

Math 6 5 4 3 2 1 0

Econ 0 30 55 75 93 98 100

Total Math 100 94 86 77 65 40 0

100 124 141 152 158 138 100

An equivalent solution, however, is obtained by considering just the marginal changes A marginal change is the change in the total associated with studying an extra hour. Econ Math Hour score marginal hour score marginal increase increase 0 0 0 0 1 30 30 1 40 40 2 55 25 2 65 25 3 75 20 3 77 12 4 93 18 4 86 9 5 98 5 5 94 8 6 100 2 6 100 6 Note: This process has the advantage that it requires less information.

Lecture 4

Problems: Return Problem Set 1, Problem Set 2 – due Monday.

REVIEW I. Chapter 1. The Fundamentals of Managerial Economics B. Components of Effective Decision Making 5. Recognize the Time Value of Money. a. Discounting the Future. b. Calculating Net Present Value of a Project Comment: Recall problem 1. A student asked if in deciding whether to undertake a project, it made a difference if the net present value if a project was less than the cost the project. I ERRED IN MY RESPONSE. The correct answer is: ANY PROJECT WITH A POSITIVE NPV SHOULD BE UNDERTAKEN. 22

To see this, suppose you are given the chance to invest $100,000 in a project that will yield $60,000 for each of the next two years. If i=.10, then the PV of the returns is 60,000/1.1 + 60,000/1.12 =54,540 + 49,587 =104,132. The Net Present value is 104,132-100,000 = 4,132. (That is, you end up with 4,132 MORE than 100,000 in present value terms.) Suppose, alternatively, that you took the 100,000 and put it in the bank for two years. If i = .10, you would have 110,000 after one year, and $121, 000 after two years. The present value of that money is (by definition) $121,000/(1.1)2 = 100,000 c. The present value of a firm/ Discounting over an infinite horizon. With the first payment coming in one year, PV = π/i If the first payment is tomorrow, PV

=

π/i + π =

[(1+i) π]/i

Example: Suppose you can purchase a share of a firm that will pay a dividend of $10 each year, starting one year from today. If the discount rate is . 05, what is the present value of this stock? 10/.05 = $200. How would your answer change if the first payment came tomorrow? 10/.05 + 10 = $210. 5. Appreciate Marginal Analysis. Marginal decisions are an easy way to optimize totals that require less information in the decision-making process. a. Discrete Decisions - Allocating time for a test Preview__________________________________________________________ 5. Marginal Analysis Continued - Comparing TR to TC b. Continuous Decisions LECTURE______________________________________________

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5. Using Marginal Analysis. A final principle in intelligent decision-making pertains to the unit of analysis used. One can often cut through a very difficult optimization process by confining attention to incremental changes. a. Discrete Decisions. Example. Suppose you were faced with the problem of trying to allocate study time between two courses for a test on the same day. If you had a total of 6 hours to study, you might have the following possibilities. Econ Hours score 0 0 1 30 2 55 3 75 4 93 5 98 6 100

Math Hours 0 1 2 3 4 5 6

score 0 40 65 77 86 94 100

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One way to approach this problem would be to consider all combinations of all totals that were available:

Scores Econ 0 1 2 3 4 5 6

Math 6 5 4 3 2 1 0

Econ 0 30 55 75 93 98 100

Total Math 100 94 86 77 65 40 0

100 124 141 152 158 138 100

An equivalent solution, however, is obtained by considering just the marginal changes A marginal change is the change in the total associated with studying an extra hour. Econ Math Hour score marginal hour score marginal increase increase 0 0 0 0 1 30 30 1 40 40 2 55 25 2 65 25 3 75 20 3 77 12 4 93 18 4 86 9 5 98 5 5 94 8 6 100 2 6 100 6 Note: This process has the advantage that it requires less information. More generally, we might consider a situation in which there were both costs and benefit (for example the case of profit maximization, where π = TR TC Control Variable TB 0 0 1 90 2 170 3 240 4 300 5 350 6 390 7 420 8 440 9 450

TC 0 10 30 60 100 150 210 280 360 450

NB 0 80 140 180 200 200 180 140 80 0

MB 90 80 70 60 50 40 30 20 10 25

MC 10 20 30 40 50 60 70 80 90

MNB 80 60 40 20 0 -20 -40 -60 -80

10

450

550

-100

0

100

-100

Definition: The Marginal Principle: To maximize net benefits, the manager should increase the managerial control variable to the point where marginal benefit equals marginal costs. Graphically, this can be illustrated both by graphs of totals and of marginal changes: Total changes 600 500 TC TB

400 300 200 100 0 0

1

2

3

4

5

6

7

8

9

10

7

8

9

10

Output

100

MB, MC

80 60 40 20 0 0

1

2

3

4

5

6

Output

Observe the role of marginals and totals. (Notice that the totals and marginal lines should not line up exactly. There are two points of total maximization. This is due to the discreteness of decisions here. )

Lecture 5

Problems: Problem Set 2 – due Monday.

REVIEW___________________________________________________: I. Chapter 1. The Fundamentals of Managerial Economics 26

B. Components of Effective Decision Making 5. Appreciate Marginal Analysis. a. Discrete Decisions - Allocating time for a test. (Recall the point, making the best incremental decisions at each step in a sequence will drive you to the maximum total. - Comparing TR and TC On a graph, the point where π is maximized is where the difference between TR and TC is maximized. This is also the point where MR =MC. The DISTANCE between TR and TC equals the AREA above MC and below MR (We will use this to show that equilibrium is efficient in Chapter 2.) Note, however, in your homework that your marginals never quite line up. This is a problem with discrete analysis. Your rule in such a case is to take (produce) the last unit such that MR>MC. Example: Q 0 1 2 3 4 5 6

TR 0 19 36 51 64 75 84

TC 1 3 9 19 33 51 73

TNB -1 16 27 32 31 24 11

MR

MC

MNB

19 17 15 13 11 9

2 6 10 14 18 22

17 11 5 -1 -7 -13

If you plot this you will see that MR and MC never equal, given we are restricted to discrete changes. In a continuous world, we could find an exact answer.. Preview__________________________________________________________ 5. Marginal Analysis Continued b. Continuous Decisions c. Incremental Decisions LECTURE______________________________________________ b. Continuous Decisions. Notice that in some circumstances, it is possible to make adjustments more continuously Notice in my graphical analysis that my graphs are always a bit off. This is a problem of discreteness.

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More generally, we might consider a situation in which there were both costs and benefit (for example the case of profit maximization, where π = TR TC Now, suppose that I tell you that in the problem in the introduction that TR = 20Q – Q2 and that TC = 1 + 2Q2 I could come closer to finding the optimum if I used a finer grid. For example, suppose I reduce Q steps to .5 Q 0 0.5 1 1.5 2 2.5 3 3.5 4

TR 0 9.75 19 27.75 36 43.75 51 57.75 64

TC 1 1.5 3 5.5 9 13.5 19 25.5 33

TNB -1 8.25 16 22.25 27 30.25 32 32.25 31

MR

MC

MNB

9.75 9.25 8.75 8.25 7.75 7.25 6.75 6.25

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5

9.25 7.75 6.25 4.75 3.25 1.75 0.25 -1.25

What if I wanted to find the exact maximum? I could do this by taking a infinitesimal changes. Let’s do this in parts. Start with the Total Revenue relationship. TR = 20Q -Q2 Consider the slope of the line tangent to the curve at Q=4. Q 0 1 2 3 4

TR 0 19 36 51 64

Graphically,

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120 100 80 60 40 20 0 0

2

4

6

8

Consider the slope of the line tangent to the curve at Q =4. We could estimate this by calculating the average slope over progressively narrower ranges, e.g., (64 - 0 )/(4 - 0) = 64/4 = 16 (64 - 19 )/(4 - 1) = 45/3 = 15 (64 -36 )/(4 - 2) = 28/2 = 14 (64 -51)/(4 - 3) = 13/1 = 13 If we really wanted the slope of the line tangent to the curve, we must take an infinitesimally small change -h. Then 64 - [20(4-h) - (4-h)2] 4 -(4-h) = 64 - 80 + 20h +16 – 8h + h2 h = _Q2 +12h h and as h → 0 this becomes 12. This is the idea of a derivative. The only difference between taking limits, and the rules of derivation that you learned is that the rules are just a shorthand, for example, TR = 20Q -Q2 TR' = MR =20 - 2Q At Q = 4, TR'= 12.

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You could do the same thing for costs TC = 1+2Q2 TC = MC = 4Q This is the slope of the line tangent to the TC curve To maximize profits, set MR = MC TR = 20 – 2Q Q =

= 4Q 20/6 = 3.33

=

TC

Comments a) I assume that you all have been exposed to simple differential calculus. The above development was done only to complete a little intuition pertaining to calculus. In the event that your calculus is a bit rusty, I can assure you that with only a few exceptions, our derivatives will be restricted to the following functional forms. Derivative of a constant f(x) = a; f’(x) = 0 Derivative of a linear equation f(x)= ax; f’’(x) = a Derivative of an exponential function f(x) = xn; f’(x) nxn-1 You may also find it useful to recall the following: f(x) = g(x) + h(x); f’(x) = g’(x) + h’(x) f(x) = g(x)h(x); f’(x) = g’(x)h(x) + h’(x) g(x) f(x) = g(h(x)) = g’(h(x))h’(x) b) Finally, in your homework, I would like for you to report your marginal revenue and marginal costs as derivates, rather than as incremental changes.

Lecture 6

Problems: Collect Problem Set 2. (Other review problem, 2, 3, 5, 8, 10) REVIEW___________________________________________________: I. Chapter 1. The Fundamentals of Managerial Economics B. Components of Effective Decision Making

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5. Appreciate Marginal Analysis. a. Discrete Decisions b. Continuous Decisions TR = 10Q – Q2 and that TC = .25Q2 (In problem 2). I can see the relationship of marginals to the totals on the marginals graph, as well as on a totals graph. But we also learned the idea of a derivative, which is just a slope over an infinitesimally small range. Derivative of a constant f(x) = a; f’(x) = 0 Derivative of a linear equation f(x)= ax; f’’(x) = a Derivative of an exponential function f(x) = xn; f’(x) nxn-1 You may also find it useful to recall the following: f(x) = g(x) + h(x); f’(x) = g’(x) + h’(x) f(x) = g(x)h(x); f’(x) = g’(x)h(x) + h’(x) g(x) f(x) = g(h(x)) = g’(h(x))h’(x)

Preview__________________________________________________________ c. Incremental Decisions Some review problems. LECTURE______________________________________________ Incremental analysis: For many (if not most) decisions, the manager must make a binary (yes or no) choice. In that case, the tools described above are appropriate. However, rather than considering the entire set of possibilities, consider only the changes from the status quo, and determine whether the incremental change is desirable. The trick to this incremental analysis is to attend only to the things that actually change with the decision, and ignore the rest. One practical way express this is the following: a) In making a decision pay attention to marginal costs and marginal benefits b) In making a decision, pay attention only to marginal costs and marginal benefits (That is, ignore sunk costs) Example, suppose you wait in a line in a grocery store. Another line opens up. What value should you place on the time you’ve spent waiting in your present line (none)

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Example; Suppose you have a 12 month lease on an apartment. You must pay $700 per month. If you get a new job in May that forces you to leave town in May and if your lease runs through August, how much, at a minimum must you get to sublease the apartment? (Answer, you must cover any variable costs, and nothing more!) Example: A more involved example. Suppose you manufacture umbrellas, and you are deciding whether or not to purchase a new “game day” golf umbrella, which is big enough to keep the entire family dry in a halftime downpour. The new machine costs $40,000. For simplicity, we assume that the machine lasts one year, and is then useless. You can put the machine in a slot where a now defunct standard machine sits. Old machine removal and recycling costs are $5,000, and must be borne independent of whether or not you buy the new machine. Installation costs for the new machine are $4,000. Variable costs for the new umbrellas are $8 per umbrella for materials and energy and $4 per umbrella for labor. Suppose that you can reasonably expect to sell 2000 of these umbrellas next year, at $35 each. Is the machine a good investment? Incremental revenues are ($35)(2000) = $70,000 Incremental Costs are $40,000 $4,000 $24,000 $68,000

new machine installation variable expenses ($12)(2000)

Result: Yes, purchase the machine. Notice, however, that the $5,000 removal expenses should not be considered in this analysis.

Lecture 7 REVIEW___________________________________________________: c. Incremental Decisions In attempting to optimize, two rules: - Attend to marginal benefits, attend to marginal benefits and marginal costs. -Attend only to marginal benefits and marginal costs. (Ignore sunk costs) Preview__________________________________________________________ II. Chapter Market Forces: Demand and Supply A. Introduction and Overview. 1. Overview 2. The structure of the supply and demand model.

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B. The Demand Side. 1. Motivation: Diminishing marginal utility: 2. Definition of Demand Curve 3. Determinants of Demand. 4. Changes in demand vs. changes in qty demanded. LECTURE______________________________________________ A. Introduction and Overview. 1. Overview. The purpose of this chapter. Economics proceeds via models. A model is an abstraction from reality, done for the purpose of explanation, or prediction. It is important to emphasize that these models are necessarily unrealistic. A “model” that captured all the complexity of reality wouldn’t be useful at all. Rather the oversimplification of a model is useful if it serves effectively an explanatory or predictive function. For example, the first model presented in this class was the present value characterization of the firm, introduced in chapter 1. This model, of course misses many elements, including the uncertainty of returns over time, as well as the possibility that interest rates may change. Nevertheless, it is useful in that it provides some insight into the issues relevant to considering the inter-temporal value of a firm. This chapter presents a second model, the theory of price and quantity determination. This model should be a review for most of you. Nevertheless, it is of prominent importance. The purpose of this model is both explanatory and predictive. It is the primary tool that you can use to infer the effects of market impacts on prices and outputs. You are expected to master the mechanics of this model. A second function of this review is to present this model in simple algebraic terms. This presentation should help “acclimatize” you to the type of analysis we will do in this course. 2. The structure of the supply and demand model. a. Overview. In this model, we divide people into two groups i. Households: Who attempt to maximize utility, they face diminishing marginal utility, and are subject to a budget constraint. ii Firms: Attempt to maximize profits. Firms fact cost constraints, and are subject to a law of diminishing returns in production. We will look at Demand (household behavior) Supply (firm behavior) and equilibrium, the interaction of these parts that generates price and output predictions B. The Demand Side. 1. Motivation: Consider an example of consuming a good. Suppose that it’s 100 degrees F outside, and you play 3 sets of tennis and then run 10 miles. Then you put on a coat,

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jump in the car, turn the heater up to full blast, and drive 3 hours in the sun. At the end of all this, you 1/2 dozen chili peppers. Now stop at a gas station and purchase cans of Sprite, one by one. Consider how much you would pay, for the first can, for the second, the third, and etc. The fact that you are gradually getting full is the notion of diminishing marginal utility. Diminishing marginal utility: In a given time frame, consumption of additional units of a good yields decreasing increments to total well being due to relative satiation (fullness). 2. Definition (for output market): The Demand Curve: A curve indicating varying quantities of a good or service that consumers are ready, willing and able to purchase at varying prices, per unit of time, other things constant. Demand is down-sloping due to the diminishing marginal utility of consumption. There are a number of important components in this decision a. Price/Quantity relationship: Price is the most important determinant of Quantity b. Ready, willing and able: Defines the market. Ready - in the market. Willing - desires the good. Able - has the wherewithal. c. Per unit of time: Time must be specified, as it affects diminishing marginal utility. d. Other things constant. A number of things aside from the price affect qty purchased (including substitutes, complements, and advertising, and etc.) e. Down-sloping due to diminishing marginal utility (Fullness). This is the reason that there is an inverse relationship between price and quantity. 3. Determinants of Demand. Things that affect the Marginal Utility of purchasers in the market. In addition to price, determinants include: Ps -Price of substitutes Pc Price of complements I Income (Normal goods or Inferior goods) E Expectations (regarding relative future prices B Number of buyers (population) 4. Changes in demand vs. changes in qty demanded. When one of the non-price determinants of demand changes, it is necessary to draw a new demand schedule. This is known as a change in demand (schedule). When there is a change in price, other things held constant, this is called a change in quantity demand (a movement along a schedule)

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Example, consider Qd = f(P, Ps, Pc, I) This is a demand function. It is a relationship between quantity demanded, and the entire collection of elements that determine sales quantity. The demand curve is a relationship between price and quantity alone, holding all other elements constant. Suppose income increases. Then it would be necessary to shift the demand schedule. Note: The one thing that CANNOT change demand (curve) is a change in the price of the good! Lecture 8 REVIEW___________________________________________________: II. Chapter Market Forces: Demand and Supply A. Introduction and Overview. 1. Overview 2. The structure of the supply and demand model. B. The Demand Side. 1. Motivation: Diminishing marginal utility: 2. Definition of Demand Curve 3. Determinants of Demand. 4. Changes in demand vs. changes in qty demanded. Preview__________________________________________________________ 5. The Notion of Consumer Surplus 6. An Analytical Example LECTURE______________________________________________ 4. Changes in demand vs. changes in qty demanded. When one of the non-price determinants of demand changes, it is necessary to draw a new demand schedule. This is known as a change in demand (schedule). When there is a change in price, other things held constant, this is called a change in quantity demand (a movement along a schedule) Example, consider Qd = f(P, Ps, Pc, I)

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This is a demand function. It is a relationship between quantity demanded, and the entire collection of elements that determine sales quantity. The demand curve is a relationship between price and quantity alone, holding all other elements constant. Suppose income increases. Then it would be necessary to shift the demand schedule. Note: The one thing that CANNOT change demand (curve) is a change in the price of the good! 5. The Notion of Consumer Surplus In markets where all consumers pay a uniform price for a good, most of the consumers who purchase the good place a higher value on the product than the purchase price. This difference between purchase price and value is termed consumer surplus. P $8 Consumer Surplus for unit Q1 $5 D Q1

10

QD

For example, a consumer who values unit Q1 at $8 and pays $5 for the unit enjoys a consumer surplus of $3. Notice that the entire consumer surplus for the market is the area between the demand curve and the price. Notice that in some contexts, it is possible for a seller to collect some of the consumer surplus realized in a single-price market. In particular, the seller may sell “packages” of units at a higher price than single quantities of the same unit, to achieve a given sales total. (We will discuss this later in the semester. 6. An analytical example Consider the following, simple demand function. Qd = 10 - 2P + .33I. Suppose I=30, then the demand curve can be written as Qd = 20 - 2P Or inverse demand: P = 10 - Q/2 This is shown as D on the figure below

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16 14 12 10 8 6

D' 4 2

D

0 0

5

10

15

20

25

If I increases to 60 then Qd = 10 - 2P+ .333(60) Qd = 30-2P So inverse demand is P= 15-Q/2, illustrated as D’ in the above figure. Suppose that the price is $5. How much consumer surplus to consumers receive at that price? When 15-Q/2 = 5, Q = 20. So the area of the C.S. triangle is (.5)(15-5)(20) = 100 This is the triangle illustrated below

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16 14 12

15-5

D'

10 8 6

D

4 2

20

0 0

5

10

15

20

25

Lecture 9 REVIEW___________________________________________________: II. Chapter Market Forces: Demand and Supply B. The Demand Side. 5. The Notion of Consumer Surplus 6. An Analytical Example Preview__________________________________________________________ C. The Supply Side. 1. Driving Force. The Law of Diminishing Returns 2. Definition of Supply Curve 3. Determinants of supply: 4. Changes in supply vs. changes in quantity supplied. 5. Producer Surplus. LECTURE______________________________________________ C. The Supply Side. In output market, this defines the behavior of sellers, 1. Initial assumption. Firms are motivated by the profit incentive, but constrained by increasing marginal costs (or, better yet, the law of diminishing returns (crowding).

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Example, consider conditions under which you would produce for sale quartz lamps from your uncle's shack in Southern Montana. As the amount of variable inputs (quartz, and workers) increases, the room should become “crowded,” and unit costs should increase as more variable inputs (labor) becomes “imbed” in each unit of output. This, we would expect, there would be a direct relationship 2. Definition The supply curve: A schedule of intentions indicating varying quantities of a good or service that sellers are ready, willing and able to place on the market at varying prices, per unit of time, other things constant. The supply curve is upsloping due to the law of diminishing returns (“crowding”) Important elements a. Schedule of intentions: An estimate b. Price/Quantity relationship: Price is the most important determinant of quantity. c. Ready, willing and able: Defines the market of relevant suppliers. Ready: Has access to market. Willing: Is a reasonable use of resources, Able: Has productive means d. Per unit of time: Time must be specified, as it affects LDR. e. other things constant. f. Upsloping due to the law of diminishing returns (crowdedness) 3. Determinants of supply: Things other than the price that affect how r.w. and a. sellers are to offer goods to the market. As a class, these are things that affect production costs Technology Factor prices. NUMBER OF SELLERS. Price expectations (e.g. hold grain in silo if price is expected to increase next year). Taxes (excise or ad valorem) 4. Changes in supply vs. changes in quantity supplied. Definition. (As with demand): A change in quantity supplied occurs in response to a change in the price of a good, all other things held constant. A change in supply occurs in response to a change in something other than price. Again, price is, by definition, the one thing that cannot change supply. 5. Producer Surplus.

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a. Definition Symmetric to the notion of consumer surplus, in a market where a single price is charged for all transactions, producers typically receive more from a sale than is necessary to induce them to offer a unit to the market. P S $5 Producer Surplus for unit Q1 $3 D Q1

10

QD

The producer surplus for unit Q1 is $5 - $3 = $2. The producer surplus for the market is the triangle bounded by the vertical axis, the production cost, and the price. b. Observations -Producer surplus is not the same as profit. We will talk about this more later, when we discuss the theory of the firm. -There are ways for a savvy purchaser to extract producer surplus in making purchasing decisions. Similar to demand, this is typically accomplished via bulk purchases.

Lecture 10 REVIEW___________________________________________________: II. Chapter Market Forces: Demand and Supply C. The Supply Side. 1. Driving Force. The Law of Diminishing Returns 2. Definition of Supply Curve 3. Determinants of supply: 4. Changes in supply vs. changes in quantity supplied. 5. Producer Surplus. Preview__________________________________________________________ 6. An Analytical Example. D. Equilibrium. Putting Supply and Demand Together 1. Definition. 40

2. Binding the market. Price floors Price ceilings LECTURE______________________________________________ C. The Supply Side. 6. An analytical example. Consider the market supply schedule for small laser-light paper erasers. The supply function is given by Qs = -44 + 20P - 4W - 2M, where P = the price of the erasers W = the average hourly wage for labor M = an index measuring materials costs. If W = 10 and M = 8, what is the market supply curve? Qs

= -44 + 20P - 4(10) -2(8) = -100 + 20P, thus Inverse supply becomes

P

=

5 + .05Q

Plotting in a table Q

P 5 10 15 20 25

5.25 5.5 5.75 6 6.25

Now, suppose that M increases to 18, then what happens to supply, or to quantity supplied? Qs

= =

-44 + 20P - 4(10) -2(18) -120 + 20P, thus

There is a change in supply P = 6 + .05Q Q

P 5 10 15 20

6.25 6.5 6.75 7

41

25

7.25

Alternatively, suppose that P increases from 6.5 to 17what happens to Q? There is a change of quantity supplied from 10 to 20. 8.5

S2

8 7.5 S1

7 6.5 6 5.5 5 0

10

Graphically Q P1 0 10 2 9 4 8 6 7 8 6

20

30

40

50

P2 15 14 13 12 11

D. Equilibrium. Putting Supply and Demand Together 1. Definition. Equilibrium: A price quantity combination where Qs = Qd, and where Ps = Pd. Analytically. Suppose Qd = 100 - 4P +10I, and Qs = 10 + 6P -3W If W = 30, I =10, what are equilibrium values? Qd = 100 - 4P +10(10), and Qs = 10 + 6P -3(30) Qd = 200-4P Qs = 80+6P

42

Setting Qd = Qs implies that P

Qd 15 14 13 12 11 10 9

Qs 140 144 148 152 156 160 164

170 164 158 152 146 140 134

Observe at a price of 15 dollars, there is a surplus, Qs = 170 > Qd = 140. Conversely, at a price of $9, there is a shortage, Qd = 164 > Qs = 134. 2. The stability and desirability of equilibrium. Absent a tendency for markets to equilibrate (or given regulations which prevent such convergence), the surplus or shortages just discussed would be permanent. However, markets do equilibrate. Given excess supply the sellers have an incentive to reduce prices. This price reduction prompts changes in quantity supplied and quantity demanded. Similarly, given an excess demand, buyers have an incentive to bid prices up, again causing a change in quantity supplied and quantity demanded. Importantly, if the assumption of ‘pure privacy’ is satisfied, the equilibrium outcome is also socially desirable. Given an absence of externalities, the TC curve equals TSC and the TB curve equals TSB. Thus, D=MSB and S=MSC. At the equilibrium, where S=D, the net difference between TSB and TSC are maximized. 3. Binding the market. Permanent shortages and surpluses can be caused by regulation. A price floor: A regulated minimum price, below which the market price cannot fall. If the floor is below the equilibrium, the regulation exerts no effect. If the floor is above the equilibrium, there is a permanent shortage that the market cannot eliminate. a. Example. A price floor: Suppose the government refuses to let cheese be sold for less than $3.00 per pound. Result: A permanent surplus, and one that cannot be resolved by the market A price ceiling: A regulated maximum price, above which the market price cannot rise. If the floor is above the equilibrium, the regulation exerts not effect. If the floor is below the equilibrium, there is a permanent shortage that the market cannot eliminate. b. Example: A Rent control. Result: A shortage of housing, and one that cannot be resolved by the market.

43

Complications: One solution by sellers is to force multiple purchases (e.g., Impose a price ceiling on rents, but then make people agree to unusual lease terms, or to purchase other high cost items along with the lease). In fact, it is possible that given rent controls, the non-monetary components associated with increasing the price of a good may generate a full price for each consumer that equals the total market consumer surplus. Notice that when a ceiling binds the market, the full economic price is the sum of the pecuniary plus the non-pecuniary price (e.g., the price of waiting, purchasing undesired packages of goods, etc.) In general, with a price ceiling, buyers who purchase a good will pay the demand price, at the restricted quantity. For example P S Pf

D

Pc

Qc Q Given a Price ceiling Pc, Qc units will be sold. The full economic price paid by buyers will equal Pf. There are parallel examples in input markets (where the government acts more aggressively). Usury laws (a market for loanable funds) Minimum wage legislation. The point: Equilibrium is a socially desirable outcome. We interfere with the workings of a competitive market at our peril!

Lecture 11 REVIEW___________________________________________________: II. Chapter Market Forces: Demand and Supply D. Equilibrium. Putting Supply and Demand Together 1. Definition. 2. The Stability and desirability of equilibrium 3. Binding the market. Price floors 44

Price ceilings Point: Binding the market imposes high social costs Preview__________________________________________________________ E. Comparative Statics. 1. Single market changes. 2. Multiple Market Changes III. Quantitative Demand Analysis A. Price Elasticity of Demand 1. Motivation LECTURE______________________________________________ E. Comparative Statics. Given the tendency of markets to converge to competitive predictions in an unfettered and competitive market, we can use this model to predict the effects of changes in the world. 1. Single market changes. Strategy: To find the new equilibrium, consider the old equilibrium price, and the new equilibrium supply and demand curves. Then shortages or surpluses will motivate an adjustment. a. Change in demand, supply stable. Example, suppose the price of coffee falls by half. What should this do to the market for pastries? Example: What should the current economic recession do to the price and quantity of automobiles sold? b. Change in supply, demand stable Example: Suppose a new process for manufacturing computers is developed that cuts production costs by 50%. What is the predicted effect on the number of computers sold, and the price of computers? c. Change in supply and demand… (and ambiguous effects). Example: Suppose software costs fall, and that at the same time a new Pentium X chip is developed that can be installed to do twice as much at 1/2 the price. What is the net effect of these changes on the price and quantity of personal computers sold? Example: Consider the market for cheese produced by U.S. farmers. Suppose that due to the flooding in Northern Europe, Farmers in the Netherlands lose half of

45

their dairy herd. Suppose also that new environmental deregulation cuts production costs in half. What are the net effects of these changes on the market for cheese produced by U.S. Farmers? A more complicated story variant: Consider the above problem, but suppose that at the outset the U.S. government imposed a price floor for cheese that at the initial equilibrium. How does the price ceiling affect results?

Lecture 12 REVIEW___________________________________________________: II. Chapter Market Forces: Demand and Supply D. Equilibrium. Putting Supply and Demand Together Equilibrium is 1. Stable 2. Socially desirable E. Comparative Statics. 1. Single market changes. 2. Multiple Market Changes Preview__________________________________________________________ III. Quantitative Demand Analysis A. Price Elasticity of Demand 1. Motivation 2. Calculation a. Arc price elasticity of demand: b. Point price elasticity of demand c. Percentage Changes Lecture ______________________________________________________ III. Chapter 3. Quantitative Demand Analysis Introduction: In the preceding chapter we reviewed the basic supply and demand model used to predict price and quantity outcomes. This model is an extremely useful device for making qualitative predictions. An important limitation of the model as it has been presented, however, is that it does not allow quantitative predictions. For quantitative predictions, it is necessary to more fully characterize the arguments in the demand and supply functions. We start with demand in this chapter. The presentation is divided into two parts. The first will deal with the quantitative conclusions that may be fairly limited elasticity

46

information. In the second part, we turn more comprehensive analysis of demand estimation via the use of regression. A. Price Elasticity of Demand 1. Motivation: Elasticity this is a tool for estimating responsiveness of some dependent variable to a change in a dependent variable, based on very little information. Definition: Elasticity: The percentage change in an independent variable brought about by a 1% change in an independent variable. Intuitively, elasticity may be regarded as a measure of sensitivity. If people are sensitive, we will say that they are elastic. If they are insensitive, we will regard them as inelastic. For concreteness, we will focus initially on price elasticity of demand (change definition accordingly) Price Elasticity of Demand: The percentage change in Quantity Demanded brought about by a 1% change in the price of a good, or η = %∆Qd/%∆P

=

∆Q/Q ∆P/P

=

∆QP ∆PQ

2. Calculating Elasticity of Demand. There are three ways to calculate price elasticity of demand: arc price elasticity, point price elasticity, and direct percentage changes. The method that is appropriate in any particular context depends on the information provided. a. Arc Price Elasticity. Applies to a discrete change. For example, consider the demand curve implied by the following table: P

Q

4 5

40 10 P 5

4 D 10

40

47

Q

Notice ∆Q may be calculated as Q1-Q0, and ∆P = P1-P0. Then η = (Q1-Q0)P/(P1-P0)Q But it makes a big difference if you use (P0,Q0) as your divisor, or (P1,Q1). For example: (40-10) (4) (4-5) (40)

=

30(4) -1(40)

= -3.00

(40-10) (5) (4-5) (10)

=

30(5) -1(10)

= -15.00

Neither of these points is inherently more correct. As a convention, we calculate the arc price elasticity of demand using the average of the distance between the 2 points: η = (Q1-Q0)(P1+P0)/2 (P1-P0)(Q1+Q0)/2. In this case =

(40-10) (4+5)/2 (4-5) (40+10)/2

=

30(4.5) -1(25)

= -5.4

Arc Price elasticity is interpreted as follows: Over the range of prices between $4 and $5 on average, a 1% reduction in price increases quantity demanded by 5.4 %. b. Point price elasticity: When you are given a slope, and a point. Insight η = (dQ/dP)(P/Q) Example: Suppose a demand curve is Q = 30 - 10P Then, if P = 2, then Q=10 and elasticity is -10 ( 2/10) = -2. Uses: Mostly when given a demand function. Point Price elasticity is interpreted as follows: At a price of $2 a 1% reduction in price increases quantity demanded by 2 %.

48

c. Percentage changes. For rough policy purposes. Insight η = (%∆Q)/(%∆P) Example. Suppose that beer sales at Joe's Inn increased 20% in response to a “half price” (50% off night). What is the implied elasticity of demand? -20/ 50 = -.4 Example: Suppose that Joe sells 400 beers per day. What would be the effect of a 10% increase in beer prices on his sales? -.4 = %∆Q/10 implies 4 % decrease, or a decrease of .04(400) = 16 beers per day.

Lecture 13 REVIEW___________________________________________________: II. Chapter Market Forces: Demand and Supply A. Price Elasticity of Demand 1. Motivation 2. Calculation a. Arc price elasticity of demand: Example: If Rick Redfern reduces the price of potato chips from $2 per bag to $1 per bag, and if daily sales increase from 10 to 15, what is the arc price elasticity of demand?

η

=

(10-15)(2+1) = -5(3) (2-1) (10+15) 1(25) b. Point price elasticity of demand

=

-3/5

Example: If demand is given by Q = 100 – 10P and P = 6, what is price elasticity of demand?

η -10 (6)/40 = -1.5 (Notice: If P = 4, elasticity becomes η

-10 (4)/60

=

-.67

A preview: Price elasticity changes with position on the demand curve. c. Percentage Changes

49

Example: If Ford Taurus sales increase by 20% in response to a 10% off sale, what is the implied price elasticity of demand?

η

=

-20/10

=

-2

Preview__________________________________________________________ III. Quantitative Demand Analysis 3. A Graphical Interpretation of Price Elasticity. 4. Some Observations about Price Elasticity of Demand a. Most Demand curves have elastic and inelastic segments b. Exceptions c. Elasticity and the Slope of Demand Curves 5. Elasticity TR and MR Lecture ______________________________________________________ 3. A Graphical Interpretation of Price Elasticity. a. Intuition: One way to consider the problem of sensitivity is to ask the following question: What happens to total revenue (TR) when price is changed? Consider a price increase. If TR increases, then we will say that people are "insensitive" to the change (meaning that more revenues were gained from people staying in the market and paying the higher price, than were lost from people who left the market. On the other hand, if TR falls, then people are "sensitive" in the sense that more revenues are lost from people leaving the market in response to a price decrease, than were gained from the higher prices. b. Illustration. This can be graphically illustrated as follows. Consider the problem of calculating price elasticity for a standard linear demand curve. P

Po Price box P1 Quantity Box Q0 Q1 Associated with a price change are competing effects, ∆PQ a "price" box.

50

D Q

∆QP a "quantity" box. Elasticity is the ratio of the qty box to the price box. Let’s explain this in words. Suppose we talk about a price reduction. The ‘price box’ is the loss in revenues on units that would have sold at the higher price The ‘quantity box’ is the increase in revenues due to new units that are sold as a result of the price reduction. Elasticity is the ratio of the qty box to the price box. When inelastic, the coefficient is small (close to zero) When elastic, the coefficient is large (far from zero). 4. Some observations about price elasticity of demand (η): a. In general − η is between 0 and infinity − η Qty box. Price box = Qty. box Price box < Qty. box

Lecture 14 REVIEW___________________________________________________: II. Chapter Market Forces: Demand and Supply A. Price Elasticity of Demand 3. A Graphical Interpretation of Price Elasticity. 4. Some Observations about Price Elasticity of Demand a. Most Demand curves have elastic and inelastic segments b. Exceptions c. Elasticity and the Slope of Demand Curves Preview__________________________________________________________ 5. Elasticity TR and MR 6. Determinants of Price elasticity B. Other Demand Elasticities 1. Cross Price Elasticities

52

η1

Lecture ______________________________________________________ 5. Price Elasticity, MR and TR a. Motivation: What can we say about the optimality of prices, given limited information. (Say, only information about the demand schedule, and perhaps MC information). Some important inferences can be drawn only from information about elasticity. Definition of Marginal Revenue (MR). Recall that on most demand curves, there are elastic, unitary and inelastic segments. (Motivate from comparison of quantity box to price box). Price elasticity is the ratio of the quantity box to the price box. Marginal revenue is the difference between the quantity box and the price box. P E

MR

D

TR

Q MR (at max)

TR E

I Q

b. Relation between MR, TR and η |η| >1, MR >0 |η| C(Q1, Q2) C(Q1, 0)

=

f

+ Q12

C(0, Q 2)

=

f

+ Q22

Thus, economics of scope exist if 2f+ + Q12+ Q22 > f+ aQ1Q2 +Q12+Q22 Or if

f - aQ1Q2 > 0.

Comparing the two conditions, it is seen that cost complementarities are a stronger condition than economies of scope. Given a C(Q1, Q2) Economies of scope are an important reason why firms produce multiple products. For example, it may be more efficient to produce both cars and light trucks in a single plant than to produce both good separately, the two products may share many parts of the same assembly (such as the chassis) and producing the products separately would require considerable duplicative construction. b. Cost complementarities: These exist in the marginal cost of producing one good increases when the output of another product is increased. Mathematically, when: ∂ MC1(Q1, Q2)< 0 ∂Q2 This often arises when one product is a by-product of another. For example there are cost complementarities in the production of in the production of Flouride and Aluminum Ingot from Alumina.

98

Cost complementarities are an important reason for economies of scope. These notions are conveniently expressed algebraically with at quadratic cost function: C(Q1, Q2)

=

f

+

Then MC1

=

aQ2 + 2Q1

aQ1Q2 + Q12 + Q22

Cost complementarities exist whenever a < 0. Economies of scope exist whenever C(Q1, 0) + C(0, Q2) > C(Q1, Q2) C(Q1, 0)

=

f

+ Q12

C(0, Q 2)

=

f

+ Q22

Thus, economics of scope exist if 2f+ + Q12+ Q22 > f+ aQ1Q2 +Q12+Q22 Or if

f - aQ1Q2 > 0.

Comparing the two conditions, it is seen that cost complementarities are a stronger condition than economies of scope. Given a 0 implies substitutes ηxy< 0 implies complements ηxy = 0 implies unrelated goods. 2. Income Elasticities ηI = %∆ Q/%∆ I ηI > 1 normal, cyclical good 1> ηI > 0 normal, noncyclical good ηI< 0 inferior good.

131

3.Other Elasticites. Advertising elasticity ηA = %∆ Q/%∆ A For any successful advertising campaign, ηA >0 C. Elasticities and demand functions 1. Linear Demand functions. Given Qx = a + bP + cI + dPy

η = b(Q/P)

ηI = c(Q/I)

ηxy =d(Qx/Py)

2. Logrithmic Demand. Given Qx

η=b

=

ηI = c

aPbIcPyd

ηxy =d

Note: An equivalent expression for this function is ln Qx = lna + blnP+ clnI + dlnPy

Review Outline. E303 Second Examination Spring 2006 III. Quantitative Demand Analysis (Continued) D. Estimating Demand: Regression Analysis. 1. Interpreting the significance of individual parameter estimates 2. Forecasting IV. Chapter 5. The Production Process and Costs A. Introduction: B. The Production Function 1. Short Run Production. a. Diminishing Marginal Productivity and Marginal Product b. Relationships between Productivity Measures. c. Optimal Use of a single input. i. VMP and PL ii. Shifts in the VMP schedule. 2. Long Run Production (Optimal use of multiple inputs) C. Costs.

132

1. The relationship of production functions to cost functions. 2. Short run costs. a. Cost curves b. Sunk vs. Variable Costs c. Algebraic forms of cost curves 3. Long-Run Costs a. Long Run Average Costs b. Economics of Scale c. Returns to Scaels: Measuring Scale Economies 4. Multiple Output Cost functions a. Economies of Scope b. Cost complementarities V. The Organization of the Firm. Ch. (6.) A. Overview and Motivation. The optimal structure of the firm is narrow and focused. All inputs would be purchased, and all outputs would be sold on spot markets. B. Optimal Methods of Obtaining Inputs 1. Options a. Spot b. Contract c. Internal Production 2. Factors affecting choice of the optimal method a. Costly Bargaining b. Underinvestment c. The Hold-up Problem. 3. Decision Rule a. Spot is optimal unless the costs of opportunism are too high. b. The choice between contractual arrangements and internal production are determined by the contracting costs, particularly the relative uncertainty of the contracting environment. C.Getting the Most out of Human Factors. 1. The Principal-Agent Problem. 2. Structuring Contracts for Managers (review). 3. The Manager/Worker Problem. a. Profit Sharing. b. Revenue Sharing. c. Piece Rates. d. Time clocks and time checks

133

VI. Chapter 7. The Nature of Industry (Introduction) E. Market Structure a. Definition b. Types of Structures i. Competition ii. Monopoly iii. Monopolistic Competition iv. Oligopoly F. A Paradigm for Analyzing Markets VII. Chapter 8. Managing in Competitive, Monopolistic and Monopolistically Competitive Markets. A. Introduction a. Rule for determining optimal quantity (Compare MR to MC) b. Rule fro determining profits and losses (Compare AR to ATC) B. Competition a. Assumptions b. Optimal Short Run Decisions c. The Intermediate run (entry but no expansion) d. The Long run (expansion but no entry) C. Monopoly a. Assumptions Optimal Decisions

KEY

Problem Set #1

1. To attract Walt Snore to the job of CEO of Good Sleep Inc. Walt is given the following (a) a signing bonus of $750,000. (b) In addition to his salary Walt will be paid a bonus of $750,000 in any year that company return on assets exceeds 7%. Also (c) Walt receives 500 shares per annum of the stock, which he may not sell for 5 years. Comment on the likely effectiveness of each of these components of as a means to mitigate the principle-agent problem. Most Likely: Stock Least Likely: Signing Bonus Reason: The signing bonus doesn’t induce effort. The earnings bonus helps some, but is imperfect, the restricted sale stock does promote attention to the long term value of the firm. 2. Good Sleep anticipates the following earnings for the next 5 years. Years in the Future

Anticipated Profit

134

1 2 3 4 5

22 24 26 28 30

If the discount rate is 10% and the machine costs $90 (000), what is the net present value of the machine? Is it a good purchase? PV = NPV = =

22/(1.1) + 24/(1.1)2+ 26/(1.1)3 + 28/(1.1)4+ 30/(1.1)5= $97.120 $97,120 – 90,000 $7,120

Good purchase YES

135

3. Joe Holiday has the opportunity to operate a business renting beach umbrellas next summer. He will operate the concession for 3 months. Looking at weather patterns, Joe observes that rain is frequent along this stretch of beach, and on average, there are only 60 rentable days in a summer. In each of these days, Joe believes he can rent 40 umbrellas per day at $7 per rental. Joe will run the concession by himself day, and must pay Beachcomber Enterprises $9,000 for the concession (the use of the umbrellas and for the beachfront rental location). Suppose Joe could earn $4500 working construction. a. What are Joe’s Accounting Profits for undertaking the business? What are his Economic Profits

πA

= = = =

TR 60(40× $7) $16,800 $7,800

-

TCEX $9,000 $9,000

πE

= = =

TR $16,800 $3,300

-

TCEX $9,000

-

TCIM $4,500

b. Can Joe expect economic profits from the venture? If so, to what are these profits attributable? Yes, he can expect positive economic profits. This is a return to his risk-taking (it might, after all, rain all summer!) or to locational rents (he may have the only stand on the beach)

Problem Set #1 4. To attract Walt Snore to the job of CEO of Good Sleep Inc. Walt is given the following (a) a signing bonus of $750,000. (b) a bonus of $750,000 in any year that company return on revenues exceeds 7%, and (c) receives 500 shares per annum of the stock, which he may not sell for 5 years. Which of these components best mitigates the principle-agent problem? Which is does the least? Why? Most Likely:_____________ Least Likely:____________ Reason: _________________________________________________________________

136

_______________________________________________________________________ _ 5. Good Sleep Inc. is considering the purchase of a new mattress assembler that allows the construction of multiple firmness levels in the same mattress. Good Sleep anticipates the following 5-year earnings stream from the sale of this mattress. Years in the Future 1 2 3 4 5

Anticipated Profit (‘000’s) 22 24 26 28 30

If the discount rate is 10% and the machine costs $90 (000), payable at once, what is the net present value of the machine? Is it a good purchase? (Write out the net earnings stream to generate your answer ) Net Present Value__________________________________________________ Good purchase?:______

137

6. Joe Holiday has the opportunity to operate a business renting beach umbrellas next summer. He will operate the concession for 3 months. Looking at weather patterns, Joe observes that rain is frequent along this stretch of beach, and on average, there are 60 rentable days in a summer. In each of these days, Joe believes he can rent 40 umbrellas per day at $7 per rental. Joe will run the concession by himself day, and must pay Beachcomber Enterprises $9,000 for the concession (the use of the umbrellas and for the beachfront rental location). Suppose Joe could earn $4500 working construction. a. What are Joe’s Accounting Profits for undertaking the business? What are his Economic Profits Accounting profits (πA):___________________________________________________ Economic profits (πE):___________________________________________________ b. Can Joe expect economic profits from the venture? If so, to what are these profits attributable? Positive economic profits? ( Y / N ) Justification: _________________________________________________________

Problem Set #2 (Note: On this problem, you may use EXCEL to generate numbers, but please fill in your answers 1. Consider the total profit function

π= =

TR - TC (10 –Q)Q –.25Q2

a. Create a table that shows Total Revenue, Total Cost and Total Profit, (in your table, let quantity run from 0 to 8 in increments of 1.) Indicate in your table where total profits are maximized Q TR TC T Profit 0 0 0 0 1 9 0.25 8.75 2 16 1 15 3 21 2.25 18.75 4 24 4 20 138

5 6 7 8

25 24 21 16

6.25 9 12.25 16

18.75 15 8.75 0

b. Next illustrate the relationship between TR, TC and total profit in the coordinate axes below 30 MR

25 20

Profit Max

TR TC

15 10 5

MC

0 0

5

10

On your graph, -highlight the point where total revenues are maximized. -show how profits may be seen. -highlight the point where total profits are maximized c. Next, create a table showing marginal revenues, marginal costs and marginal profits. Indicate in this table where TOTAL profits are maximized Q MR MC M PRO 0 10 0 10 1 8 0.5 7.5 2 6 1 5 3 4 1.5 2.5 4 2 2 0 5 0 2.5 -2.5 6 -2 3 -5 7 -4 3.5 -7.5 8 -6 4 -10

d. Finally, in the coordinate axes below create a graph that illustrates the relationships between marginal revenue and marginal cost. 139

- show the point where TOTAL profits are maximized - show the point where marginal profits are zero. . 12 10 8 6 4 2 0 -2 0 -4 -6 -8

M PR0 = 0

MC MR MR 5

10 MR

140

2.Take the derivatives of the following functions. Do not simplify. a. f(x) =

10

f’(x)

=

___0___________________________

b. f(x) =

20x2

f’(x)

=

___40x_________________________

c. f(x) =

30x

f’(x)

=

____30_________________________

d. f(x) =

20x + 30x3

f’(x)

=___20+90x2_____________________

e. f(x) = (10 + 15x2)(3x – 4x3) f’(x) =_30x(3x – 4x3)+ (3-12x2)(10 + 15x2)_____________________________ 10/x2

f. f(x) =

f’(x)

=___-20/x3________________

Problem Set #2 (Note: On this problem, you may use EXCEL to generate numbers, but please fill in your answers in the table below.) 1. Consider the total profit function

π= =

TR - TC (10 –Q)Q –.25Q2

a. Create a table that shows Total Revenue, Total Cost and Total Profit, (in your table, let quantity run from 0 to 8 in increments of 1.) Indicate in your table where total profits are maximized Q

TR

TC

T Profit

0 1 2 3 4 5 6 7 141

8 b. Next illustrate the relationship between TR, TC and total profit in the coordinate axes below π

Qty On your graph, -highlight the point where total revenues are maximized. -show how profits may be seen. -highlight the point where total profits are maximized c. Next, create a table showing marginal revenues, marginal costs and marginal profits. Indicate in this table where TOTAL profits are maximized Q

MR

MC

M Profit

0 1 2 3 4 5 6 7 8 d. Finally, in the coordinate axes below create a graph that illustrates the relationships between marginal revenue and marginal cost. - show the point where TOTAL profits are maximized - show the point where marginal profits are zero. . 142

MR, MC

Qty

143

2.Take the derivatives of the following functions. Do not simplify. a. f(x) =

10

f’(x)

=

_______________________________

b. f(x) =

20x2

f’(x)

=

_______________________________

c. f(x) =

30x

f’(x)

=

_______________________________

d. f(x) =

20x + 30x3

f’(x)

=_______________________________

e. f(x) =

(10 + 15x2)(3x – 4x3) f’(x)

=_______________________________

f. f(x) =

10/x2

=_______________________________

f’(x)

Problem Set #3 1. The American Bagel Co. is considering opening a Bagel bakery and coffee shop near Campus. In an effort to predict the profitability of this venture, their in-house consulting team estimated that the daily demand for Bagels in the area to be the following Q = -5P + 20Pp - 30Pc +5I Where P = the price of bagels, Pp = the price of pastries (each), Pc = the price of coffee (per cup), and I = Income (average annual per capita, for local residents in thousands of dollars) a. Comment on this estimated demand function. Are the parameters reasonable? Why or why not? (Restrict your commentary to the signs of the parameters) Reasonable Sign? (Y/N) Reason P _________________________________________________ Pp _________________________________________________ Pc _________________________________________________ I __________________________________________________

144

b. Suppose that the price of pastries = $1, coffee costs $.50 per cup, and average per capita income in the fan area is $12,000. Calculate the inverse demand curve (e.g., express price as a function of quantity). Demand:

__________________________________

Inverse demand _________________________________ c. What happens to the predicted number of bagels sold per day if the price of bagels is increased from $1.00 to $2.00? Is this a change in demand or a change in quantity demanded? Initial Quantity:

__________________________________

Terminal Quantity _________________________________ Change in Demand or Change in Quantity Demanded (Circle One)

145

d. Holding the price of bagels again at $1.00, what happens to the predicted number of bagels sold per day if the price of coffee increases from $.50 to $1.00 per cup. Is this a change in demand or a change in quantity demanded? Initial Quantity: __________________________________ Terminal Quantity _________________________________ Change in Demand or Change in Quantity Demanded (Circle One) e. In the coordinate axes below, illustrate the changes that occurred above in parts c and d above. (Note, your graph need not be precise) P

Q e. Suppose that the price of Bagels is set at $1. How much consumer surplus do consumers receive at that price? Consumer Surplus: __________________________________ Problem Set #3 1. The American Bagel Co. is considering opening a Bagel bakery and coffee shop near Campus. In an effort to predict the profitability of this venture, their in-house consulting team estimated that the daily demand for Bagels in the area to be the following Q = -5P + 20Pp - 30Pc +5I

146

Where P = the price of bagels, Pp = the price of pastries (each), Pc = the price of coffee (per cup), and I = Income (average annual per capita, for local residents in thousands of dollars) a. Comment on this estimated demand function. Are the parameters reasonable? Why or why not? (Restrict your commentary to the signs of the parameters) Reasonable Sign? (Y/N) Reason P _______Y__________________________Downsloping Demand Curve (d.m.u.) Pp ______Y_________________________Pastries and Bagels are Substitutes Pc ______Y_________________________Coffee is a complement__________ I _______Y________________________Food consumed at a café s probably a normal good b. Suppose that the price of pastries = $1, coffee costs $.50 per cup, and average per capita income in the fan area is $12,000. Calculate the inverse demand curve (e.g., express price as a function of quantity). Demand:

Q

Inverse demand _______P

= -5P + 20(1)- 30(.5)+ 5(12) = -5P +65 = 13 - Q/5______________________

c. What happens to the predicted number of bagels sold per day if the price of bagels is increased from $1.00 to $2.00? Is this a change in demand or a change in quantity demanded? (Note: The appropriate was corrected via an email broadcast) Quantity Changes from:

65-5(1)= 60 to 65 – 5(2) = 55

Change in Demand or Change in Quantity Demanded (Circle One) d. Holding the price of bagels again at $1.00, what happens to the predicted number of bagels sold per day if the price of coffee increases from $.50 to $1.00 per cup. Is this a change in demand or a change in quantity demanded? For these problems you need a new demand curve Q = -5P + 20(1)- 30(1)+ 5(12) = -5P +50

147

Demand:

Q

= =

-5P + 20(1)- 30(1)+ 5(12) 50 – 5P

Inverse demand _P = 10 – Q/5________________ Before, at Pc = .50, Q = 60 Now, at P = 1, Q = 50 Change in Demand or Change in Quantity Demanded (Circle One) e. In the coordinate axes below, illustrate the changes that occurred above in parts c and d above. (Note, your graph need not be precise) P

(c)

(d) Q e. Suppose that the price of Bagels is set at $1. How much consumer surplus do consumers receive at that price? The demand curve is _P = 13 - Q/5. When P=1, Q = 60. When P = 13, Q = 0. Thus, we need to find the area of a triangle with a length of 60 and a height of 12 Consumer Surplus: _.5(12)(60) = 360_________________________

Problem Set #4. Equilibrium Analysis. 1. Consider the market for “popcorn crisps” a new product that you prepare fresh (like popcorn) but that has the look and feel of a potato chip.

148

a. What relationship should characterize the relationship between the price of popcorn crisps and the number of packages sold per month? Why? Relationship: __ ___________________________ Reason: __ ______________

b. What relationship should characterize the relationship between the price of popcorn crisps and the number of packages produced per month? Why? Relationship: _ ____________________________ Reason: __ _____________ c. Suppose that Crisp-Makers of America, Local #458, a trade union that manufactures the crisps, successfully negotiates a wage increase. Will this affect the supply of or the demand for the crisps. How would the curve be affected? Supply / Demand (circle one). Direction of adjustment: ________________ d. Relative to the initial equilibrium, identify the price and/or quantity adjustment. What process causes the adjustment to the new equilibrium? Equlibrium Price Change: Equilibrium Quantity Change

Increase /Decrease /No Change (Circle One) Increase /Decrease /No Change (Circle One)

Adjustment Process: _______________________________________________________ _______________________________________________________________________

149

3.

Suppose that the free market equilibrium price of bourbon is $6.00 a bottle, and that the government sets a price ceiling of $4.50 a bottle on bourbon. The most likely result of this action is that: a. b. c. d.

there will now be an excess demand for bourbon the market price of bourbon will remain at $6.00 a bottle. there will be a large reduction in the quantity of bourbon demanded. there will now be an excess supply of bourbon.

4. “The winds of the recent hurricanes in Florida are bringing soothing financial gain to California citrus growers. Due to the extensive damage to the Florida citrus corp, California citrus products are commanding their highest prices ever.” Which of the following statements best explains the economics of the quotation? a b. c. d.

5.

The supply of Florida oranges has increased, causing their price to increase and the demand for the substitute California oranges to also increase. The supply of Florida oranges has decreased, causing the demand for California oranges to increase and their prices to rise. The demand for Florida oranges has been reduced by the hurricanes, causing a greater demand for the California oranges and an increase in their price. The demand for Florida oranges has been reduced causing their prices to fall and therefore increasing the demand for the substitute California oranges.

Suppose that a new, influential research study proves conclusively that cigarette smoking causes cancer in a way that causes people to start to pay more attention to the warning that "cigarette smoking is injurious to health." At the same time, suppose that new restrictions on the use of fertilizer dramatically raise tobacco production costs. Using conventional supply and demand analysis, one would expect the combined effect of these changes on the cigarette market to be: a. b. c. d.

an increase in equilibrium price, with the change in equilibrium quantity uncertain a decrease in equilibrium price, with the change in equilibrium quantity uncertain. an increase in equilibrium quantity, with the change in equilibrium price uncertain. a decrease in equilibrium quantity, with the change in equilibrium price uncertain.

150

/ Problem Set #4. Equilibrium Analysis. 1. Consider the market for “popcorn crisps” a new product that you prepare fresh (like popcorn) but that has the look and feel of a potato chip. a. What relationship should characterize the relationship between the price of popcorn crisps and the number of packages sold per month? Why? Relationship: _Inverse___________________________ Reason: __Diminishing Marginal Utility ______________

b. What relationship should characterize the relationship between the price of popcorn crisps and the number of packages produced per month? Why? Relationship: _ Direct____________________________ Reason: __Law of Diminishing Returns (Crowding) _____________ c. Suppose that Crisp-Makers of America, Local #458, a trade union that manufactures the crisps, successfully negotiates a wage increase. Will this affect the supply of or the demand for the crisps. How would the curve be affected? Supply / Demand (circle one). Direction of adjustment: __Supply will shift up and in __ d. Relative to the initial equilibrium, identify the price and/or quantity adjustment. What process causes the adjustment to the new equilibrium? Equlibrium Price Change: Equilibrium Quantity Change

Increase /Decrease /No Change (Circle One) Increase /Decrease /No Change (Circle One)

Adjustment Process: _At the initial price with new supply and old demand a shortage exists_______

151

3.

Suppose that the free market equilibrium price of bourbon is $6.00 a bottle, and that the government sets a price ceiling of $4.50 a bottle on bourbon. The most likely result of this action is that: a. b. c. d.

there will now be an excess demand for bourbon the market price of bourbon will remain at $6.00 a bottle. there will be a large reduction in the quantity of bourbon demanded. the market price of bourbon will fall because the price ceiling will create an excess supply.

4. “The winds of the recent hurricanes in Florida are bringing soothing financial gain to California citrus growers. Due to the extensive damage to the Florida citrus corp, California citrus products are commanding their highest prices ever.” Which of the following statements best explains the economics of the quotation? a b. c. d.

5.

The supply of Florida oranges has increased, causing their price to increase and the demand for the substitute California oranges to also increase. The supply of Florida oranges has decreased, causing the demand for California oranges to increase and their prices to rise. The demand for Florida oranges has been reduced by the hurricanes, causing a greater demand for the California oranges and an increase in their price. The demand for Florida oranges has been reduced causing their prices to fall and therefore increasing the demand for the substitute California oranges.

Suppose that a new, influential research study proves conclusively that cigarette smoking causes cancer in a way that causes people to start to pay more attention to the warning that "cigarette smoking is injurious to health." At the same time, suppose that new restrictions on the use of fertilizer dramatically raise tobacco production costs. Using conventional supply and demand analysis, one would expect the combined effect of these changes on the cigarette market to be: a. b. c. d.

an increase in equilibrium price, with the change in equilibrium quantity uncertain a decrease in equilibrium price, with the change in equilibrium quantity uncertain. an increase in equilibrium quantity, with the change in equilibrium price uncertain. a decrease in equilibrium quantity, with the change in equilibrium price uncertain.

152

Spring 2006 Problem Set #5 1. Chez What has recently opened a stand between the Commons and the School of Business. They sell mostly breakfast items, particularly coffee, and croissants. The operators are particularly concerned about the demand for croissants. In an effort to assess the wisdom of their pricing strategy, they asked an economist client to estimate the demand for croissants sold at Chez What. He came with the following information. Q = 102-2P - 10Pc + 15Pa Where P = the price of croissants, Pc = the price of coffee sold at Chez What, and Pa = the price of coffee sold at the nearby Alpine bagel bakery a. Suppose that the price of coffee at Chez What is $1 and that the price of coffee at the Alpine Bagel Bakery is $2 per cup. Calculate the inverse demand curve (e.g., express price as a function of quantity). Demand:

__________________________________

Inverse demand _________________________________ For parts b and c assume that the price of croissants is $1. b. Calculate the point price elasticity of demand. Would Chez What increase profits by Raising the price of croissants? η

___________________________________

Raise Price? ___________________________________ c. Calculate the cross price elasticity of demand for croissants with respect to the price of coffee. How is coffee related to croissants? Why? ηXY

___________________________________

Relationship

________________________

153

2. Joe is evaluating the marketing strategy at his restaurant and inn. Suppose that in response to a $2.00 off" sales promotion for Spaghetti dinners, Joe finds that nightly dinner sales increase from 20 per night to 40. Normally, the dinners sell for $6.00. a. What is the arc price elasticity of demand? η

=

__________________________

b. Would Joe increase revenues by further reducing the price? What about profits? Explain. Price reduction prompts revenue increase Price reduction prompts profit increase

Y / N / Can’t tell Y / N / Can’t tell

Explanation _____________________________________________

3. Fred McCutchen a new employee at McCutchoni Frozen Foods estimates that the price elasticity of demand for McCutchoni Frozen Pizzas to be -1.5, as compared to a price elasticity of demand for frozen pizzas in general of -2.34. In light of the relative inelasticity of McCutchoni Frozen Pizza's, Fred recommends raising the price to increase sales revenues. You, a more experienced member of the firm, are suspicious of Joe's estimate, and are skeptical of his recommended plan of action? Why? (Hint: Think about the determinants of price elasticity of demand) Reason to suspect Fred’s estimate______________________________________________ Reason to doubt Fred’s plan of action _________________________________________ E303, Problem Set #5 1. Chez What has recently opened a stand between the Commons and the School of Business. They sell mostly breakfast items, particularly coffee, and croissants. The operators are particularly concerned about the demand for croissants. In an effort to assess the wisdom of their pricing strategy, they asked an economist client to estimate the demand for croissants sold at Chez What. He came with the following information. Q = 102-2P - 10Pc + 15Pa

154

Where P = the price of croissants, Pc = the price of coffee sold at Chez What, and Pa = the price of coffee sold at the nearby Alpine bagel bakery a. Suppose that the price of coffee at Chez What is $1 and that the price of coffee at the Alpine Bagel Bakery is $2 per cup. Calculate the inverse demand curve (e.g., express price as a function of quantity). Demand:

Q

= = =

102 – 2P – 10(1) + 15(2) 102 – 2P +20 122 – 2P

Inverse demand ____P = 61 - .5Q________________________ For parts b and c assume that the price of croissants is $1. b. Calculate the point price elasticity of demand. Would Chez What increase profits by Raising the price of croissants? ? η

____dQ/dP (P/Q)___= -2(1)/120 = -.0167__________

Raise Price? ______Yes, the firm is on the inelastic portion of demand. c. Calculate the cross price elasticity of demand for croissants with respect to the price of coffee (at Chez What). How is coffee related to croissants? Why? ηXY

dQ/dPc (Pc/Q) = -10(1)/120_= -.0813___________

Relationship __Complements: Inverse relationship_________________

155

2. Joe is evaluating the marketing strategy at his restaurant and inn. Suppose that in response to a $2.00 off" sales promotion for Spaghetti dinners, Joe finds that nightly dinner sales increase from 20 per night to 40. Normally, the dinners sell for $6.00. b. What is the arc price elasticity of demand? η

=

_ (Q1-Q0)(P1+P0) (P1-P0)(Q1+Q0)

=

(20 – 40)(6+4) = -20(10) = (4 – 6)(20+40) 120

-1.67

b. Would Joe increase revenues by further reducing the price? What about profits? Explain. Price reduction prompts revenue increase Price reduction prompts profit increase

Y / N / Can’t tell Y / N / Can’t tell

Explanation Joe is on the elastic portion of demand. A price reduction will increase revenues. However, the profitability of such an action cannot be discerned absent cost information 3. Fred McCutchen a new employee at McCutchoni Frozen Foods estimates that the price elasticity of demand for McCutchoni Frozen Pizzas to be -1.5, as compared to a price elasticity of demand for frozen pizzas in general of -2.34. In light of the relative inelasticity of McCutchoni Frozen Pizza's, Fred recommends raising the price to increase sales revenues. You, a more experienced member of the firm, are suspicious of Joe's estimate, and are skeptical of his recommended plan of action? Why? (Hint: Think about the determinants of price elasticity of demand) Reason to suspect Fred’s estimate: Elasticity for a group should be lower than for a particular product in that group Reason to doubt Fred’s plan of action: If McCutchoni is on the elastic portion of demand, a price increase will reduce revenues. E303, Problem Set #6 1. We-R-Food's, a restaurant consulting firm estimates that in the Southeastern United States a 10% reduction in the price of fried potatoes will increase sandwich sales by 20%. But they further estimate that a 10% reduction in the price of salads will decrease sandwich sales by 15%.

156

a. What is the implied cross price elasticity of sandwiches with respect to changes in the price of fried potatoes?

ηsandwiches ff = _________________________________________ b. What is the implied cross price elasticity of sandwiches with respect to changes in the price of. salads?

ηsandwiches salads = _________________________________________ c. From your cross price elasticity estimates, what can you say about the relationship between fried potatoes and sandwiches, and between salads and sandwiches at fast food restaurants in the Southeastern United States? Why? French fries and Sandwiches_______________________________ Reason ________________________________________________ Salads and Sandwiches_______________________________ Reason ________________________________________________ 2. Suppose that for Mazda Miata's, the income elasticity ηI = 3. a. What does the above information suggest about the kind of product a Mazda Miata is? Why? Kind of Product _______________________________ Reason ________________________________________________ b. Economists predict a strong rebound in economic performance this year, and predict that GNP will grow by 4%. What effect will this have on Miata sales? Estimated percentage change in sales _______________________________ 3. The demand for Sorby ZIP disks is given by the following equation Q

=

10P-3PH1.5I2.

157

Where P is the price of the ZIP disks PH is the price of Hard disk drive space, and I is income (in thousands of dollars) a. What is the price elasticity of demand?

η

=

_______________________________

b. What is the income elasticity of demand? What does the income elasticity of demand suggest about the kind of good Sorby disks are?

ηI

=

______________________________

Kind of Good _____________________________________________. c. Suppose that due to a recession in the market for information goods income for ZIP disk users is projected to fall by 4% next year. How will sales be affected?

ηI

=

____________________________________________________

Problem Set #6 1. We-R-Food's, a restaurant consulting firm estimates that in the Southeastern United States a 10% reduction in the price of fried potatoes will increase sandwich sales by 20%. But they further estimate that a 10% reduction in the price of salads will decrease sandwich sales by 15%. a. What is the implied cross price elasticity of sandwiches with respect to changes in the price of fried potatoes?

ηsandwiches ff = __%∆ Qs/%∆ Pff = -20/10 = -2______________________________________

158

b. What is the implied cross price elasticity of sandwiches with respect to changes in the price of. salads?

ηsandwiches salads = _%∆ Qs/%∆ Psalads = -15/-10 = 1.5 c. From your cross price elasticity estimates, what can you say about the relationship between fried potatoes and sandwiches, and between salads and sandwiches at fast food restaurants in the Southeastern United States? Why? French fries and Sandwiches___Complements, ________________________ Reason __ηxy0______________________________________________ 2. Suppose that for Mazda Miata's, the income elasticity ηI = 3. a. What does the above information suggest about the kind of product a Mazda Miata is? Why? Kind of Product __Normal Cyclical Good_________________________ Reason __ηI>1_____________________________________________ b. Economists predict a strong rebound in economic performance this year, and predict that GNP will grow by 4%. What effect will this have on Miata sales? Estimated percentage change in sales __η =%∆ Q/%∆ I thus, 3 = %∆ Q/4 %∆ Q = 12% 3. The demand for Sorby ZIP disks is given by the following equation Q

= 10P-3PH1.5I2. Where P is the price of the ZIP disks PH is the price of Hard disk drive space, and I is income (in thousands of dollars)

a. What is the price elasticity of demand?

159

η

=

__-3_____________________________

b. What is the income elasticity of demand? What does the income elasticity of demand suggest about the kind of good Sorby disks are?

ηI

=

___2.___________________________

Kind of Good ____Normal, cyclical__________________. c. Suppose that due to a recession in the market for information goods income for ZIP disk users is projected to fall by 4% next year. How will sales be affected?

ηI

=

_%∆ Q/%∆ I. Thus, 2 = %∆ Q/-4, %∆ Q=-8

Problem Set #7 Regression Analysis Consider the following data Sales Adv Yi Xi 3 4 6 5 7 6 5 9 10 9

1 2 3 4 5 6 7 8 9 10

1. Input this data on a spreadsheet. Using the regression option, generate regression predictions. Write your results as an equation, as we did in class. In particular, (a) Write the regression equation, with estimated coefficients,

160

(b) Below the regression equation, list in parentheses the standard errors of the coefficient estimates (c) To the right of the estimated equation write R2 = ^ Equation: ____Y_=___________________________________ R2 = Std Errors ( ) ( )

2. Multivariate Regression. Now add to your above regression in a price variable, with values: 8, 7.5, 7.25, 7.25, 6, 6.75, 6, 5, 4.4, 5.2. Estimate the new regression equation. Print regression results. Write out the estimated demand function, as in 1 above. Equation: ____Y_=___________________________________ R2 = Std Errors ( )( )( )

3. Evaluating regression results: A Descriptive Statistic. With the data you generated in (2) above do the following. a. Interpret the R2. (In a sentence) _________________________________________________________________ _ b. At an approximate 95% level of confidence, can you conclude that price affects sales? Explain Price Affects Sales? Y/N (circle one) Reason: ____________________________________________________

Problem Set #7 Regression Analysis Consider the following data

161

Sales Yi

Adv Xi

3 4 6 5 7 6 5 9 10 9

1 2 3 4 5 6 7 8 9 10

1. Input this data on a spreadsheet. Using the regression option, generate regression predictions. Write your results as an equation, as we did in class. In particular, (a) Write the regression equation, with estimated coefficients, (b) Below the regression equation, list in parentheses the standard errors of the coefficient estimates (c) To the right of the estimated equation write R2 = ^ Equation: ____Y_=___2.733____+ 0.667Xi__________________ R2 = .757 Std Errors (0.827 ) ( 0.133 )

162

2. Multivariate Regression. Now add to your above regression in a price variable, with values: 8, 7.5, 7.25, 7.25, 6, 6.75, 6, 5, 4.4, 5.2. Estimate the new regression equation. Print regression results. Write out the estimated demand function, as in 1 above. Equation: ____Y_=__17.68_ + 0.005 – 1.78 _______________________ R2 = 0.868 Std Errors ( 6.19) (0.133 ) ( 0.734)

3. Evaluating regression results: A Descriptive Statistic. With the data you generated in (2) above do the following. a. Interpret the R2. (In a sentence) 86.8% of the movement in the sales is explained by movements in price and advertising. _________________________________________________________________ _

b. At an approximate 95% level of confidence, can you conclude that price affects sales? Explain. Price Affects Sales? Y/N (circle one) Reason: The interval about price, -3.52

to

-0.048 doesn’t include 0.

Problem Set 8. E303 Davis, Spring, 2006. 1. Bill Smith is the new Director of Marketing at the Jonesfield Ham Company. In the interest of assessing Jonesfield’s pricing policy, Bill examined sales data for the last 24 months, and estimated the following relationship Q

=

Where Q P

125 (15)

-

14P (2.8)

+

R2 =

.71,

MSE = 2.75

5Ps (3.2)

+

4I (3.6)

number of sugar cured hams sold in the Richmond area per month price per pound of the hams

163

Ps I

price per point of Smithfield salt-cured country hams Per capita income (in thousands of dollars.)

Assume that at present P = $3.50; Ps = $5.00, I = $12 (000). 1. Construct an approximate 95% confidence interval about the price variable. Does this suggest that price is an important explainor of sales? Why or why not? Interval ______________

to

_____________

Price an important explainor of sales? Y / N. (circle one) Explanation __________________________________________________________________. 2. Construct an approximate 95% confidence interval about the income variable. Does this suggest that income is an important explainor of sales? Why or why not? Interval ______________

to

_____________

Income an important explainor of sales? Y / N. (circle one) Explanation __________________________________________________________________. 3. Assume your answer to 2 was no. Should you eliminate the income variable from your regression? Eliminate? Y / N (circle one) Explanation __________________________________________________________________.

164

4. Using current values (e. g., P = $3.50; Ps = $5.00, I = $12 (000).) a) forecast sales for the next month.

Forecast ______________ b) Provide an approximate 95% confidence band about your projection.

Interval ______________

to

_____________

c) Aside from the width of the interval, what factor would tend to make you less confident of your projection? Why? Factors

:_______________________

________________________ Reason that they would undermine your confidence in the forecast _______________________________________________________________________ _

KEY

Problem Set 8. E303 Davis, Spring, 2006.

1. Bill Smith is the new Director of Marketing at the Jonesfield Ham Company. In the interest of assessing Jonesfield’s pricing policy, Bill examined sales data for the last 24 months, and estimated the following relationship Q

=

Where Q

125 (15)

-

14P (2.8)

+

R2 =

.71,

MSE = 2.75

5Ps (3.2)

+

4I (3.6)

number of sugar cured hams sold in the Richmond area per month

165

P Ps I

price per pound of the hams price per point of Smithfield salt-cured country hams Per capita income (in thousands of dollars.)

Assume that at present P = $3.50; Ps = $5.00, I = $12 (000). 1. Construct an approximate 95% confidence interval about the price variable. Does this suggest that price is an important explainor of sales? Why or why not? 14 + 2(2.8) 19.6

to 14 – 2(2.8) to 8.4

Yes, price is an important explainor of sales. The interval does not include 0. 2. Construct an approximate 95% confidence interval about the income variable. Does this suggest that income is an important explainor of sales? Why or why not? 4 + 2(3.6) 11.2

to to

4 – 2(3.6) -3.2

No, I cannot conclude that income is an important explainor of sales. The interval includes 0. 3. Assume your answer to 2 was no. Should you eliminate the income variable from your regression? No. Eliminating relevant variables can create bias.

166

4. Using current values a) forecast sales for the next month. Q

= 125 - 14(3.5) + 5(5) + 4(12) = 125 – 49 + 25 + 48 = 149 b) Provide an approximate 95% confidence band about your projection.

149 + 2(2.75) to 154.5 to

149 – 2(2.75) 143.5

c) What would tend to make you less confident of your projection? Why? Factors that make the future look different from the past, such as - Independent variable values that deviate from their means - Some probability of a change in the underlying legal or social environment These factors are not included in the estimates

KEY

Fall 2005

1. Optimal Use of a Single Input. Julian Smyth is manages production at Taffy Apple Inc., a company that produces a variety of taffy/fruit candies. Over the last several months, he has varied then number of employees on his caramel apple production line, and found the following relationship. Labo r 5 6 7 8 9 10 11 12

TP 100 150 230 300 360 410 450 480

MP

MRP

50 80 70 60 50 40 30

250 400 350 300 250 200 150

a. In the column labeled MP, calculate the marginal product of labor. (Note, make your first entry in row 6, as the change between 5 and 6 units of labor) See listings under MP 167

b. Suppose the apples sell for $5 per (dozen) box. Calculate the Marginal Revenue Product (MRP) See listing under MRP c. If labor costs $225 per day, how many laborers should the firm hire? Number ______10___________________________________

168

2. Optimal Use of a Single Input. A Graphical Representation. a. In the coordinate axes provided below, illustrate the general relationship between MRP and the Price of Labor. Identify the equilibrium quantity of labor to hire. (Note, your graph need not use the numbers in problem 3. Just be certain to include ranges that illustrate gains from specialization and the law of diminishing returns in your graph. $

PL MRP L*

Q

b. Suppose that the candy workers union agrees to way concessions, that make the price of labor fall. In the coordinate axes below illustrate the effect on the equilibrium quantity of labor $

PL’ PL L*’ L* Q c. Finally, suppose that the price of caramel apples increases. Illustrate the effect of this change on the equilibrium quantity of labor employed. $

MRP* MRP L*

169

L*’

Q

3. Optimal use of multiple inputs. In his shop, Julian Valenti retrofits sunroofs into automobiles. The process can use a combination of skilled labor and unskilled labor. Given his current mix of employees, the marginal product of the last unit of skilled labor is 3 sunroofs per day, and the marginal product of the last unit of unskilled labor is 1 sunroof per day. Current market rates for skilled and unskilled labor is $40 and $10, respectively. Is Julian using a least cost combination of inputs? If not, which of type of labor should he use relatively more? Comparison Expression: Compare __MPS/Ps_to MPU/PU_here 3/40 vs. 1/10___ Result:_Hire relatively more unskilled labor_________________________ Problem Set #9 Spring 2006 1. Optimal Use of a Single Input. Julian Smyth is manages production at Taffy Apple Inc., a company that produces a variety of taffy/fruit candies. Over the last several months, he has varied then number of employees on his caramel apple production line, and found the following relationship. Labo r 5 6 7 8 9 10 11 12

TP 100 150 230 300 360 410 450 480

MP

MRP

50 80 70 60 50 40 30

250 400 350 300 250 200 150

d. In the column labeled MP, calculate the marginal product of labor. (Note, make your first entry in row 6, as the change between 5 and 6 units of labor) e. Suppose the apples sell for $5 (per dozen) box. Calculate the Marginal Revenue Product (MRP) f. If labor costs $225 per day, how many laborers should the firm hire? Number ___________________________________________

170

2. Optimal Use of a Single Input. A graphical representation. a. In the coordinate axes provided below, illustrate the general relationship between MRP and the Price of Labor. Identify the equilibrium quantity of labor to hire. (Note, your graph need not use the numbers in problem 3. Just be certain to include ranges that illustrate gains from specialization and the law of diminishing returns in your graph. $

Q b. Suppose that the candy workers union agrees to way concessions, that make the price of labor fall. In the coordinate axes below illustrate the effect on the equilibrium quantity of labor $

Q c. Finally, suppose that the price of caramel apples increases. Illustrate the effect of this change on the equilibrium quantity of labor employed. $

Q

171

2. Optimal use of multiple inputs. In his shop, Julian Valenti retrofits sunroofs into automobiles. The process can use a combination of skilled labor and unskilled labor. Given his current mix of employees, the marginal product of the last unit of skilled labor is 3 sunroofs per day, and the marginal product of the last unit of unskilled labor is 1 sunroof per day. Current market rates for skilled and unskilled labor are $40 and $10, respectively. Is Julian using a least cost combination of inputs? If not, which of type of labor should he use relatively more? Comparison Expression:_______________________________________ Result:______________________________________________________ Problem Set #10 Costs of the Firm 1. Short run costs for the firm. Consider a firm with the following Fixed Costs and Marginal Costs Q

TFC

0

15

TVC

TC

MC

1

3

2

2

3

1

4

2

5

5

6

9

7

14

8

20

AFC

AVC

ATC

a) Total Costs a. Fill in the blanks for TVC and TC Construct a graph that illustrates the TVC, TFC, and TC curves b. On this graph, show how MC may be illustrated (at any arbitrary point) b) Unit Costs 172

a. Fill in the blanks for AVC, AFC and ATC b. Construct a graph that illustrates MC,AVC, and ATC c. What is the relationship between AVC and ATC? Why? Relationship _________________________ Reason: ____________________________. d. What is the relationship between MC and AVC? MC and ATC? Why? Relationship _______________________________ Reason: _________________________________ 2. Production for a firm in the Short Run. a. In general, how should the firm determine the optimal output level? Rule:_________________. b. Referring again to table 1, if the price is $10 per unit, how much should the firm produce? Illustrate this result in your unit cost figure. Is the firm earning economic profits at that level of output? c. What is the minimum price at which the firm would produce? Why? Shutdown point:_________________________________________

d. When does the firm breakeven? Why? Breakeven point:____________________________________________. Problem Set #10 Costs of the Firm

173

3. Short run costs for the firm. Consider a firm with the following Fixed Costs and Marginal Costs Q 0.00

TFC 15.00

TVC 0.00

TC 15.00

MC

AFC

AVC

ATC

1.00

15.00

3.00

18.00

3.00

15.00

3.00

18.00

2.00

15.00

5.00

20.00

2.00

7.50

2.50

10.00

3.00

15.00

6.00

21.00

1.00

5.00

2.00

7.00

4.00

15.00

8.00

23.00

2.00

3.75

2.00

5.75

5.00

15.00

13.00

28.00

5.00

3.00

2.60

5.60

6.00

15.00

22.00

37.00

9.00

2.50

3.67

6.17

7.00

15.00

36.00

51.00

14.00

2.14

5.14

7.29

8.00

15.00

56.00

71.00

20.00

1.88

7.00

8.88

c) Total Costs a. Fill in the blanks for TVC and TC Construct a graph that illustrates the TVC, TFC, and TC curves 80.00

TC

70.00 60.00

TVC

50.00

MC

40.00 30.00 TFC

20.00 10.00 0.00 0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

b. On this graph, show how MC may be illustrated (at any arbitrary point) At any point, MC is the slope of the line tangent to the curve d) Unit Costs a. Fill in the blanks for AVC, AFC and ATC See table above b. Construct a graph that illustrates MC,AVC, and ATC 174

25

MC

20

15 ATC 10 AVC 5

0 0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

c. What is the relationship between AVC and ATC? Why? Relationship _The curves approach each other as quantity expands. Reason: The difference between them is AFC d. What is the relationship between MC and AVC? MC and ATC? Why? Relationship MC cuts both AVC and ATC at their minimum points Reason: The Marginal Drives the average

Production for a firm in the Short Run. a. In general, how should the firm determine the optimal output level? Rule:_Compare MR (price) to MC________________. b. Referring again to table 1, if the price is $10 per unit, how much should the firm produce? Illustrate this result in your unit cost figure. Is the firm earning economic profits at that level of output? The firm should produce 6 units. The firm is earning profits because at a price of $10 AR (=P) exceeds ATC.

175

c. What is the minimum price at which the firm would produce? Why? Shutdown point:_When price is such that P=MC = AVC. Here at an output of 4, (and AVC=MC = 2 At prices below $2, the firm would not only lose it’s fixed costs, but it would also be paying variable costs to produce d. When does the firm breakeven? Why? Breakeven point: When price is such that P = MC = ATC. At this point the firm just covers all costs of operation.

Problem Set #11 1. Characterizing Cost Functions Analytically. Consider the Cost function TC =

100 +10Q + Q2 a. What are the fixed costs for this relationship? What are Variable Costs?

Fixed Costs: ____100__________________________________ Variable Costs: _10Q + Q2 ________________________________ b. What is the marginal cost function? Marginal Cost: ___10+2Q___________________________________ c. Identify Expressions for Average Variable and Average Total Cost Average Variable Costs: __ 10+Q_________________________________ Average Total Costs: ____ 100/Q + 10 + Q________________________________ d. Finally, identify the output levels where AVC and ATC are minimized.

176

AVC min: ___0___________________________________ 100/Q + 10 + Q = 10 + 2Q 100/Q = Q ATC min: _Q = 10_________________________________ 2. Sunk Cost vs. Fixed Cost: Radio broadcaster CoolPlay Inc., paid $50,000 for an operating license last year, and the company is not meeting its advertising revenue expectations. Currently, they company is taking in $6,000 per month in revenues and has $5,000 per month in variable expenses. What difference does it make to CoolPlay if the license is transferable (e.g., resalable) or not? Under which condition would CoolPlay remain in the market longer (resalable or not resalable?) Difference ___If the license is nontransferable, it is a sunk costs. Condition Under Which CoolPlay will remain in the market longer? Saleable/ Not Resalable (Circle one)

177

3. Long Run Costs for the Firm. Consider the following long run cost curve. 25

MES

a. On the figure to the left, identify the range of the LRAC where the firm enjoys economics of scale What factors might allow a firm to enjoy economies of scale?

20 LRAC

15 10 5

Economies of Scale

Diseconomies of Scale

0 0

2

4

6

8

10

Reasons for scale economies: __Gains from specialization. Physical relationships b. Identify the range of the LRAC where the firm suffers diseconomies of scale. What factors would result in diseconomies of scale Reasons for diseconomies of scale: Transportation Costs, Managerial Inefficiency (‘Crowding’) c. What is MES on the above figure? Suppose that at an average cost of $10 per unit demand is such that the industry could sell 40 units. What is the maximum number of firms that are sustainable in this market? Why? Maximum number of sustainable firms: __If MES is 4, the industry could suppose 10 firms (students might see MES at 3 units as well.) Firms must operate at MES to efficiently survive. 4. Returns to Scale. Jake’s Free Runoff Bottled Water Company Produces with the Long Run Production Function Q = (KL)2/3 Currently K = 4 and L = 4. If Jake’s doubles inputs to K=8 and L=8, will it realize increasing, constant or decreasing returns to scale (circle one)? As a result, does Jake’s enjoy economies of scale, diseconomies of scale, or does Jake’s appear t be operating at Efficient Scale? (circle one)

178

Problem Set #12 1. Multi-Product Production. Consider the following cost relationship for a firm that can produce 2 products, Q1 and Q2. C(Q1, Q2) a.

=

300

+ 5Q1 + 5Q2

+

Q1Q2

Does the firm exhibit cost complementarities? Explain.

Cost Complementarities? (Y / N) __________________________ b. At an output level Q1 = 20 and Q2 = 20 does the firm exhibit economies of scope? Explain Economies of Scope? (Y/ N) Justification: ____________________________ 2. Input Acquisition. The Roasted Pepper Pizza Company features roasted fresh peppers and goat cheese on its Mediterranean Style Pizzas. The local company purchases 200 pounds of fresh peppers 250 pounds of goat cheese from a local Grocery wholesaler each day at the market price. a. What kind acquisition is this? (Circle One) Spot Market Purchase,

Contract or Vertical Integration

b. What features of this transaction suggest that a contractual arrangement might be a good idea? What problem would a contract alleviate? _________________________________________________________ _________________________________________________________

179

3. Compensation Issues. Stevens Cards produces and sells a low-volume high-end holiday cards. The company is particularly well-known for the elegant poems printed on the inside of the cards. At present the company compensates poets on a perpoem basis. On the other hand, company executives, disguised as customers monitors sales people, who are paid an hourly fee. a. How might the company alter its compensation package for the poets to improve firm performance? Why would such an alteration help? Alteration:_______________________________________________ Why the alteration may help:________________________________ ________________________________________________________ b. How might the company alter its compensation for salespeople to improve firm performance? Alteration:_______________________________________________ Why the alteration may help:________________________________ _________________________________________________________

180

Homework Problem Set #13 NEW E303 Davis, Spring 2006 1. The Competitive Firm in the Intermediate Run. a. In the two coordinate axes below, illustrate the relationship between market supply and demand and optimizing decisions of a firm. Illustrate a situation where the firm is earning economic profits. P

P

Market

Q

Firm

Q

b. What dynamic tends to drive profits to zero? Illustrate this dynamic in the same graph. Dynamic:________________________________________________________

2. Finding the Competitive Price. Consider a firm with a TC function TC

=

49

+

7Q

+

Q2

What price would this firm charge if it was in a long run competitive equilibrium? What Profits would it earn? Why? Optimal Price _________________________________________________ Optimal Profits ________________________________________________ Reason: _______________________________________________________ _____________________________________________________________

181

3. The Competitive Firm in the Long Run. In the 1990’s many firms went through a period of ‘downsizing’ that was induced by technological developments (in large part, the computer spreadsheet). a. In the right most panel of the two-panel graph below, illustrate the ‘carrot’ and the ‘stick’ that drives firms to ‘downsize’. P

P

Market

Q

Firm

Q

b. Illustrate the market response to downsizing in the rightmost panel of the above figure. c. Explain how the market price can fall as firms reduce their scale of operation. Explanation___________________________________________________ Homework Problem Set #13 NEW E303 Davis, Spring 2006 4. The Competitive Firm in the Intermediate Run. a. In the two coordinate axes below, illustrate the relationship between market supply and demand and optimizing decisions of a firm. Illustrate a situation where the firm is earning economic profits. P

P MC S

182

Profits S’ (b)

P=MR ATC (a) D Market

Q

Firm

Q*

Q

b. What dynamic tends to drive profits to zero? Illustrate this dynamic in the same graph. Dynamic:___Entry causes supply to shift out, which drives down prices and profits 5. Finding the Competitive Price. Consider a firm with a TC function TC

=

49

+

7Q

+

Q2

What price would this firm charge if it was in a long run competitive equilibrium? What Profits would it earn? Why? ATC = 49/Q + 7 + Q = MC = 7 + 2Q Q=7 Optimal Price ________P = MC = 7 + 2(7) = 21________________ Optimal Profits π = 0 _______________________________________ Reason: __In an intermediate run competitive equilibrium entry and exit drive, P = ATC.

183

6. The Competitive Firm in the Long Run. In the 1990’s many firms went through a period of ‘downsizing’ that was induced by technological developments (in large part, the computer spreadsheet). a. In the right most panel of the two-panel graph below, illustrate the ‘carrot’ and the ‘stick’ that drives firms to ‘downsize’. P

P S1 MC2 Profit (Carrot)

S1

MC1 ATC2

ATC1

D Market

Q

Firm

Q

b. Illustrate the market response to downsizing in the rightmost panel of the above figure. Market supply will shift out. c. Explain how the market price can fall as firms reduce their scale of operation. Explanation__ Entry will occur _________________________________________

Homework Problem Set #14 E303 Davis, Spring 2006 7. Monopoly Pricing. A Graphical Analysis. The two panel graph below illustrates the relation between market forces and optimizing decisions for a firm in the canned peaches market, a competitive industry. a. In the rightmost panel illustrate the optimal output, price and profit levels for the competitive firm. P

184

S

MC

ATC

\

Market

D Q

Firm Q*

Q

b. Suppose that due to concerns regarding the paucity of domestic peach producers the government gives to USAPeaches Inc. an exclusive right to domestically produce and sell canned peaches. Circle the components in the competitive chart that you would use to generate predictions for the monopolist. c. In the coordinate axis below, identify the optimal monopoly output, monopoly price and monopoly profits. Compare these predictions to the price and profit conditions for the firm as a competitor that you developed in part a.. P

Q Comparing Monopoly to Competitor. In each case, circle the one that is greater. Output: Monopolist / Competitor _______________________________________ Price:__ Monopolist / Competitor _______________________________________ Profit: __ Monopolist / Competitor _______________________________________

185

8. Monopoly Pricing. An Analytical Example. Consider a firm with the demand curve P = 500 – Q and a cost function TC = 2500 + 4Q2. a. What is the marginal revenue function for this firm? MR_________________________________________________________________ b. Intuitively, why is marginal revenue more steeply sloped than demand (average revenue?) Reason for Steeper MR Slope:____________________________________________ ____________________________________________________________________ c. Identify the optimal level of output, price and profits for this firm.

Qm ________________

Pm__________________

π m_____________________

d. Were this firm a member of a competitive industry, what would be the quantity, price and profit level for the firm? Qc _________________

Pc___________________

186

π c_____________________

9. Monopolistic Competition. Schliezal Hickendorfer operates a small restaurant in the fan that specializes in German/Chinese Cuisine. The market is monopolistically competitive. The below demand and cost conditions illustrate current market conditions for Schliezal. P MC ATC

D Q a. Identify short run output, price and profit conditions for Schiezal.

b. Why doesn’t the outcome in a define a long run equilibrium? What will alter these predictions? Change: __________________________________ c. Illustrate Schliezal’s long run competitive equilibrium output, price and profits. P

Q Problem Set #14 E303 Davis, Spring 2006

187

10. Monopoly Pricing. A Graphical Analysis. The two panel graph below illustrates the relation between market forces and optimizing decisions for a firm in the canned peaches market, a competitive industry. a. In the rightmost panel illustrate the optimal output, price and profit levels for the competitive firm. P S

MC

Pc

ATC

P* π c =0

Market

D Q

Firm Q*

Q

b. Suppose that due to concerns regarding the paucity of domestic peach producers the government gives to USAPeaches Inc. an exclusive right to domestically produce and sell canned peaches. Circle the components in the competitive chart that you would use to generate predictions for the monopolist. c. In the coordinate axis below, identify the optimal monopoly output, monopoly price and monopoly profits. Compare these predictions to the price and profit conditions for the firm as a competitor that you developed in part a.. P Monopoly Profit MC

Pm

ATC

D MR Qm Firm Q Comparing Monopoly to Competitor. In each case, circle the one that is greater. Output: Monopolist / Competitor _______________________________________

188

Price:__ Monopolist / Competitor _______________________________________ Profit: __ Monopolist / Competitor _______________________________________

11. Monopoly Pricing. An Analytical Example. Consider a firm with the demand curve P = 500 – Q and a cost function TC = 2500 + 4Q2. a. What is the marginal revenue function for this firm? MR____500 – 2Q_________________________________________________ b. Intuitively, why is marginal revenue more steeply sloped than demand (average revenue?) Reason for Steeper MR Slope:_To sell more units the firm must reduce the price on unit that would have sold at a higher price c. Identify the optimal level of output, price and profits for this firm. = 500 –Q = 500 – 50 = 450

π

MR = MC 500 – 2Q = 8Q 10Q = 500 Q = 50

P

= TR - TC = 450(50) – [2500 + 4(50)2] = 10,000

Qm __50_________

Pm___450_________ π m___10,000__________

d. Were this firm a member of a competitive industry, what would be the quantity, price and profit level for the firm? MC = ATC P = MC = ATC 2 8Q =2500/Q +4 Q Q = 625 = 8(25) 4Q2 = 2500 Q = 25 = 200 Qc _=25__________ Pc___200___________

189

π c__=0___________

12. Monopolistic Competition. Schliezal Hickendorfer operates a small restaurant in the fan that specializes in German/Chinese Cuisine. The market is monopolistically competitive. The below demand and cost conditions illustrate current market conditions for Schliezal. P Profits MC ATC

Pmc

D MR Qm

Firm

Q

a. Identify short run output, price and profit conditions for Schiezal. See above b. Why doesn’t the outcome in a define a long run equilibrium? What will alter these predictions? Change: Entry will shift in residual demand. c. Illustrate Schliezal’s long run competitive equilibrium. P Profit =0 MC ATC Pm

D MR Qm

Firm

Problem Set #15

190

Q

13. Joe Holiday is a monopoly provider of Fishing Reels in a remote fishing village on a barrier island off the Gulf Coast. Currently he is selling is BassMaster reels for $50 each. Joe doesn’t know the precise demand function for fishing reels, but he estimates price elasticity of demand to be -2. If the reels cost Joe $30 each, is he maximizing profits? If not, what would be the profit maximizing price? Is $50 a profit maximizing price? Y/N (circle one) Profit Maximizing Price_____________________________________

14. Consider the inverse demand relationship P = 21-Q. The total cost function is TC = 50 – Q. a. What is the optimal price, quantity and maximum profits available to the seller, if the seller can post only a single price to all consumers? Optimal Price_______________________ Optimal Profits ______________________ b) Illustrate in the coordinate axes provided below the maximal profits available to this seller, if the seller is forced to post a single price. P

Q

191

15. Now suppose that the seller is free to post consider post different prices to each different consumer. a) Identify the profit maximizing quantity and maximal profits for the seller under these circumstances.

Maximum Profits with Perfect Price Discrimination______________ b) Shade in the appropriate area in the figure below. P

Q c) What are the two conditions must be satisfied in order for a seller to realize maximum profits with perfect price discrimination? Why is each condition necessary? Condition 1: _____________________________ Condition 2:_____________________________

192

16. Consider again the demand relationships in (2) and (3) above, but suppose that the demand relationship was for a single consumer who was considering joining a health club. Describe the membership and acess fee structure that would optimize profits. (Be explicit) Membership Price: ____________________ Access Fee:

__________________________

17. Suppose that Handsome Joe Hedley needs a new summer suit. He is willing to pay up to $300 for a first linen suit, and $200 for a second. If suits cost Smith & Co. Fine Clothiers $100 each, identify the sales quantity from setting price equal to $300 and $200 what pricing structure would maximize profits? Quantity

Profits

Price $300: Price $200 How might Smith use Second Degree price discrimination to increase profits? What are the maximum profits available? Pricing Strategy: ___________________________________ _________________________________________________ Maximum Profits: __________________________________ _________________________________________________ 18. Suppose that an airline can divide travelers into economy class and business class. The price elasticity of demand for the business class is -1.5, and for the economy class is -3. If the marginal cost of a seat on an flight from Richmond to New York is $20, what are the optimal prices for each group?

Business Class__________________________________ Economy Class__________________________________

193

KEY

Homework Problem Set #15

19. Joe Holiday is a monopoly provider of Fishing Reels in a remote fishing village on a barrier island off the Gulf Coast. Currently he is selling is BassMaster reels for $50 each. Joe doesn’t know the precise demand function for fishing reels, but he estimates price elasticity of demand to be -2. If the reels cost Joe $30 each, is he maximizing profits? If not, what would be the profit maximizing price? Is $50 a profit maximizing price? Y/N (circle one) Profit Maximizing Price_______P = MC/(1+1/η)

=

30/(1-1/2) =

60

20. Consider the inverse demand relationship P = 21-Q. The total cost function is TC = 50 – Q. a. What is the optimal price, quantity and maximum profits available to the seller, if the seller can post only a single price to all consumers? MR = 21-2Q = 1 implies that Q = 10, so P = 21-10 = 11 and profits are ($11(10) – [50-$1(10)] = $55. Optimal Price______11_______________ Optimal Profits ____50________________ b) Illustrate in the coordinate axes provided below the maximal profits available to this seller, if the seller is forced to post a single price. P

$ 6 $ 1 5

Q

194

21. Now suppose that the seller is free to post consider post different prices to each different consumer. a) Identify the profit maximizing quantity and maximal profits for the seller under these circumstances. The firm would charge a different price to each consumer equal to their marginal valuation. Profits would equal .5(21-1)(20) = 200 Maximum Profits with Perfect Price Discrimination_$150 (take out fixed cost) b) Shade in the appropriate area in the figure below. P 1 1

1 10

Q

c) What are the two conditions must be satisfied in order for a seller to realize maximum profits with perfect price discrimination? Why is each condition necessary? Condition 1: - No resales: Low value sellers will drive price down via resales Condition 2:- Ability to size up willingness to pay______________.

195

22. Consider again the demand relationships in (2) and (3) above, but suppose that the demand relationship was for a single consumer who was considering joining a health club. Describe the membership and access fee structure that would optimize profits. (Be explicit) Membership Price: $200 (equal to consumer surplus) Access Fee:

$1 per unit (marginal cost).

23. Suppose that Handsome Joe Hedley needs a new summer suit. He is willing to pay up to $300 for a first linen suit, and $200 for a second. If suits cost Smith & Co. Fine Clothiers $100 each, identify the sales quantity from setting price equal to $300 and $200 what pricing structure would maximize profits? Price $300: Price $200

Quantity 1 2

Profits $200 $200

How might Smith use Second Degree price discrimination to increase profits? What are the maximum profits available? Pricing Strategy: Charge a high price for a first suit, but then a lower price for additional suits. Maximum Profits: Charging $300 for the first suit and $200 for the second, Smith earns $300. 24. Suppose that an airline can divide travelers into economy class and business class. The price elasticity of demand for the business class is -1.5, and for the economy class is -3. If the marginal cost of a seat on an flight from Richmond to New York is $20, what are the optimal prices for each group? P1

=

20/[1+1/-1.5]

60

P2

=

20/[1+1/-3]

30

196

197