Homework Assignment #3 ECO 3203, Fall Consider a closed economy with demand for goods as follows:

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1 Homework Assignment #3 ECO 3203, Fall 2017 Due: Friday, December 8 th at the beginning of class 1. Consider a closed economy with demand for goods as follows: C = (Y T) I = 1200 G = 700 T = 1000 a. What is autonomous expenditure for this economy? a. According to the Keynesian Cross model of income determination, what would be the short run equilibrium value of real aggregate income (Y) for this economy? b. All else equal, what is the new short run equilibrium value of income if government purchases (G) increased by 300 (from 700 to 1000)? c. What is the government spending multiplier (i.e - Y G ) for this economy? d. If government purchases are held constant at 700 and income taxes are cut by 300 (from 1000 to 700), what is the new short run equilibrium value of income? e. What is the tax multiplier (i.e - Y T ) for this economy? b. According to the Keynesian Cross model, which is more effective at raising aggregate income in the short run, tax cuts or government spending? Why 2. Consider the following model of a closed economy in which household income taxes are proportional to income: Y = Y d C = (Y T) I = 1200 G = 1000 T = 0.20Y a. What is autonomous expenditure for this economy? Hint: by definition, it will not depend on the value of real aggregate income (Y). b. What is the short run equilibrium value of real aggregate income (Y) for this economy? c. All else equal, what would the new short run equilibrium value of income be, if government purchases were to increase from 1000 to 1500? d. What is the basic expenditure multiplier for this economy? Hint: it is NOT equal to 1/(1-0.60).

2 e. Suppose that the government is required by law to keep its budget balanced, so that government purchases must always equal income tax revenue (G = T = 0.20Y). What is the basic expenditure multiplier in that case? f. Would a balanced budget requirement make a nation s real income more or less sensitive to spending shocks? Explain. 3. According to the Keynesian model of income determination, what determines a nation s real aggregate income? According to the classical model of income determination, what determines a nation s real aggregate income? What accounts for the difference between the two models? 4. Consider a closed economy with the following consumption function: C = (Y T) a. What is the marginal propensity to consume for this economy? b. What is the basic spending multiplier for this economy (i.e. - Y E 0 )? c. Assuming that investment (I) and taxes (T) are unaffected by the change, how would autonomous expenditure be affected (up or down, and by how much) by a 200 unit increase in government purchases? How would the equilibrium value of income be affected? d. Assuming that investment (I) and government purchases (G) are unaffected by the change, how would autonomous expenditure be affected (up or down, and by how much) by a 200 unit increase in taxes (T)? How would the equilibrium value of income be affected? e. What would be your answers to (c) and (d) if the consumption function were, instead C = (Y T)? 5. Consider an economy with the following real money demand function, real aggregate income, nominal money supply, price level, and expected rate of inflation: M d /P = 0.5Y 10,000(r + π e ) Y = 3000 M S = 4000 P = 5 π e = 0.02 a. According to Liquidity Preference Theory, what is the equilibrium real interest rate (r*)? b. All else equal, what will the new equilibrium real interest rate be, if the nominal money supply (M S ) is increased from 4000 to 5000? c. If the central bank wants the equilibrium real interest rate (r*) to be 10%, what value should it pick for the nominal money supply (M S ), assuming that Y, P, and e remain at their initial levels?

3 6. According to Keynes Liquidity Preference Theory, what determines the overall level of interest rates in the short run? Based on that theory, what will happen to interest rates when a nation s real aggregate income increases, all else equal? Explain. 7. Use the IS/LM model to predict how each of the following shocks would likely affect real aggregate income (Y) and the overall level of real interest rates (r) in the short run, all else equal. In each case, be sure to make a prediction for both variables, explain your predictions intuitively, and illustrate them with the relevant diagrams. a. Government purchases decline (G down) b. The nominal money supply increases (M S up) c. Autonomous consumption increases (c0 up) d. Total factor productivity increases (A up) 8. Consider the following IS/LM model of a closed economy: C = (Y T) I = r Y = Y d M d /P = 0.05(Y/(r + π e )) M S /P = M d /P G = 195; T = 400 M s = 4800; P = 2 π e = a. Find the equation that describes the IS curve for this economy. b. Find the equation that describes the LM curve for this economy. c. What are the short run equilibrium values of real aggregate income (Y) and the real interest rate (r) for this economy? d. What happens to the equilibrium value of aggregate income (up or down, and by how much) when autonomous consumption rises from 300 to 400? Hint: it won t increase by (1/(1-0.75))*100. e. Why does your answer in part d differ from the impact predicted by the simple spending multiplier?

4 9. Consider the following AS/AD model of a closed economy: Y s = AK 1/2 L 1/2 Y s = Y d C = (Y T) I = ,000r M d /P = 0.40Y 5000r M S /P = M d /P G = 400; T = 500 K = 100; L = 225 M s = 2000 A = 20 a. Calculate the long run equilibrium values of Y, r, and P for this economy. b. Use the IS/LM diagram to illustrate how an increase in government purchases would affect Y and r in the short run, all else equal. c. What would the new short run equilibrium values of Y and r be for this economy if government purchases increased by 200? Hint: Assume that the price level is at its initial long run equilibrium value (from part a) at the time of the shock. d. Use the IS/LM diagram and the AS/AD diagram to illustrate how an increase in government purchases would affect P and r in the long run, all else equal. e. What would the new long run equilibrium values of P and r be for this economy if government purchases increased by 200? 10. Use the AS/AD model to predict how each of the following shocks would likely affect real aggregate income (Y), the overall level of real interest rates (r), and the price of goods and services (P) in the long run, all else equal. In each case, be sure to make a prediction for each variable, and illustrate your predictions with an IS/LM diagram and a supply/demand diagram for the goods market. a. Autonomous consumption falls. b. The nominal money supply decreases. c. Aggregate income tax collections fall. d. The aggregate supply of capital increases 11. In Solow s model of economic growth, what is break-even investment? According to the model, what determines the amount of investment (per person) a nation needs to breakeven at any given level of capital per worker? Explain.

5 12. Consider the following version of Solow s model of economic growth with no population growth and no technological progress: 1/2 y t = k t c t = (1 s)y t i t = sy t k t+1 = k t + sy t (n + δ)k t s = 0.25 δ = 0.05 n = 0.00 a. If capital per worker (k) is 4.0 at time 0 (k0 = 4.0), what will capital per worker be at times 1, 2, and 3? What will income per person (y) be at times 0, 1, 2, and 3? b. What is the steady-state value of capital per worker (k*) for this economy? c. When capital per worker reaches its steady-state value, what will income per person (y), consumption per person (c), and investment per person (i) be? d. If the savings rate (s) doubles from 0.25 to 0.50, what will the new steady-state value of capital per worker be? e. In the new steady-state, what will y, c, and i be? 13. What are the three processes that change the size of the labor force (L) and/or the economy s supply of capital (K) between each pair consecutive periods in Solow s model of economic growth? Under what conditions do they not change capital per worker (k)? 14. Use the relevant diagram(s) to depict the effect (up, down, or no change) of each of the following shocks on the steady-state values of capital per worker (k*), income per person (y*), and investment per person (i*) in Solow s model of economic growth. a. The saving rate increases (s up) b. The population growth rate increases (n up) c. Total factor productivity increases 15. Consider the following version of Solow s model of economic growth with no technological progress: 2/3 y t = k t c t = (1 s)y t i t = sy t k t+1 = k t + sy t (n + δ)k t

6 s = 0.12 δ = 0.02 n = 0.02 a. If capital per worker (k) is 8 at time 0 (k0 = 8.0), what will capital per worker be at times 1, 2, and 3? What will income per person (y) be at times 0, 1, 2 and 3? What will the growth rate of income per person (% y) be between times 0 and 1, 1 and 2, and 2 and 3? b. Suppose the population size is 1.0 at time zero (L0 = 1). What will aggregate income (Y = y L) be at times 0, 1, 2, and 3? Hint: By definition, Lt+1 = (1+n)Lt. What will the growth rate of aggregate income (% Y) be between times 0 and 1, 1 and 2, and 2 and 3? c. What is the steady state value of capital per worker (k*) for this model? What will income per person (y) be when k reaches its steady state value? d. What will the growth rate of income per person (% y) be when k reaches its steady state value? What will the growth rate of aggregate income (% Y) be when capital per worker reaches its steady state value? Explain. 16. According to Solow s model of economic growth, the growth rate of income per person is entirely determined by the growth rate of capital per worker when there is no technological progress. What determines the growth rate of capital per worker? In what sense does the model predict that nations will need ongoing technological progress to sustain growth of income per person in the long run?