Econ 303: Intermediate Macroeconomics II

Instructions:

▪Show all steps you would take to reach your answer, i.e., do not skip any logical steps to get full credits.

▪You should begin with the correct formula, if necessary.

▪You can discuss questions in the assignment with your classmates but write your own answers. ▪Also, you can ask questions to the professor to ensure that your approaches and answers are     correct.

▪You should submit homework #1 by 11:59 PM on July 28 (Thursday).

▪Late homework will never be accepted unless you obtain permission from a professor!

1. (60 pts) In the United States, the capital share of GDP is about 30 percent, the average growth in output is about 3 percent per year, the depreciation rate is about 4 percent per year, and the     capital-output ratio is about 2.5. Suppose that the production function is Cobb-Douglas, Y = A . F(K, N) = AKa N 1−a, so that the capital share in output is constant, and that the United States   has been in s steady state.

a) What must the saving rate be in the initial steady state?

b) What is the marginal product of capital in the initial steady state?

c) Suppose that public policy raises the saving rate so that the economy reaches the Golden Rule level of capital. What will the marginal product of capital be at the Golden Rule steady state?     Compare the marginal product at the Golden Rule steady state to the marginal product in the      initial steady state. Explain.

d) What will the capital-output ratio be at the Golden Rule steady state?

e) What must the saving rate be to reach the Golden Rule steady state?

2. (20 pts) In the economy of Solovia, the owners of capital get two-third of national income, and the workers receive one-third.

a) The men of Solovia stay at home performing household chores, while the women work in    factories. If some of the men started working outside the home so that the labor force increased by 5 percent, what would happen to the measured output of the economy? Does labor               productivity – defined as output per worker – increase, decrease, or stay the same? Does total   factor productivity increase, decrease, or stay the same?

b) In year 1, the capital stock was 6, the labor input was 3, and output was 12. In year 2, the capital stock was 7, the labor input was 4, and output was 14. What happened to total factor productivity between the two years?

3. (20 pts) Suppose an economy described by the Solow model is in a steady state with              population growth gN of 1.8 percent per year and technological progress gA  of 1.8 percent per   year. Total output and total capital grow at 3.6 percent per year. Suppose further that the capital share of output is 1/3. If you used the growth-accounting equation to divide output growth into three sources – capital, labor, and total factor productivity – how much would you attribute to   each source? Compare your results to the following figures for the United States.