economics problem set

ECO 301 Problem Set 3 Deadline: Tuesday, December 8, AT THE BEGINNING OF CLASS

[I will collect all works and then discuss the solutions in class, so you may wish to make a copy of your work before submitting]

1. Aneconomyhas the followingCobb-Douglasproduction function: F(K;L) = K1=6 (EL)

5=6. The depreciation rate is 1% and the saving rate is 48%. The econ- omy is in a steady state, where the population decreases at a rate 1%, while real GDP per capita grows at a rate 1.5%. (a) Find the GROWTH RATE of the following variables:

(i) the e¤ective labor force, EL (ii) the ratio of labor to capital, L=K (iii) the labor income, wL (iv) the capital income rK

(b) Use growth accounting to calculate what portion of output growth is due to:

(i) an increase in capital (ii) an increase in labor (iii) an increase in total factor productivity

(c) If total capital K is 64 million THIS year, �nd real GDP NEXT year. (d) By how many percentage points should the government change the saving

rate so that the economy may converge to the Golden rule steady state (use a "+" foran increaseand a"�" fora decrease)? Howwould thecurrentgeneration feel about the change?

2. An economy has two factors of production: capital and labor. The production function is known to exhibit constant returns to scale. The capital stock is about 3 times one year�s real GDP. Approximately 10% of GDP is used to replace depreciating capital. Labor income is 70% of real GDP. Real GDP grows at an average rate of 3% 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. Consider a closed economy and use graphical analysis to illustrate how the equilibrium output, price level, and interest rate would be a¤ected in the short run by: (a) a stock market boom (absent any policy response) (b) a substantial increase in credit card usage (absent any policy response) (c) an exogenous increase in the price of oil (absent any policy response)

(i) What can the government do to stabilize output? (ii) What can the Fed do to stabilize the interest rate?

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4. Consider a closed economy where:

C = 150+0:5(Y �T) G = 50; T = 100;

I = 150�10r, where r is measured in percent M=P = Y �10r , where r is measured in percent

M = 1;000; P = 2

(a) Assume that government spending G decreases by 10% and tax revenue T decreases by 4%

(i) Calculate the corresponding horizontal shift in the IS curve. (ii) Calculate the resulting change in the equilibrium income and the

equilibrium interest rate. (iii) How would the price level evolve over time (increase, decrease, or

remain the same)? (b) Assume that government spending and tax revenue are as before: G = 50

and T = 100, but the Fed increases money supply M by 10%. (i) Calculate the vertical shift in the LM curve. (ii) Find the short-run equilibrium income and interest rate. (iii) How would the price evolve over time (increase, decrease, or remain

the same)?

5. Suppose that the government increases the tax revenue T . Use graphical analysis to show how this a¤ects the short-run equilibrium interest rate and income in a closed economy if: (a) the Fed keeps money supply constant (b) the Fed keeps output constant (c) the Fed keeps the price level constant

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