978-0132992282 Chapter 3 Solution Manual

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 Additional Issues for Classroom Discussion

1. Is the Unemployment Rate a Good Measure of Economic Distress?

Macroeconomists often treat the unemployment rate as the key indicator of the business cycle. But terms

2. What Else Is Important for Production?

To ensure that your students haven’t forgotten what they learned in their principles course, you may want

3. As Your Wage Rises, Do You Supply More Labor? Or Less?

The textbook discusses the offsetting income and substitution effects on labor supply of an increase in the

wage rate in the Appendix to Chapter 4. Since this chapter uses the basic ideas that an increase in wealth

reduces labor supply while an increase in the reward to working increases labor supply, you can combine

4. Why Do Oil Price Shocks Hurt the Economy So Much?

The textbook points out that our last four recessions were all associated with increases in oil prices. The

1. A production function shows how much output can be produced with a given amount of capital and

labor. The production function can shift due to supply shocks, which affect overall productivity.

2. The upward slope of the production function means that any additional inputs of capital or labor

produce more output. The fact that the slope declines as we move from left to right illustrates the idea

3. The marginal product of capital (MPK) is the output produced per unit of additional capital. The

MPK can be shown graphically using the production function. For a fixed level of labor, plot the

output provided by different levels of capital; this is the production function. The MPK is just the

slope of the production function.

4. The marginal revenue product of labor represents the benefit to a firm of hiring an additional worker,

while the nominal wage is the cost. Comparing the benefit to the cost, the firm will hire additional

workers as long as the marginal revenue product of labor exceeds the nominal wage, since doing so

increases profits. Profits will be at their highest when the marginal revenue product of labor just

5. The MPN curve shows the marginal product of labor at each level of employment. It is related to the

production function because the marginal product of labor is equal to the slope of the production

6. A temporary increase in the real wage increases the amount of labor supplied because the substitution

effect is larger than the income effect. The substitution effect arises because a higher real wage raises

the benefit of additional work for a worker. The income effect is small because the increase in the real

wage is temporary, so it doesn’t change the worker’s income very much, thus the worker won’t reduce

7. The aggregate labor supply curve relates labor supply and the real wage. The principal factors shifting

the aggregate labor supply curve are wealth, the expected future real wage, the country’s working-age

8. Full-employment output is the level of output that firms supply when wages and prices in the economy

have fully adjusted; in the classical model of the labor market, this occurs when the labor market is in

9. The classical model of the labor market assumes that any worker who wants to work at the

equilibrium real wage can find a job, so it is not very useful for studying unemployment.

10. The labor force consists of all employed and unemployed workers. The unemployment rate is the

fraction of the labor force that is unemployed. The participation rate is the fraction of the adult

11.An unemployment spell is a period of time that a person is continuously unemployed. Duration is

the length of time of an unemployment spell. Two seemingly contradictory facts are that most

unemployment spells have a short duration and that most people who are unemployed at a particular

time are experiencing spells with long durations. These can be reconciled by realizing that there may

be a lot of people with short spells and a few people with long spells. On any given date, a survey

12. Frictional unemployment arises as workers and firms search to find matches. A certain amount of

frictional unemployment is necessary, because it is not always possible to find the right match right

13. Structural unemployment occurs when people suffer long spells of unemployment or are chronically

unemployed (with many spells of unemployment). Structural unemployment arises when the number

14. The natural rate of unemployment is the rate of unemployment that prevails when output and

employment are at their full-employment levels. The natural rate of unemployment is equal to the

15. Okun’s Law is a rule of thumb that tells how much output falls when the unemployment rate rises. It

1. (a) To find the growth of total factor productivity, you must first calculate the value of A in the

production function. This is given by A  Y/(K.3N.7). The growth rate of A can then be

1960 13.392 —

1970 15.791 17.9%

1980 16.447 4.2%

1990 18.298 11.3%

2000 21.237 16.1%

2010 23.169 9.1%

(b) Calculate the marginal product of labor by seeing what happens to output when you add 1.0 to N;

Y1Y2MPN

1960 2829 2859 30

1970 4266 4304 38

1980 5834 5875 41

1990 8027 8074 47

2000 11,216 11,273 57

2007 13,063 13,129 66

2. (a) The MPK is 0.2, because for each additional unit of capital, output increases by 0.2 units. The

slope of the production function line is 0.2. There is no diminishing marginal productivity of

capital in this case, because the MPK is the same regardless of the level of K. This can be seen

in Figure 3.8 because the production function is a straight line.

3. (a)

N Y MPN MRPN (P 5) MRPN (P 10)

1 8 8 40 80

2 15 7 35 70

3 21 6 30 60

4 26 5 25 50

5 30 4 20 40

6 33 3 15 30

(b) P  $5.

(1) W  $38. Hire one worker, since MRPN ($40) is greater than W ($38) at N  1. Do not hire

two workers, since MRPN ($35) is less than W ($38) at N  2.

(2) W  $27. Hire three workers, since MRPN ($30) is greater than W ($27) at N  3. Do not hire

8 widgets in part a when the firm hired only one worker. So the increase in the price of the

product increases the firm’s labor demand and output.

(e) If output doubles, MPN doubles, so MRPN doubles. The MRPN is the same as it was in part d

when the price doubled. So labor demand is the same as it was in part d. But the output produced

4. MPN  A(100  N)

(a) A  1. MPN  100  N.

(1) W  $10. w  W/P  $10/$2  5. Setting w  MPN, 5  100  N, so N  95.

(2) W  $20. w  W/P  $20/$2  10. Setting w  MPN, 10  100  N, so N  90.

97.5.

(2) W  $20. w  W/P  $20/$2  10. Setting w  MPN, 10  2(100  N), so 2N  190, so N  95.

5. (a) If the lump-sum tax is increased, there’s an income effect on labor supply, not a substitution

effect (since the real wage isn’t changed). An increase in the lump-sum tax reduces a worker’s

wealth, so labor supply increases.

(b) If T  35, then NS  22  12w  (2  35)  92  12 w. Labor demand is given by

6. Since w  4.5 K0.5 N0.5, N0.5  4.5 K0.5/w, so N  20.25 K/w2. When K  25, N  506.25/w2.

(a) If t  0.0, then NS  100w2. Setting labor demand equal to labor supply gives 506.25/w2 

100w2, so w4  5.0625, or w  1.5. Then NS  100 (1.5)2  225. [Check: N  506.25/1.52  225.]

Y  45N0.5  45(225)0.5  675. The total after-tax wage income of workers is (1  t) w NS  1.5 

225  337.5.

(b) If t  0.6, then NS  100 [(1  0.6) w]2  16w2. The marginal product of labor is MPN 

22.5/N0.5, so N  100 [(1  0.6)  22.5/N0.5]2, so N2  8100, so N  90. Then Y  45N0.5 

45(90)0.5  426.91. Then w  22.5/900.5  2.37. The total after-tax wage income of workers is (1

 t) w NS  0.4  2.37  90  85.38. Note that there’s a big decline in output and income,

22  400. Unemployment is 273.4. Income of workers is wN  2  126.6  253.2, which is lower

than without a minimum wage, because employment has declined so much.

7. (a) At any date, 25 people are unemployed: 5 who have lost their jobs at the start of the month and

20 who have lost their jobs either on January 1 or July 1. The unemployment rate is 25/500  5%.

(b) Each month, 5 people have one-month spells. Every six months, 20 people have six-month spells.

8. Number who become unemployed:

From not in the labor force: 3% of 88.3 million  2.649 million

From employed: 2% of 142.2 million  2.844 million

Total  5.493 million

Number who become employed:

Figure 3.13 Figure 3.14

(b) In the initial situation, capital K1 and labor N1 produce output Y1; when productivity rises they

produce output 1.1 Y1. Suppose that a small increase in capital to K2 with labor left at N1 produces

output Y2 in the initial situation. Then it produces 1.1 Y2 when productivity rises by 10%. The

2. (a) An increase in the number of immigrants increases the labor force, increasing employment and

increasing full-employment output.

(b) If energy supplies become depleted, this is likely to reduce productivity, because energy is a

factor of production. So the reduction in energy supplies reduces full-employment output.

3. (a) As shown in Figure 3.17, when the real wage (w) is above its market-clearing level, labor

supply (NS) exceeds labor demand (ND). The difference is the amount of unemployment (U).

4. (a) The increased value of Helena’s home increases her wealth. The rise in wealth leads to an income

effect that leads Helena to reduce her labor supply.

(b) The permanent rise in Helena’s real wage gives rise to offsetting income and substitution effects.

The income effect of the higher wage reduces Helena’s labor supply, but the substitution effect

5. The tax reduces the marginal product of labor by 6%, since that portion of output goes to the

government rather than to the firm. Thus labor demand is reduced. With labor supply unchanged, the

6. Yes, it is possible for the unemployment rate and the employment ratio to rise during the same month.

For example, suppose the population falls, the labor force is constant, the number of unemployed

rises, and the number of employed falls (but by less than the decline in population). Then the

unemployment rate rises, since there are more unemployed but the same labor force, but

7. (a) Since Sally earns $150,000 per year, she is far above the cap, so the Social Security tax doesn’t

affect her after-tax wage (so there’s no substitution effect)—the higher tax only affects her

income—and thus has only an income effect. Since both proposals reduce Sally’s income by the

same amount, she’ll increase her labor supply by the same amount under both proposals.

(b) Under proposal A, Fred’s labor supply doesn’t change because his tax rate stays the same and he