Economics Chapter 3 This chapter develops one of the basic building

Chapter 3

Aggregate Production and Productivity

◼ Chapter Outline, Overview, and Teaching Tips

Chapter Outline

Determinants of Aggregate Production

Factors of Production

Application: Why Are Some Countries Rich and Others Poor?

Cobb-Douglas Production Function Characteristics

Changes in the Production Function: Supply Shocks

Determination of Factor Prices

Demand for Capital and Labor

Distribution of National Income

Application: Explaining Real Wage Growth

Chapter Overview and Teaching Tips

This chapter develops one of the basic building blocks for all the macroeconomic analysis throughout this

book, the aggregate production function. Not only is the aggregate production function used in the study of

economic growth, where it plays a central role, it also is a key element of business cycle analysis because

it determines the level of potential output given the factor inputs.

24 Mishkin • Macroeconomics: Policy and Practice, Second Edition

This chapter has several applications to both stimulate students’ interest and to convince them that the

analysis helps explain the real world. The first application, “Why Are Some Countries Rich and Others

Poor?” shows how the aggregate production function can help us to understand the sources of huge

income differences between countries. Why some countries are so poor and some so rich is an inherently

◼ Answers to End of Chapter Review Questions and Problems

Answers to Review Questions

Determinants of Aggregate Production

1. The aggregate production function represents the relationship between the quantities of inputs that go

into the production process and the output that is produced with those inputs. In the production

2. Total factor productivity measures the productivity of all inputs. It is the average output produced by

one unit of capital together with one unit of labor. Labor productivity measures the average output

3. The Cobb-Douglas production function is Y = AK0.3L0.7, where Y = output, A = total factor productivity,

4. The Cobb-Douglas production function exhibits constant returns to scale and diminishing marginal

products for each input. Constant returns to scale means that if all inputs increase by an identical

proportion, output rises by that same proportion. For example, if the amounts of capital and labor

5. Supply shocks are events that either increase or decrease the amount of output that can be produced

with given amounts of capital and labor. In other words, they cause output to change even though

Chapter 3 Aggregate Production and Productivity 25

Determination of Factor Prices

6. Factor prices are the prices firms pay for each unit of labor and capital they hire. They pay the wage

rate for each unit of labor they hire and the rental price of capital for each unit of capital they hire.

7. The profit function is



= P  F(K,L) − RK − WL.



denotes economic profits, which are revenues

earned from production minus the costs of production. Revenues are P  F(K,L), where P is the

8. Firms will hire additional units of capital and labor inputs as long as the additional revenue they can

earn by doing so—the marginal product of capital or labor times the average price level—is greater

9. A factor demand curve for capital or labor shows how much of the factor firms will demand at various

real factor prices—the real rental price of capital or the real wage rate of labor—when all other variables

(including amounts of the other factor) are held constant. The negative slopes of the demand curves for

10. Equilibrium occurs in a factor market when the quantity of the factor demanded by firms equals the

quantity of the factor its owners offer for sale. The factor price at which this condition is met is the

equilibrium price of the factor. When there is an excess demand, firms want to hire more of the factor

26 Mishkin • Macroeconomics: Policy and Practice, Second Edition

Distribution of National Income

11. Based on the Cobb-Douglas production function and assuming that labor and capital inputs are hired

in perfectly competitive factor markets, national income is divided between labor and capital with the

Answers to Problems

Determinants of Aggregate Production

1. Replacing K and L by 2K and 2L respectively yields:

2. a.

0.4 1.0

0.4 (1.0 1.0) 0.4 .

dY dAK L

MPL AK L AK

dL dL

−

= = = =

b. According to the answer to part (a), this production function does not exhibit diminishing

3. a. Mexico total factor productivity:

0.3 0.7

1.0

0.065 .

0.18 105

=

45

c. Spain’s per capita income is around four times Mexico’s per capita income. This difference is

explained by the fact that total factor productivity is higher in Spain than in Mexico (twice as

large). Spain has also a higher capital per worker ratio than Mexico:

Chapter 3 Aggregate Production and Productivity 27

4. a. The unusually high crop yield is interpreted as a positive supply shock. This increases output for

any given combination of capital and labor, shifting the production function upward.

Determination of Factor Prices

5. a. This firm is not maximizing its profit because it is hiring too many employees and using less

equipment (capital) than it should. At this current real wage, the marginal product of labor (worker’s

6. a. When L = 80 the marginal product of labor is

0.3

52 14.

80

MPL ==

As one can see from the formula

for the marginal product of labor, MPL decreases as L increases.

28 Mishkin • Macroeconomics: Policy and Practice, Second Edition

Graphically:

b. The new real rental rate of capital is given by:

= → =

0.7

70

10 14.

10

K

Distribution of National Income

8. A Cobb-Douglas production function uses the labor income and capital income shares of total income

9. Your boss is not correct because an important characteristic of a Cobb-Douglass production function

is that both the labor and capital income shares of total income are constant. Therefore, the Cobb-

Douglas production function is a good representation only for countries whose labor and capital

Chapter 3 Aggregate Production and Productivity 29

◼ Answers to Data Analysis Problems

1. a. From 1980 to 2012, nominal wage growth has averaged 4.3 percent, and CPI inflation has

averaged 3.6 percent per year. Thus, inflation has eroded away a substantial part of the

2. a. From 2000:Q1 through 2013:Q1, output per person has grown by 28.4 percent; from January

2000 to March 2013, the labor force participation rate fell from 67.3 percent to 63.3 percent, a

3. a. Generally, labor productivity rises during expansions and declines or does not grow much during

recessions, particularly near the beginning and middle of recessions. Generally, real

compensation per hour rises during expansions and declines or grows slowly during recessions.

b. If output per worker and the MPL are closely linked, then declines in output per worker (MPL)

30 Mishkin • Macroeconomics: Policy and Practice, Second Edition

◼ Data Sources, Related Articles, and Discussion Questions

A. For Information About Application: Why Are Some Countries Rich and

Others Poor?

Data Source

2. World Bank Classification (Atlas method):

http://data.worldbank.org/indicator/NY.GNP.PCAP.CD/countries/latest?display=default. This

Discussion Question

The “total factor productivity” term is usually conceived to be a “black box”: it could represent different

technologies, production processes, or even the efficiency of the financial system. Propose different ways

to fill that “black box”: factors that can increase a country’s income per worker (everything else given).

Answer: Even though there are no simple answers to this question, economists all over the world keep

B. For Information About Application: Explaining Real Wage Growth

Data Source

The Bureau of Labor Statistics: http://data.bls.gov/PDQ/outside.jsp?survey=pr. To reproduce (and expand)

Table 3.2: Select “nonfarm business” for sector, then “real hourly compensation” (real wages) and “Labor

productivity (output per hour)” for measures, and finally “percentage change from same quarter a year

ago” for duration. When done, click “get data.”

Chapter 3 Aggregate Production and Productivity 31

Answer: According to the previous “Application,” increases in total factor productivity will result in increases

in income per capita, thereby increasing the standards of living of the whole society. If real wage growth is

C. For Information About Application: Oil Shocks, Real Wages, and the Stock

Market

Data Sources

Federal Reserve Bank of Saint Louis database:

Discussion Question

Fluctuations in the price of oil impact stock prices; real wages and can potentially create a recession. Can

you think of a way for countries to avoid such dependence on the price of oil?

Answer: There is no easy answer to this question. Many political leaders have pointed out the need for