Chapter 1. Chapter 9 – Problem 3

Step 1

Work It Out
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You must read each slide, and complete any questions on the slide, in sequence.

Question

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 = fwIPnBkWdu4=%

Review pages 58-61 in Chapter 3 for a discussion of the Cobb-Douglas production function. Review text pages 242-245 in Chapter 9 and Table 9-1 for a discussion of the steady state in the Solow growth model.
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Step 2

Question

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 = /X23qClMHdmoIRSg

Review pages 58-61 in Chapter 3 for a discussion of the marginal product of capital in the Cobb-Douglas production function. Review text pages 242-245 in Chapter 9 for a discussion of the steady state in the Solow growth model.
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Step 3

Question

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 = g0z/PGhhpYWxdn+f

Question

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 = h4XZagboIgc=

Review text pages 244-245 in Chapter 9 for a discussion of the Golden Rule steady state in the Solow growth model.

Question

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

Saving Rate at Golden Rule = sgold = tBxBgtJuS+A=%

Review text pages 244-245 in Chapter 9 for a discussion of the Golden Rule steady state in the Solow growth model.
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