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ECON751309: Problem Set 1

Chapter 8: Economic growth I (Chapter 7 in textbook edition 7)

5. Draw a well-labeled graph that illustrates the steady state of the Solow model with population growth. Use the graph to find what happens to steady-state capital per worker and income per worker in response to each of the following exogenous changes.

a. A change in consumer preferences increases the saving rate.

b. A change in weather patterns increases the depreciation rate.

c. Better birth-control methods reduce the rate of population growth.

d. A one-time, permanent improvement in technology increases the amount of output that can be produced from any given amount of capital and labor.

7. Consider how unemployment would affect the Solow growth model. Suppose output is produced according to the production function

Y = Ka [  1 − u  L]1−a, where K is capital, L is the labor force and u is the natural rate of unemployment. The national saving rare is s, the labor force grows at rate n and the capital depreciates at rate 6.

a. Express output per worker (y = Y/L) as a function of capital per worker (k = K/L) and the natural rate of unemployment (u).

b. Write an equation that describes the steady-state of this economy.Illustrate the steady state graphically.

c. Suppose that some change in government policy reduces the natural rate of unemployment. Using the graph you drew in part (b), describe how this change affect output both immediately and over-time. Is the steady-state effect on

output larger or smaller than the immediate effect? Explain.

Chapter 9: Economic growth II (Chapter 8 in textbook edition 7)

2. Suppose an economy described by the Solow model has the following production function: Y = K1/2(LE)1/2 .

a. For this economy, what is f(k)?

b. Use your answer to part (a) to solve for the steady-state value of y as a function of s, n, g and 6.

c. Two neighboring economies have the above production function, but they have different parameter values. Atlantis has a saving rate of 28 percent and a population growth rate of 1 percent per year. Xanadu has a saving rate of 10   percent and a population growth rate of 4 percent per year. In both countries,

g = 0.02 and 6 = 0.04. Find the steady-state value of y for each country.

3. Two countries, Richland and Poorland, are described by the Solow growth model. They have the same Cobb-Douglas production function,

F(K, L) = AKα L1-α, but with different quantities of capital and labor. Richland saves 32 percent of its income, while Poorland saves 10 percent. Richland has population growth of 1 percent per year, while Poorland has population growth of 3 percent. (The numbers in this question are chosen to be approximately realistic descriptions of rich and poor nations.) Both nations technological progress at a rate of 2 percent per year and depreciation at a rate of 5 percent per year.

a. What is the per-worker production function f(k) ?

b. Solve for the ratio of Richland’s steady-state income per worker to Poorland’s. (Hint: the parameter α will play a role in your answer.)

c. If the Cobb-Douglas parameter α takes the conventional value of about 1/3, how much higher should income per worker be in Richland compared to Poorland?

d. Income per worker in Richland is actually 16 times income per worker in Poorland. Can you explain this fact by changing the value of the parameter α? What must it be? Can you think of any way of justifying such a value for this parameter? How else might you explain the large difference in income between Richland and Poorland?