Chapter 1. Chapter 3 – Problem 2

Question 1

Work It Out

true

true

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

Question

Suppose the production function in an economy is Y = K^0.5L^0.5, where K is the amount of capital and L is the amount of labor. The economy begins with 64 units of capital and 16 units of labor. Use a calculator and equations in the chapter to find a numerical answer to each of the following questions.

How much output does the economy produce? M2l5iUDUXlw=

Review text pages 58-61 for a discussion of the Cobb-Douglas production function.

0:51

Question 2

Question

Suppose the production function in an economy is Y = K^0.5L^0.5, where K is the amount of capital and L is the amount of labor. The economy begins with 64 units of capital and 16 units of labor. Use a calculator and equations in the chapter to find a numerical answer to each of the following questions.

What are the wage and the rental price of capital?

The wage is equal to 0VV1JcqyBrI= unit(s) of output and the rental price of capital is equal to Krc9lGqKlGMakegq unit(s) of output.

Review text pages 51-61 and Case Studies on pages 58 and 62-63 for a discussion of how the wage and rental price of capital are related to the marginal products of labor and capital. Review pages 58-61 for a discussion of how to compute labor and capital shares using a Cobb-Douglas production function.

Question

What share of output does labor receive? fwIPnBkWdu4= %

Review text pages 51-61 and Case Studies on pages 58 and 62-63 for a discussion of how the wage and rental price of capital are related to the marginal products of labor and capital. Review pages 58-61 for a discussion of how to compute labor and capital shares using a Cobb-Douglas production function.

2:38

Question 3

Question

Suppose the production function in an economy is Y = K^0.5L^0.5, where K is the amount of capital and L is the amount of labor. The economy begins with 64 units of capital and 16 units of labor. Use a calculator and equations in the chapter to find a numerical answer to each of the following questions.

If a sudden immigration quadruples the size of the population, while the capital stock is unchanged, what is the new level of output? A3dntz/wRAI= units

Review text pages 51-61 and Case Studies on pages 58 and 62-63 for a discussion of how the wage and rental price of capital are related to the marginal products of labor and capital. Review pages 58-61 for a discussion of how to compute labor and capital shares using a Cobb-Douglas production function.

Question

What is the new wage and rental price of capital?

The new wage is equal to 95WUcul3RuLR/Ap0 unit(s) of output and the new rental price of capital is equal to 95WUcul3RuLR/Ap0 unit(s) of output.

Review text pages 51-61 and Case Studies on pages 58 and 62-63 for a discussion of how the wage and rental price of capital are related to the marginal products of labor and capital. Review pages 58-61 for a discussion of how to compute labor and capital shares using a Cobb-Douglas production function.

Question

What share of output does labor receive now?

Labor continues to receive a share of fwIPnBkWdu4=% of output.

Review text pages 51-61 and Case Studies on pages 58 and 62-63 for a discussion of how the wage and rental price of capital are related to the marginal products of labor and capital. Review pages 58-61 for a discussion of how to compute labor and capital shares using a Cobb-Douglas production function.

Question

National Income = $A3dntz/wRAI=

Review text pages 51-61 and Case Studies on pages 58 and 62-63 for a discussion of how the wage and rental price of capital are related to the marginal products of labor and capital. Review pages 58-61 for a discussion of how to compute labor and capital shares using a Cobb-Douglas production function.

2:12