Tutorial - Chapter 4 - Cost of Production - Questions

 

 Ma  M ana nage geri ri al E cono conom mics –  Tutor  Tutor i al –   Cos C ostt o off P r oduct uctii on H i nt: T uto utorr i al q quest uestii ons are co com mprehe prehensi nsive ve.. H ow owe ever ver , the r espe specti ctive ve lect lectur ure er s should utili uti lize ze the questi questions ons base based d on the d de ept pth h of the kn know owled ledgge a acqui cquisi siti tion on by stude students. nts. E ssa ssayy A Analy nalytical tical Que Questions stions 1. Explain why the marginal cost curve intersects a U-shaped average cost curve at its minimum  point.

2. Suppose firm has a constant marginal product of labor - one additional worker adds four units of output given any initial quantity of workers. What do the average variable and marginal costs look like for this firm? Provide a graph of the MC and AVC.

3. Ed's construction company has the following short-run cost function: q 3 - 10q2 + 36q. a. What level of output will minimize the average cost? What is the AC at this point?  b. Does the production process indicate diminishing returns? How can you tell? 4. Evren wants to go into the donut business. For $500 per month he can rent a bakery complete with all the equipment he needs to make a dozen different kinds of donuts ( K = l, r  =   = 500). He must pay unionized donut bakers a monthly salary of $400 each. He projects his monthly  production function to be Q = 5 KL  where Q is tons of donuts. a. With the current level of capital, what is the marginal marginal product of labor? Is Is the marginal product diminishing? Explain.  b. If Evren wishes to make 25 tons of o f donuts, do nuts, how many bakers are required given the current level of capital? How much will it cost to produce this (total cost)? c. Derive Evren's short-run cost function with with K=1. d. Derive the marginal marginal cost curve from from your answer to c. and show the relationship between the the marginal cost and marginal product of labor. 5. Consider a general Cobb-Douglas production function  b  q = ALaK  Where A, a and b are positive constants. Using this production function, derive the short-run cost function for a fixed capital stock, K 0, wage rate w, and capital rental rate r. 6. Alison lives in in a small town town where she plans to to hire workers to help her make candy. Her  production function for candy is 5  q = 4LK ..5

 

She begins producing with K = 4. The cost of capital is $50/unit. The wage depends on the amount of workers she employs. Specifically, w (L) = 10 + 2L. a. Does Alison's Alison's production function exhibit diminishing marginal return return to labor? Explain.  b. Derive Alison's short-run cost function. function. c. What is the shape of Alison's Alison's Marginal Cost? Cost? d. Does the relationship w/MP w/MP = MC hold? Show this explicitly. 7. Joey notices that by employing an additional hairdresser, he will be able to increase the number of haircuts in his salon by 15 haircuts per day. The daily salary he will need to pay the hairdresser is $200. How much is the cost for an additional haircut? Describe the general relationship between the marginal product and marginal cost curves. 8. Consider a firm with two technologies to choose choo se between when producing o output. utput. The cost function when using technology 1 is given by: c1(q) = 3600 + 65q + 36q2  The cost function when using technology 2 is given by: c2(q) = 900 + 900q +q2 Assume that the firm can only implement one of the two technologies at a time.   a. If the firm wishes to produce output at the lowest per-unit cost, which technology should should it choose and how much output should it produce?  b. Which technology should the firm choose if it wishes to produce 15 units of output? What about 25 units of output? 9. A firm produces output according to the following function: (For advance level)   1/3  q = f (L, K) = L 1/2 K 1/3 The cost of labor is $9 per pe r hour and the rental cost of capital is $4 per hour. a. With the given prices, prices, use the Lagrangian method to compute the optimal (cost-minimizing) (cost-minimizing) capital to labor ratio (K/L) for the firm.  b. Suppose the firm wishes to produce 72 units of output. How much capital and how much labor does the firm employ? c. What is the total cost of producing 72 units of output? d. Suppose that the firm firm suddenly decides to double the quantity of output output but only has a day to complete the order. Therefore, in that time, the amount of capital is fixed but labor hours are not. How much will it cost to produce 144 1 44 units of output? How much would it cost if the firm could also vary capital? Compute as well as providing a graph (isocost/isoquant) illustrating the optimal bundles.

 

 

 Mult  M ultipl iple e Cho Choice ice Que Quest stii ons 1. Suppose the total cost of producing T-shirts can be represented as TC = 50 + 2q. Which of the following statements is TRUE at all levels of production? A) MC = AVC B) MC = AC C) MC > AFC D) All of the above. 2. If average cost is decreasing, A) marginal cost equals average cost. B) marginal cost exceeds average cost. C) marginal cost is less than average cost. D) Not enough information is provided. 3. In the short run, the point at which average cost is minimized, the line from the origin to the  point on the A) total cost curve is tangent to the curve. B) total cost curve has the largest slope. C) total variable cost curve has the largest slope. D) total variable cost curve has the smallest slope. 4. At the XYZ Co., a unit of capital costs three times as much as a unit of labor. If MPK = 10, MPL = 5, then this firm A) is minimizing its cost at current output level. B) should use more capital and less labor to raise output at current cost. C) should use less capital and more labor labo r to raise output at current cost. D) None of above. 5. The total cost of producing one unit is $50. The total cost of producing two units is $75. At a  production level of two units, the cost function exhibits A) economies of scale. B) rising average costs. C) increasing marginal costs. D) constant returns to scale. 6. If a production function is represented as q = Lα  K β, the long-run average cost curve will be horizontal as long as A) α + β = 0.  B) α + β = 1.  

 

C) q > 0. D) L = K. 7.Suppose that each worker must use only one shovel to dig a trench, and shovels are useless by themselves. In the long run, an increase in the price of shovels will result in A) fewer shovels being purchased to produce the same number of trenches. B) more workers being hired to produce the same number of trenches. C) the firm wishing to produce more trenches. D) no change in the firm's input mix. 8. Suppose that each worker must use only one shovel to dig a trench, and shovels are useless by themselves. In the long run, the firm's cost function is A) TC = (w/r)  q. B) TC = (w + r)/q. C) TC = (w + r). D) TC = (w + r)  q. ∗

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9. Which of the following will cause the average fixed cost curve of makin making g cigarettes to shift? A) a $5 million penalty charged to each cigarette maker B) a $1 per pack tax on cigarettes C) a $3 per hour wage increase D) an increase in the demand for cigarettes