1. Consider the following Cobb-Douglas Production function: Y = K1/2L1/2 = √KL
a. Compute the value of Y for K = 100 and L = 25
b. Define the term constant returns to scale.
c. Now show that the production function for this problem has constant returns to scale by completing the following table:
|
K
|
L
|
Y=K^(1/2)* L^(1/2)=√KL
|
|
100
|
25
|
|
|
200
|
50
|
|
|
2,500
|
625
|
|
d. Using the original values of K and L (100 and 25), compute the marginal product of labor by calculating how much output would rise if an additional worker were employed. This can be done by substituting L = 26 and K = 100 in the production function and noting the increase in Y.
e. If firms had decided to employ 25 workers (L = 25) what would the equilibrium wage be?
2. Consider an economy described by the following equations:
Y = C + I + G
Y = 5,000
G = 1,000
T = 1,000
C = 250 + 0.75( Y - T)
I = 1,000 - 50r
a. In this economy, compute private saving, public saving, and national saving
b. Find the equilibrium interest rate
c. Now suppose that G rises to 1,250. Compute private saving, public saving, and national saving
d. Find the new equilibrium interest rate
3. Suppose that the money demand function takes the form (M/P)d = L(i,Y) = Y/5i
a. If output grows at rate g, at what rate will the demand for real balances grow (assuming constant nominal interest rates)?
b. What is the velocity of money in this economy?
c. If inflation and nominal interest rates are constant, at what rate, if any, will velocity grow?
d. How will a permanent (once-and-for-all) increase in the level of interest rates affect the level of velocity? How will it affect the subsequent growth rate of velocity?
4. a. What is the inflation tax?
b. In what ways is the inflation tax a tax, and in what ways is it not a tax?
c. Who pays for the inflation tax?