economic

ECO 301 C Problem Set 3 Deadline: Friday, April 24

1. An economy has a Cobb-Douglas production function. Capital income is 1/4 of real GDP. The depreciation rate is 8% and the saving rate is 5%. (a) Assume there is neither population growth nor technological progress.

(i) Find the steady-state capital per worker, output per worker, and consumption per worker.

(ii) Would output Y grow at the state state. If yes, at what rate? What about capital K? (b) Assume that the population grows at a rate 0.7% and there is no tech-

nological progress. (i) Find the steady-state capital per worker, output per worker, and

consumption per worker. (ii) Would total output Y grow at the state state. If yes, at what rate?

What about capital K? (c) Assume that rate of population growth is 0.7% and the rate of labor-

augmenting technological progress is 2%. (i) Find the steady-state capitalper e¤ective worker, outputper e¤ective

worker, and consumption per e¤ective worker. (ii) Would output per worker Y=L grow at the state state. If yes, at

what rate? What about capital per worker K=L? (iii) Would output Y grow at the state state. If yes, at what rate? What

about capital K? (iv) Would real rental rate r grow at the steady state? If yes, at what

rate? What about the real wage w? (v) Assume the economy is at the steady state. Use growth accounting

to calculate what portion of output growth is due to: (v-i) an increase in capital (v-ii) an increase in labor (v-iii) an increase in total factor productivity

(vi) Assume the economy is at the steady state. You are a policy maker and your goal is to maximize steady-state consumption per e¤ective worker. By how much should you change the saving rate in the economy (use a "+" for an increase and a "�" for a decrease)? Give an example of a policy that could achieve such a change. Now, assume that your policy is implemented and the saving rate reaches its target level immediately. Sketch the (approximate) transitional dynamics of output per e¤ective worker, consumption per e¤ective worker, and investment per e¤ective worker (in other words, sketch how they evolve in time). Make sure that you indicate on your graph the moment at which your policy is implemented. Would your policy be well accepted by the current generation? Explain.

2. An economy has two factors of production: capital and labor. The production function is known to exhibit constant returns to scale. The capital

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stock is about 2 times one year�s real GDP. Approximately 5% of GDP is used to replace depreciating capital. Labor income is 80% of real GDP. Real GDP grows at an average rate of 1.5% per year. Assume the economy is at a steady state. Is the capital per e¤ective worker lower or larger than it would have been at the Golden Rule steady state? [To receive points on this question, you need to show me your calculations]

3. Use graphical analysis to show how an exogenous decrease in the price of oil would a¤ect prices and output in the short run and in the long run if: (a) the Fed keeps money supply constant (b) the Fed keeps output constant (c) the Fed keeps the price level constant

4. Consider a version of the Keynesian cross model where planned expendi- tures are given by:

PE = C + c� (Y �T)+ I +G; T = 20 c = 0:8 I = 80 G = 20;

where C is autonomous consumption and c is the marginal propensity to consume. (a) �nd the equilibrium level of income if

(i) C = 5 (ii) C = 10

(b) Illustrate the shift in planned expenditure due to a decrease in govern- ment spending by 5. Calculate the respective change in income. (c) Illustrate the shift in planned expenditure due to an increase in taxes by

5. Calculate the respective change in income.

5. Consider a closed economy and use graphical analysis to illustrate how output, interest rates, and prices would be a¤ected in the short and long run by: (a) a stock market boom (b) widespread credit card frauds

6. Consider a closed economy where:

C = 250+0:8(Y �T) I = 150�20r G = 80 T = 100

(M=P)d = Y �200r M = 1500;

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where r is measured in percent. (a) Derive the equation of the aggregate demand curve and graph it. Calcu-

late the horizontal shift (indicate whether it is an increase by "+" or decrease by "�") in the aggregate demand curve resulting from:

(i) a decrease in government spending by 5. (ii) a decrease in money supply by 100.

(b) Assume that P = 1:5. (i) Derive the equations of the IS and LM curves and graph them. (ii) Which curve shifts, in what direction, and by how much (calcu-

late the horizontal shift) if government spending decreases by 5. Calculate the resulting equilibrium values of Y and r.

(iii) Which curve shifts, in what direction, and by how much (calculate the horizontal shift) if the money supply decreases by 10. Calculate the resulting equilibrium values of Y and r.

(iv) Which curve shifts, in what direction, and by how much (calculate the horizontal shift) if the price level decreases by 0.5. Calculate the resulting equilibrium values of Y and r.

7. [Chapter 13] Consider a small open economy that uses peso as a national currency and allows it to �oat against foreign currencies. Suppose that the price level includes the peso prices of domestic goods and the peso equivalent of the dollar prices of imported goods. (a) Use graphical analysis to illustrate the e¤ects of a �scal contraction on

the exchange rate and aggregate income (b) Use graphical analysis to illustrate the e¤ects of a decrease in the coun-

try�s risk premium on the exchange rate and aggregate income

8.[Chapter 13] Analyze the e¤ect of the following events on the exchange rate and aggregate income in a small open economy under both �oating and �xed exchange rate regimes: (a) widespread credit card frauds. (b) a shift in tastes that favors foreign-produced goods.

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