Intermediate Macroeconomics-ECO 3203

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1 Intermediate Macroeconomics-ECO 3203 Midterm Examination Solution Sample, Summer 2018 Instructor: Yun Wang Instructions: The full points of this exam is 100, and you will have 2 hours to finish it. Show all your works (necessary steps to get the ) for every question. When drawing your graph,label all curves, axes, initial and final equilibrium values, and the direction of the change in any curve. 1. Assume an economy consumes only apples. In year 1, the Galas cost $1 each, the Fujis cost $1.3 each, the Golden Delicious cost $1 each and the Granny Smiths cost $1 each, the whole economy consumes 100 Galas, 100 Golden Delicious and 100 Granny Smiths. In year 2, the Galas cost $1.5 each, the Fujis cost $1.2 each, the Golden Delicious cost $1 each and the Granny Smiths cost $1 each, the whole economy consumes 150 Golden Delicious and 150 Granny Smiths. a. Suppose that the price of apples rises, consumers try to seek alternatives and consume fewer apples. Which of our two measures of inflation, the CPI and the GDP deflator, would give us a more accurate indication for inflation? Why? Explain in detail. (4 points) b. Compute the economy s nominal spending in each year, and compute the economy s real spending in each year with year 1 as base year. (5 points) c. According to the nominal and real spending, compute the GDP deflator in each year,and compute the inflation rate for each year based on the deflators you calculated. (5 points) a. In this case, GDP deflator will be a more accurate indication. When there is new product as alternative, for example orange been consumed. A better reflection of the inflation should include the new product in the calculation. Therefore, CPI still uses the same old basket of 1

2 goods, GDP deflator includes the new product. b. the norminal spending for year 1 = 100galas $ GD $ GS $1 = $300 the norminal spending for year 2 = 150GD $ DS $1 = $300 with year 1 as base year, use the year 1 prices for all the years the real spending for year 1 = 100galas $ GD $ GS $1 = $300 the real spending for year 2 = 150GD $ DS $1 = $300 c. GDP deflator for year 1 = the inflation rate for year 1 = 0 GDP deflator for year 2 = the norminal spending for year = = 100 the real spending for year the norminal spending for year = = 100 the real spending for year the inflation for year 2 = GDP deflator for year 2 GDP deflator for year 1 = 0 2. Consider a close economy supply and demand model. Y denote GDP, C denotes Consumption, I denotes Investment, r is the real rate of interest in percent, T denotes Taxes, and G stands for Government Spending. Suppose the aggregate production function of the economy is Y = A 1 3 KL with K denotes capital and L denotes labor input. Assume now K = 1600, L = 900 and A = The variables in the model taking these forms: C = (Y T ) I = r T = 2000 G = 2000 a. Calculate the national income. How much of the GDP goes into paying labor and capital input? (6 points) b. What are the real wage rate and real rental rate of the capital? (4 points) c. What are the equilibrium values of C, I, and r? (6 points) d. What are the values of private saving, public saving, and national saving? (6 points) e. If government spending drops to 1,000, what are the new equilibrium values of C, I, and r? (6 points) 2

3 f. What are the new equilibrium values of private saving, public saving, and national saving? (6 points) a. Y = A 1 3 K 1 2 L 1 2 = = = Because the Cobb-douglas function is constant return to scale, MP L L = 1 2 Y MP K K = 1 2 Y b. c. 1 W P = MP L = Y 2 L 1 R P = MP K = Y 2 K = = = = 3.75 C = (Y T ) = ( ) = 8000 I = S = Y C G = = 2000 I = r 2000 = r we will get r = 10 d. S private = Y T C = = 2000 S public = T G = = 0 S national = S private + S public = = 2000 e. if G to1000, Y would be unchanged, T unchanged, so C = C(Y T ) is unchanged: C = (Y T ) = 8000 the only change here is G, so only public saving changed: S public = T G = =

4 the private saving still unchanged: S private = Y T C = 2000 in the equilibrium I = S national = S private + S public = = We plug in I = r 3000 = r r = 0 f. as we know from part e, S private = Y T C = 2000 S public = T G = = 1000 I = S national = S private + S public = = The monetary base of Econland is $1200 million. The current-deposit ratio (cr) is 0.36 and reserve-deposit ratio (rr) is Now assume the national output growth rate is 7.5 percent and inflation is 2.5 percent. a. Calculate the money multiplier and money supply. (5 points) b. If the velocity of money remains constant, what is the percent change in nominal money balances? (5 points) a. We know that and after plug in the number we have And the money supply is M = m B m = cr + 1 cr + rr m = = M = m B = = 2720

5 b. We know that M V = P Y where M is the nominal money balances. This implies that M M with velocity be constant, we will have: V V M M = P P = P P Y Y Y Y On the other hand we are told that national output is increasing at 7.5 percent rate, and inflation is 2.5 percent. We know that we will have finally Y Y M M P P istheinflationrate isthepercentageincreaseofnatonaloutput = P P Y Y = = 10percent 4. Consider a small open economy. Let Y denote GDP, C denote Consumption, I denote Investment, r is the real interest rate in percent, NX is net exports, and is the real exchange rate. T denotes Taxes, and G stands for Government Spending. Suppose that these take the following form: Y = C = (Y T ) I = r NX = ɛ T = 2000 G =

6 a.suppose that the world real interest rate is 10%. That is, suppose that r = 10. What are the equilibrium values of investment (I) and national Savings (S)? (6 points) I(r ) = r = = 2000 We know that S = Y C G, so we need to know the value of C. C = ( ) = = 6500 Then S = Y C G = = 2000 b.assuming the values from part a., what will be the equilibrium values of Net Exports (NX) and the real exchange rate (ɛ)? (5 points) We know that NX = S I therefore NX = S I = = 0 So in the equilibrium NX = ɛ = 0 200ɛ = 1400 ɛ = 7 c.suppose that the world real interest rate rises to 12%. That is, assume that r is now 12%. What are the new equilibrium values of Net Exports (NX)and the real exchange rate (ɛ)? (6 6

7 points) We still have that NX = S I But now the value of I will change. In particular, I(r) = (12) = 1800 Therefore NX = S I = = 200 Accordingly, the equilibrium real exchange rate will change since N X = 200 and NX = ɛ = 200 which yields ɛ = 6 5. Consider a small open economy that can lend and borrow freely to foreign countries, but the both factor markets are closed. The only two factors of production in this economy are capital and labor. The production function itself assumed to be a typical Cobb-Douglas function. In this economy prices are fully flexible, factor markets are competitive, and the supply of the factors of production is fixed. Suppose there is only a positive shock of labor supply (that is an increase of L), and. a. Graph the effects of this shock on: the market of capital, the market of labor and the exchange rate. (3 5 points) b. Explain the changes of the equilibrium value of real wage, real rental price of the capital, national savings, investment, real interest rate and real exchange rate. (10 points) a. the market of labor 7

8 W P L 1 L 2 ( W P ) 1 ( W P ) 2 MP LDemand for labor L 8

9 R P the market of capital K ( R P ) 2 ( R P ) 1 MP K 2 MP K 1 Demand for Capital K ɛ S 1 I the impact on exchange rate S 2 I ɛ 1 ɛ 2 NX(ɛ) S 1 I S 2 I Net export b. 9

10 When there is a positive shock on the Labor, K, real wage W P because of Y = F (K, L), and L, Y. We know that the real return rate of capital R P = MP K = αy K Further, we know that private savings S private are equal to. Anything else is fixed, and Y, R P S private = Y C(Y T ) T which implies that S private = Y C(Y T ) T Now, since the marginal propensity to consume is less than one, then for a given increase in Y, consumers will consume a portion of the additional disposable income, and save part of the additional disposable income, which means that C will increase by less than the increase in Y. Since taxes are not changing, that is T = 0, this implies that S private = Y C(Y T ) > 0 That is, there is an increase in private savings. Since public savings are not changing. Then national savings S increase. Further, we see that in equilibrium N E increase as well, since NX = S I, real interest rate is taken the world interest rate as given because of the small open economy. The NX which leads to the decrease of the exchange rate. 10