Homework 1. Please submit a hard copy (neatly handwritten) in person. Name and ID# required. Don't forget to put TA's name as well. No late assignments accepted. See syllabus for the due date. Show works!! Without proper works, no credit will be given.
1. Determine whether each of these production functions has constant, decreasing, or increasing returns to scale. Show your work!!
a. F (K, L) = K1/3L2/3
b. F (K, L) = K2L2
c. F (K. L) = K1/2 + L1/2
2. Assume that the production function is given by Y=AK0.5L0.5, where Y is GDP, K is capital stock, and L is labor. The parameter A is equal to 10. Assume also that capital is 100, labor is 400, and both capital and labor are paid their marginal products. Show works!!
a. What is Y?
b. What is the real wage of labor?
c. What is the real rental price of capital (the amount of output paid per unit of capital)?
3. a. Suppose a government moves to reduce a budget deficit. Using the long-run model of the economy developed in Chapter 3, graphically illustrate the impact of reducing a government's budget deficit by reducing government purchases. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction curves shift; and v. the terminal equilibrium values.
b. State in words what happens to: i. the real interest rate; ii. national saving; iii. investment; iv. consumption; and v. output.
4. Consider two competitive economies that have the same quantities of labor (L=400) and capital (K=400), and the same technology (A=100). The economies of the countries are described by the following Cobb-Douglas production functions:
North Economy: Y=AL.3K.7
South Economy: Y=AL.7K.3
a. Which economy has the larger total production? Explain.
b. In which economy is the marginal product of labor larger? Explain.
c. In which economy is the real wage larger? Explain.
d. In which economy is labor's share of income larger? Explain.
5. Suppose that two countries are exactly alike in every respect except that the citizens of country A have a higher saving rate than the citizens of country B.
a. Which country will have the higher level of output per worker in the steady state? Illustrate graphically.
b. Which country will have the faster rate of growth of output per worker in the steady state?