Intermediate Macroeconomics-ECO 3203

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1 Intermediate Macroeconomics-ECO 3203 Homework 1, Summer 2018 July 3, 2018 Instructions: The full points of this homework exercise is 100. 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. Due Date: Thursday, June 29th, at the beginning of the class. 1. a. here we need to use a fixed basket of goods from year 1 to calculate CI: the price index for year1 = 100galas $ fujis $1.1 = $220 the price index for year2 = 100galas $ fujis $1.2 = $270 The CI for the year 1 (base year) is 100, the inflation for year 1 is 0. the C I for year 2 = the price index for year2 = = 123 the price index for year1 220 the inflation rate = the C I for year2 the C I for year1 = = 0.23 or 23% b. the norminal spending for year 1 = 100galas $ fujis $1.1 = $220 the norminal spending for year 2 = 200grannysmiths $0.9 = $180 with year 1 as base year, use the year 1 prices for all the years the real spending for year 1 = 100galas $ fujis $1.1 = $220 the real spending for year 2 = 200grannysmiths $1.2 = $240 c. GD deflator for year 1 = the inflation rate for year 1 = 0 the norminal spending for year = = 100 the real spending for year

2 GD deflator for year 2 = the norminal spending for year = = 75 the real spending for year the inflation for year 2 = GD deflator for year 2 GD deflator for year 1 = 0.25 or 25% 2. Consider a closed economy. 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 capital supply. a. Graph the effects of this shock on: the market of capital, the market of labor and the market of loanable funds. (35 points) b. Explain the changes of the equilibrium value of real wage, real loanable funds price, savings, investment and real interest rate. (52 points) a. the market of capital R K 1 K 2 ( R ) 1 ( R ) 2 M KDemand for capital K 2

3 W the market of labor L ( W ) 2 ( W ) 1 M L 2 M L 1 Demand for Labor L r S 1 the market of loanable funds S 2 r 1 r 2 I(r) S 1 = I 1 S 2 = I 2 S,I b. When there is a positive shock on the capital, K, real return rate of the capital R. 3

4 Anything else is fixed, because of = F (K, L), and K,. We know that the real wage W = M L = α and, W L Further, we know that private savings S private are equal to S private = C( T ) T which implies that S private = C( T ) T Now, since the marginal propensity to consume is less than one, then for a given increase in, 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. Since taxes are not changing, that is T = 0, this implies that S private = C( 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 I increase as well, since S = I, real interest rate. 3. Consider a close economy supply and demand model. denote GD, 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 = AK 1 2 L 1 2 with K denotes capital and L denotes labor input. Assume now K = 900, L = 900 and A = 10. The variables in the model taking these forms: C = ( T ) I = r T = 500 G = 500 a. Calculate the national income. How much of the GD goes into paying labor and capital input? (6 points) 4

5 b. What are the real wage rate and real rental rate of the capital? (6 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 rises to 1,000, what are the new equilibrium values of C, I, and r? (6 points) f. What are the new equilibrium values of private saving, public saving, and national saving? (6 points a. = AK 1 2 L 1 2 = = = 9000 Because the Cobb-douglas function is constant return to scale, M L L = 1 2 M K K = 1 2 b. c. 1 W = M L = 2 L 1 R = M K = 2 K = = 900 = 5 = 5 C = ( T ) = ( ) = 6550 I = S = C G = = 1950 I = r 1950 = r we will get d. r = 0.5 S private = T C = = 1950 S public = T G = = 0 S national = S private + S public = = 1950 e. if G to1000, would be unchanged, T unchanged, so C = C( T ) is unchanged: C = ( T ) =

6 the only change here is G, so only public saving changed: S public = T G = = 500 the private saving still unchanged: S private = T C = 1950 in the equilibrium I = S national = S private + S public = = We plug in I = r 1450 = r r = 5.5 f. as we know from part e, S private = T C = 1950 S public = T G = = 500 I = S national = S private + S public = = The monetary base of Econland is $1250 million. The current-deposit ratio (cr) is 0.25 and reserve-deposit ratio (rr) is Calculate the money multiplier and money supply. (10 points) We know that M = m B and after plug in the number we have m = cr + 1 cr + rr m = = And the money supply is M = m B = =

7 5. In an economy, the nominal GD growth rate is 3.5 percent and inflation is 3.8 percent. If the velocity of money remains constant, what is the percent change in real money balances? (10 points) We know that where M M V = M V = are the real money balances. This implies that M M with velocity be constant, we will have: V V = M M = On the other hand we are told that nominal GD is increasing at 3.5 percent rate, and inflation is 3.8 percent. We know that norminalgd = which means that norminalgd norminalgd = 3.5% = 3.8% + + then is decreasing at 0.3 percent, and from the above discussion it implies that real money balances are also decreasing at a rate of 0.3 percent. 7