ECON 115 - Labor Economics Drake University, Spring 2018 William M. Boal

### Version A

I. Multiple choice

(1)d. (2)a. (3)a. (4)b. (5)c. (6)e. (7)c. (8)b. (9)b. (10)c.

II. Problems

(1) [Payroll tax or subsidy: 14 pts]

1. 50 million.
2. \$15.
3. \$11.
4. \$55 million.
5. \$165 million.
6. \$200 million.
7. \$20 million.

(2) [Monopsony: 18 pts]

1. Set supply equation w=VMP and solve to get E=600.
2. MLC = -20 + 2 E/10.
3. Set VMP=MLC and solve to get E=360.
4. Substitute E=360 into labor supply equation to get w=\$16.
5. The minimum wage (\$15) is less than the monopsonist employer's profit-maximizing wage. So the minimum wage is not binding. The monopsonist employer will choose E=360, as before.

(3) [Gains from migration: 12 pts]

1. WN = \$20 thousand, WS = \$30 thousand.
2. Set WN = WS. Then substitute labor demand equations, and solve to get EN = 10 million, ES = 30 million, and WN = WS = \$25 thousand.
3. Increase in efficiency = increase in value of output in South less decrease in value of output in North = [(30+25)/2 thousand × (30-20) million] - [(20+25)/2 thousand × (20-10) million] = \$50 billion.

(4) [VSL, safety regulation: 12 pts]

1. VSL = Δ earnings / Δ risk = 65 / (1/100,000) = \$6.5 million.
2. Cost per statistical life saved = cost / reduction in death rate = \$900,000 / 0.1 = \$9.0 million.
3. No, the system should not be required becasuse VSL < cost per statistical life saved.

(5) [Simple model of schooling decision: 10 pts]

1. NPV "no college" = 150 + 324/1.05 = \$459 thousand.
2. NPV "college" = -50 + 540/1.05 = \$464 thousand.
3. Chooses "college" because NPV is larger.
4. Set 150 + 324/(1+r) = -50 + 540/(1+r) and solve to get r*=8 percent.
5. Chooses "no college" because the benefits from "college" lie entirely in the future. As r increases, then NPV of "college" falls more than NPV of "no college."

(6) [Who pays for OJT: 16 pts]

1. If training is general, the worker's productivity rises at all employers. Since worker's VMP rises to \$30,000 in the second year as a result of training, many other employers are willing to pay the worker a wage of \$30,000, so this employer must also pay the worker a wage = \$30,000 in the second year. Since the worker enjoys the returns from training, the worker must pay the cost, \$4000. So the wage is reduced by the cost of training to \$21,000 in the first year. Effectively, the worker pays for training and enjoys the entire return.
2. If training is specific to a particular employer, the value of the investment will disappear if the worker leaves the firm in the second year. To give the worker an incentive to stay and the employer an incentive not to fire the worker in the second year, both parties must share the returns from training. If they share the returns, competition in the labor market forces the parties also to share the costs of training. Suppose worker pays X in training cost and employer pays remainder, \$4000-X. So the worker's wage in first year = \$25,000 - X, where 0<X<\$4000. This implies that wage in first year lies between \$21,000 and \$25,000. If the competitive wage is \$25,000, then the average of the first and second year wages must be \$25,000. Therefore, the wage in the second year will be \$25,000 + X. This implies that the wage in the second year lies between \$25,000 and \$29,000. Effectively, training is a shared investment, with both sides paying part of the cost and enjoying part of the return.

(7) [Education in the labor market: 4 pts] Difference-in-differences may be computed two ways.

• Δ men's enrollment - Δ women's enrollment = (47-55) - (50-49) = -9 percentage points. Therefore the effect of the military draft was to increase male college enrollment by 9 percentage points.
• Δ 1970 enrollments - Δ 1976 enrollments = (49-55) - (50-47) = -9 percentage points. Again, the effect of the military draft was to increase male college enrollment by 9 percentage points.

III. Critical thinking

(1) Benefits

1. The theory of compensating differentials predicts a negative relationship between wages and job characteristics that workers like (such as health insurance) when comparing equally productive workers. In reality, some workers are more productive than others. More productive workers lie on a higher hedonic equilibrium curve than less productive workers. More productive workers thus typically enjoy higher wages and more benefits like health insurance, but this does not contradict the theory of compensating differentials.
2. Graph axes should be labelled "wage" and "health insurance." There should be two downward-sloping hedonic equilibrium curves that do not cross. The higher curve should be labeled "more productive workers" and the lower curve should be labeled "less productive workers."

(2) Regression equation

1. The person's wage is about 11.8 percent higher. (Not \$0.118 higher or 0.118 percent higher.)
2. "Ability bias" is the tendancy for more able people to get more education. Because of their higher ability, however, these people would enjoy higher wages in the labor market even if they did not have more education.
3. If ability bias is present in our data, then the true return to schooling is less than 11.8 percent, because the estimated coefficient of S (schooling) is capturing both the effects of increased schooling and higher ability.

### Version B

I. Multiple choice

(1)b. (2)e. (3)c. (4)d. (5)a. (6)c. (7)c. (8)e. (9)c. (10)b.

II. Problems

(1) [Payroll tax or subsidy: 14 pts]

1. 110 million.
2. \$13.
3. \$17.
4. \$105 million.
5. \$315 million.
6. \$440 million.
7. \$20 million.

(2) [Monopsony: 18 pts]

1. Set supply equation w=VMP and solve to get E=1200.
2. MLC = -30 + 2 E/20.
3. Set VMP=MLC and solve to get E=720.
4. Substitute E=720 into labor supply equation to get w=\$6.
5. If the minimum wage is lower than the efficient (or competitive) wage, then employment is determined by the supply curve. If the minimum wage is higher than the efficient wage, then employment is determined by the VMP curve. Here the efficient wage can be found by inserting the efficient level of employment (found in part a) into either the supply curve or the VMP curve. Since the minimum wage (\$10) is lower than the efficient wage (\$30), employment is determined by the supply curve. Substitute \$10 into the supply curve and solve to get E=800. Thus the \$10 minimum wage raises employment slightly.

(3) [Gains from migration: 12 pts]

1. WN = \$20 thousand, WS = \$10 thousand.
2. Set WN = WS. Then substitute labor demand equations, and solve to get EN = 30 million, ES = 10 million, and WN = WS = \$15 thousand.
3. Increase in efficiency = increase in value of output in North less decrease in value of output in South = [(20+15)/2 thousand × (30-20) million] - [(15+10)/2 thousand × (20-10) million] = \$50 billion.

(4) [VSL, safety regulation: 12 pts]

1. VSL = Δ earnings / Δ risk = 75 / (1/100,000) = \$7.5 million.
2. Cost per statistical life saved = cost / reduction in death rate = \$800,000 / 0.1 = \$4.0 million.
3. yes, the system should be required becasuse VSL > cost per statistical life saved.

(5) [Simple model of schooling decision: 10 pts]

1. NPV "no college" = 150 + 318/1.10 = \$439 thousand.
2. NPV "college" = -50 + 530/1.10 = \$432 thousand.
3. Chooses "no college" because NPV is larger.
4. Set 150 + 318/(1+r) = -50 + 530/(1+r) and solve to get r*=6 percent.
5. Chooses "college" because the benefits from "college" lie entirely in the future. As r decreases, then NPV of "college" increases more than NPV of "no college."

(6) [Who pays for OJT: 16 pts]

1. If training is general, the worker's productivity rises at all employers. Since worker's VMP rises to \$40,000 in the second year as a result of training, many other employers are willing to pay the worker a wage of \$40,000, so this employer must also pay the worker a wage = \$40,000 in the second year. Since the worker enjoys the returns from training, the worker must pay the cost, \$6000. So the wage is reduced by the cost of training to \$24,000 in the first year. Effectively, the worker pays for training and enjoys the entire return.
2. If training is specific to a particular employer, the value of the investment will disappear if the worker leaves the firm in the second year. To give the worker an incentive to stay and the employer an incentive not to fire the worker in the second year, both parties must share the returns from training. If they share the returns, competition in the labor market forces the parties also to share the costs of training. Suppose worker pays X in training cost and employer pays remainder, \$6000-X. So the worker's wage in first year = \$30,000 - X, where 0<X<\$6000. This implies that wage in first year lies between \$24,000 and \$30,000. If the competitive wage is \$30,000, then the average of the first and second year wages must be \$30,000. Therefore, the wage in the second year will be \$30,000 + X. This implies that the wage in the second year lies between \$30,000 and \$36,000. Effectively, training is a shared investment, with both sides paying part of the cost and enjoying part of the return.

(7) [Education in the labor market: 4 pts] Difference-in-differences may be computed two ways.

• Δ men's enrollment - Δ women's enrollment = (50-60) - (48-47) = -11 percentage points. Therefore the effect of the military draft was to increase male college enrollment by 11 percentage points.
• Δ 1970 enrollments - Δ 1976 enrollments = (47-60) - (48-50) = -11 percentage points. Again, the effect of the military draft was to increase male college enrollment by 11 percentage points.

III. Critical thinking

Same as Version A.