Econ 100.1 - Problem Set 2 - Answer Key

UNIVERSITY OF THE PHILIPPINES SCHOOL OF ECONOMICS ECONOMICS 100.1 Introduction to Macroeconomic Theory and Policy Problem Set No. 2 – Answer Key 2nd Semester, AY 2010-2011

Prof. Monsod/Arao/Libre/Bundoc/Mariano

Submission is on December 16, 2010, Thursday, during the discussion class. Please use yellow paper. Show all necessary solutions. I.

Consumption and Investment 1. In working with the consumption function and the investment demand schedule, we need to distinguish between shifts of and movement along these schedules. (Answer briefly but completely.) a. Define carefully both curve changes that would lead to shifts of and those that would produce movements along the demand schedules. Consumption is determined by disposable income, permanent income, wealth, the life cycel hypothesis, and other special influences. Any changes in disposable income corresponds to a movement along the consumption curve, and any changes in factors other than the disposable income causes a shift of the consumption curve. The demand for investment in an economy is determined by interest rates, taxes, revenues, expectations, and othe special influences. If interest rates changes, there would be a movement along the investment demand curve. On the other hand, if factors other than interest rates changes, then investment demand would shift.

b. For the following, explain verbally and show in a diagram whether they are shifts or movements

c.

along the consumption function: (i) increase in disposable income – movement along the curve (ii) decrease in wealth – shift in the consumption curve (iii) fall in stock prices – shift in the consumption curve For the following, explain in words and show in diagram whether they are shifts or movements along the investment demand curve (i) expectation of a decline in output next year – shift in the investment demand (ii) rise of interest rates – movement along the curve (iii) increase intaxes and profits – shift in the investment demand

2. Which of the following events would cause the consumption function to shift up (U), shift down (D), or not shift at all (NS)? a. An anticipated down-turn in business conditions that leads people to worry that they might lose their jobs. D b. A reduction in the interest rate paid by banks that makes saving less attractive to everyone. U c. A reduction in taxes that enables people to retain more of their incomes after taxes. NS d. An actual contraction in the economy that causes a reduction in the availability of outside or overtime employment. NS

3. Investment, as the term is used in economics, generates employment while the investment item in question is being built, and thereby generates income for those people employed in the item’s construction. In this sense, do the following, by themselves, constitute investment? a. Having a contractor build a new house for you. Yes b. Buying a house built a year ago. No c. Buying Cebu Pacific stocks on the stock market. No d. Buying stock in a newly formed corporation. No e. Using money obtained from the bond or stock issue of item d to build a new factory building. Yes

1

4. You are given the following information about the economy of Pauland (no government, closed economy):

a.

Disposable Income Consumption Expenditure (millions per year) (millions per year) 0 5 10 10 20 15 30 20 40 25 Calculate the marginal propensity to consume. MPC = Change in Consumption / Change in Income = (10-5) / (10-0) = 5/10= ½ = 0.5

Saving (millions per year) -5 0 5 10 15

b. Calculate the saving at each level of disposable income. See Table c. Calculate the marginal propensity to save. MPS = 1 – MPC = 0.5

d. Derive the consumption and saving function. C = a + b Y; Let C = 5 and Y = 0. Then a = 5. Thus consumption function: C = 5 + 0.5 Y. Savings function: S = -5 + 0.5 Y. 5.

You are given the following information about the economy of Spendthrift Island (no government, closed economy) Disposable Income Saving Consumption (millions per year) (millions per year) (millions per year) 0 -10 10 50 -5 55 100 0 100 150 5 145 200 10 190 250 15 235 300 20 280 a. Calculate the marginal propensity to save. MPS = change in savings / change in income = (5-0)/(150-100) = 5/50= 1/10 = 0.10 b. Calculate consumption at each level of disposable income. See Table c. Calculate the marginal propensity to consume. MPC = 1 – MPS = 0.9 d. Derive the consumption and saving function. C = a + b Y; Let C = 10 and Y = 0. Then a = 10. Thus consumption function: C = 10 + 0.9 Y. Savings function: S = -10 + 0.1 Y. e. Determine the break-even level of income. Break-even level of income is at Y = C. Y = 10 + 0.9 Y; Then Y = 100. f. Sketch the graph of the consumption curve with the 450 line. Indicate the equilibrium point(s). C

C+I

equilibrium point

Y

2

g. Why is the island called “spendthrift”? Because the MPS is much higher than MPC.

II. The Multiplier Model 1.

You are given the following information about the Economy of Mialand:  Autonomous consumption expenditure is Php100 billion  Marginal Propensity to consume is 0.9  Investment is Php460 billion  Government Expenditure on goods and services is Php400 billion  Net taxes are a constant Php40 billion (do not vary with income) a. What is the consumption function? C = a + b Y = 100 + 0.9 (Y – 40) = 100-36 + 0.9Y = 64 +0.9Y b. What is the equation that describes the aggregate expenditure curve? Y = C + I + G = 64 + 0.9 Y + I + G Y (1-0.9) = 64 + I + G Y (0.1) = 64 + I + G Y = 640 + 10 (I + G) c. Calculate equilibrium expenditure Y = 640 + 10 (460+400)= 640 + (10 (860)) = 640 + 8600 = 9,240 d. If investment falls to Php360 billion, what is the change in equilibrium expenditure and what is the size of the multiplier? Y’ = 9,250 – (10)100 = 9,250-1000 = 8,250 Multiplier = 10

2. The following table represents an economy that has taxes and government spending but is not yet open to trade. (1) (2) (3) (4) (5) (6) (7) GDP Taxes DI C I G C+I+G 1,200 200 900 200 300 1,400 1,000 200 1,450 1,100 200 300 1,250 1,600 200 200 1,700 1,300 300 1,500 1,800 200 200 1,950 1,500 300 1,750 2,000 200 200 2,200 1,700 300 2,000 2,200 200 200 2,450 1,900 300 2,250 2,400 200 200 2,700 2,100 300 2,500 2,600 a. Complete the table above with the assumption that Taxes, I and G are fixed. See Table b. What is the equilibrium level of GDP in the economy? GDP=2,200 c. When the economy is at equilibrium, what is the level of saving? DI-C=300 d. Determine if I = S + (T - G) when the economy is at equilibrium. Is the government borrowing or running a deficit? Explain why or why not. I = 200, S = 300, T - G = - 100. Yes, I = S + (T - G). Government is running a deficit since T-G is negative. e. What is the value of the MPC? Set-up the equation for C. MPC=0.8; C=100+0.8(Y-T) f. Sketch the graph of the C, C + I, C + I + G lines with the 450 line. Indicate the equilibrium point(s).

C, C + I, C+I+G

equilibrium point

C+I+G C+I C

3

Y

g. What is the value of the expenditure multiplier? 5 h. What is the value of the tax multiplier? 4 i. If the government increases spending by 200, what would be the new equilibrium value of GDP?

j.

What economic problem might exist for the government to make this fiscal policy change? The change in GDP equals 100 x 5 = 500. The new equilibrium value for GDP is 2700. Unemployment may be high and the economy may be in a recession. If the government wanted to achieve the same change in GDP as in i by cutting taxes instead, how large would the tax cut have to be? If the government wants GDP to increase by $500 and the tax multiplier is 4, the tax cut would have to be 125.

4