Question 1 of 3

In the nation of Wiknam, the capital share of GDP is 40 percent, the average growth in output is 4 percent per year, the depreciation rate is 6 percent per year, and the capital–output ratio is 5. Suppose that the production function is Cobb–Douglas and that Wiknam has been in a steady state. (For a discussion of the Cobb–Douglas production function, see Chapter 3.)

a. What must the saving rate be in the initial steady state? [Hint: Use the steady state relationship, sy = (δ + n + g)k.]

Saving Rate = s = %

In the nation of Wiknam, the capital share of GDP is 40 percent, the average growth in output is 4 percent per year, the depreciation rate is 6 percent per year, and the capital–output ratio is 5. Suppose that the production function is Cobb–Douglas and that Wiknam has been in a steady state. (For a discussion of the Cobb–Douglas production function, see Chapter 3.)

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

MPK*initial =

In the nation of Wiknam, the capital share of GDP is 40 percent, the average growth in output is 4 percent per year, the depreciation rate is 6 percent per year, and the capital–output ratio is 5. Suppose that the production function is Cobb–Douglas and that Wiknam has been in a steady state. (For a discussion of the Cobb–Douglas production function, see Chapter 3.)

c. Suppose that public policy alters 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?

MPK*_gold =

d. What will the capital–output ratio be at the Golden Rule steady state? (Hint: For the Cobb–Douglas production function, the capital–output ratio is related to the marginal product of capital.)

[K/Y]*_gold =

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

Saving Rate at Golden Rule = s_gold = %