ECON 115  Labor Economics
Drake University, Spring 2017
William M. Boal


EXAM 1 ANSWER KEY
Version A
I. Multiple choice
(1)a. (2)b. (3)d. (4)b. (5)c. (6)b. (7)b. (8)b. (9)b. (10)a. (11)b.
II. Problems
(1) [Regression analysis: 6 pts]
 ln(W) = 2.95.
 Wage increases by about 15 percent.
 No, not significant, because estimated coefficient of S is less than twice its standard error. Specifically 0.15/0.10 = 1.5 < 2.
(2) [Measuring the labor force: 8 pts]
 252.3 million.
 4.9 percent.
 59.7 percent.
 62.7 percent.
(3) [Budget constraint: 6 pts]
 Endowment point is at L=60 hours and C=$100.
 Kink point is at L=20 hours and C=$500.
 Intercept on consumption axis is at C=$600.
(4) [Optimal choice: 8 pts]
 The reservation wage equals the MRS at the endowment bundle.
MRS = MU_{L}/MU_{C} = (C100)/(L10). Inserting nonlabor income for C and total available time for L gives reservation wage = $4.
 Budget constraint is spending = income, or
C = 300 + (60L) 20 = 1500  20 L.
 Tangency condition is MRS = wage, or (C100)/(L10) = $20. Solve this equation jointly with the budget constraint found in part (b), to get L*= 40 hours, C*= $700.
 h*= total available time  L* = 20 hours.
(5) [Individual labor supply  income and substitution effects: 22 pts]
 50 hours.
 $100.
 $10 per hour.
 $30 per hour.
 income effect: work less.
An increase in the wage is like an increase in nonlabor income in that the budget line is now farther from the origin.
So the income effect is to "purchase" more leisure and more consumption.
 15 hours.
 substitution effect: work more.
An increase in the wage is an increase in the price of leisure compared to the price of consumption.
So the substitution effect is to "purchase" less leisure and more consumption.
 +5 hours.
 total effect: work less.
 10 hours.
 (w,h) = ($10,40 hours), ($30,30 hours). Amanda's labor supply bends backward.
(6) [SR labor demand: 9 pts]
 VMP_{E} = price of output × MP_{E}.
Set VMP_{E} = wage, insert given values, and solve to get E* = 200.
 Using production function, q* = 160 units of output.
 profit = Revenue  Total Cost = $400.
(7) [LR labor demand  scale and substitution effects: 16 pts]
 Slope of any isocost line = w/r, where r = price of capital.
The slope of isocost line #1 is 1.
We are given that r = $10, so w = $10 on isocost line #1.
 Similarly, the slope of isocost line #2 is 4, so w = $40 on isocost line #2.
 substitution effect: use less labor.
 10 units of labor.
 scale effect: use less labor.
 20 units of labor.
 total effect: use less labor.
 30 units of labor.
(8) [HicksMarshall rules: 6 pts]
 Industry X.
 Industry Z.
 Industry S.
III. Critical thinking
 Xavier and Yolanda have the same average income over their lifetimes, so comparing the two, there is no income effect, only a substitution effect. Therefore, when Xavier's wage is less than Yolanda's wage, Xavier will work fewer hours than Yolanda. When Xavier's wage is more than Yolanda's wage, Xavier will work more hours than Yolanda. (Full credit requires a lifecycle graph graph with annual hours of work on the on the vertical axis and age on the horizontal axis. Yolanda's curve should be roughly flat. Xavier's curve should slope upward, intersecting Yolanda's curve in the middle.)
 Children are not an inferior good. The total fertility rate has fallen because the "price" of children has increased relative to other goods. The "price" of children is the cost of raising children. It has increased because of the rising cost of health care and college tuition and many other things, but especially because of the rising opportunity cost of mothers' time as women's wages have risen. (Full credit requires an indifferencecurve graph with children on one axis and other goods on the other axis. The graph should show inward rotation of the budget line from an increase in the price of children. Tangencies before and after the rotation, indicating choices by typical families, should be marked.)
Version B
I. Multiple choice
(1)b. (2)c. (3)a. (4)c. (5)d. (6)a. (7)a. (8)c. (9)a. (10)b. (11)a.
II. Problems
(1) [Regression analysis: 6 pts]
 ln(W) = 2.71.
 Wage increases by about 12 percent.
 Yes, significant, because estimated coefficient of S is more than twice its standard error. Specifically 0.12/0.04 = 3 > 2.
(2) [Measuring the labor force: 8 pts]
 249.7 million.
 5.7 percent.
 59.4 percent.
 63.0 percent.
(3) [Budget constraint: 6 pts]
 Endowment point is at L=60 hours and C=$100.
 Kink point is at L=40 hours and C=$400.
 Intercept on consumption axis is at C=$800.
(4) [Optimal choice: 8 pts]
 The reservation wage equals the MRS at the endowment bundle.
MRS = MU_{L}/MU_{C} = (C200)/(L10). Inserting nonlabor income for C and total available time for L gives reservation wage = $4.
 Budget constraint is spending = income, or
C = 400 + (60L) 10 = 1000  10 L.
 Tangency condition is MRS = wage, or (C200)/(L10) = $10. Solve this equation jointly with the budget constraint found in part (b), to get L*= 45 hours, C*= $550.
 h*= total available time  L* = 15 hours.
(5) [Individual labor supply  income and substitution effects: 22 pts]
 60 hours.
 $100.
 $30 per hour.
 $10 per hour.
 income effect: work more.
A reduction in the wage is like a fall in nonlabor income in that the budget line is now closer to the origin.
So the income effect is to "purchase" less leisure and less consumption.
 +5 hours.
 substitution effect: work less.
A reduction in the wage is a decrease in the price of leisure compared to the price of consumption.
So the substitution effect is to "purchase" more leisure and less consumption.
 10 hours.
 total effect: work less.
 5 hours.
 (w,h) = ($30,40 hours), ($10,35 hours). Becky's labor supply slopes up.
(6) [SR labor demand: 9 pts]
 VMP_{E} = price of output × MP_{E}.
Set VMP_{E} = wage, insert given values, and solve to get E* = 100.
 Using production function, q* = 400 units of output.
 profit = Revenue  Total Cost = $1200.
(7) [LR labor demand  scale and substitution effects: 16 pts]
 Slope of any isocost line = w/r, where r = price of capital.
The slope of isocost line #1 is 4.
We are given that r = $10, so w = $40 on isocost line #1.
 Similarly, the slope of isocost line #2 is 1, so w = $10 on isocost line #2.
 substitution effect: use more labor.
 20 units of labor.
 scale effect: use more labor.
 10 units of labor.
 total effect: use more labor.
 30 units of labor.
(8) [HicksMarshall rules: 6 pts]
 Industry 1.
 Industry 3.
 Industry 5.
III. Critical thinking
Same as Version A.
[end of answer key]