EXAM 1 ANSWER KEY
Version A
I. Multiple choice
(1)a. (2)b. (3)c. (4)a. (5)b. (6)a. (7)b. (8)b. (9)c. (10)c. (11)a.
II. Problems
(1) [Regression analysis: 6 pts]
- ln(W) = 2.97.
- Yes, significant, because estimated coefficient of S is more than twice its standard error. Specifically 0.11/0.04 = 2.75 > 2.
- Wage increases by about 11 percent.
(2) [Measuring the labor force: 8 pts]
- 229.1 million.
- 4.7 percent.
- 63.1 percent.
- 66.2 percent.
(3) [Budget constraint: 6 pts]
- Endowment point is at L=80 hours and C=$100.
- Kink point is at L=40 hours and C=$900.
- Intercept on consumption axis is at C=$2100.
(4) [Optimal choice: 8 pts]
- MRS = (C-10)/(L-20). The reservation wage equals the MRS at the endowment bundle. Inserting nonlabor income for C and total available time for L gives reservation wage = $0.80.
- Budget constraint is spending = income, or
C = 50 + (70-L) 10 = 750 - 10 L.
- Tangency condition is MRS = wage, or (C-10)/(L-20) = $10. Solve this equation jointly with the budget constraint found in part (b), to get L*= 47 hours, C*= $280.
- h*= total available time - L* = 23 hours.
(5) [Individual labor supply - income and substitution effects: 22 pts]
- 60 hours.
- $200.
- $5 per hour.
- $20 per hour.
- income effect: work less.
- -20 hours.
- substitution effect: work more.
- +10 hours.
- total effect: work less.
- -10 hours.
- (w,h) = ($5,40 hours), ($20,30 hours).
(6) [SR labor demand: 9 pts]
- Set VMP_{E} = wage, insert given values, and solve to get E* = 100.
- Using production function, q* = 300 units of output.
- profit = Revenue - Total Cost = $600.
(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 -3/2.
We are given that r = $20, so w = $30 on isocost line #1.
- Similarly, the slope of isocost line #2 is - 1/2, so w = $10 on isocost line #2.
- substitution effect: use more labor.
- 30 units of labor.
- scale effect: use more labor.
- 20 units of labor.
- total effect: use more labor.
- 50 units of labor.
(8) [LR labor demand: 8 pts]
"According to conventional economic analysis, increasing the minimum wage reduces employment in two ways. First, higher wages increase the cost to employers of producing goods and services. The employers pass some of those increased costs on to consumers in the form of higher prices, and those higher prices, in turn, lead the consumers to purchase fewer of the goods and services.
The employers consequently produce fewer goods and services, so they hire fewer workers. That is known as a scale effect, and it reduces employment among both low-wage workers and higher-wage workers.
"Second, a minimum-wage increase raises the cost of low wage workers relative to other inputs that employers use to produce goods and services, such as machines, technology, and more productive higher-wage workers. Some employers respond by reducing their use of low-wage workers and shifting toward those other inputs. That is known as a substitution effect, and it reduces employment among low-wage workers but increases it among higher-wage workers."*
* Congressional Budget Office, The Effects of a Minimum-Wage Increase on Employment and Family Income, February 2014, http://www.cbo.gov/publication/44995, p. 6, accessed February 24, 2014.
III. Critical thinking
- Let the vertical axis denote consumption (C) and the horizontal axis denote leisure time (L). The budget constraint is a horizontal line at a height of C=$200. The endowment point is at C=$200 and L=60 hours.
- The indifference curve is tangent to this line at L=40 hours.
- This indifference curve is U-shaped instead of downward-sloping. To the right of L=40, the indifference curve slopes up. This violates our usual assumption that leisure is always valued, that the marginal utility of leisure is always positive, that more leisure is preferred to less leisure all else equal.
Version B
I. Multiple choice
(1)c. (2)c. (3)d. (4)b. (5)c. (6)c. (7)c. (8)c. (9)d. (10)b. (11)b.
II. Problems
(1) [Regression analysis: 6 pts]
- ln(W) = 2.48.
- Yes, significant, because estimated coefficient of S is more than twice its standard error. Specifically 0.15/0.05 = 3 > 2.
- Wage increases by about 15 percent.
(2) [Measuring the labor force: 8 pts]
- 234.1 million.
- 6.1 percent.
- 62.0 percent.
- 66.1 percent.
(3) [Budget constraint: 6 pts]
- Endowment point is at L=60 hours and C=$200.
- Kink point is at L=40 hours and C=$600.
- Intercept on consumption axis is at C=$1000.
(4) [Optimal choice: 8 pts]
- MRS = (C-10)/(L-20). The reservation wage equals the MRS at the endowment bundle. Inserting nonlabor income for C and total available time for L gives reservation wage = $4.
- Budget constraint is spending = income, or
C = 250 + (80-L) 20 = 1850 - 20 L.
- Tangency condition is MRS = wage, or (C-10)/(L-20) = $20. Solve this equation jointly with the budget constraint found in part (b), to get L*= 56 hours, C*= $730.
- h*= total available time - L* = 24 hours.
(5) [Individual labor supply - income and substitution effects: 22 pts]
- 50 weeks.
- $5000.
- $400 per week.
- $2000 per week.
- income effect: work less.
- -10 weeks.
- substitution effect: work more.
- +20 weeks.
- total effect: work more.
- +10 weeks.
- (w,h) = ($400, 25 weeks), ($2000, 35 weeks).
(6) [SR labor demand: 9 pts]
- Set VMP_{E} = wage, insert given values, and solve to get E* = 100.
- Using production function, q* = 80 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 -1/2.
We are given that r = $20, so w = $10 on isocost line #1.
- Similarly, the slope of isocost line #2 is -2, so w = $40 on isocost line #2.
- substitution effect: use less labor.
- -20 units of labor.
- scale effect: use less labor.
- -40 units of labor.
- total effect: use less labor.
- -60 units of labor.
(8) [LR labor demand: 8 pts] Same as Version A.
III. Critical thinking
Same as Version A.
Version C
I. Multiple choice
(1)a. (2)d. (3)e. (4)d. (5)d. (6)b. (7)d. (8)d. (9)a. (10)d. (11)d.
II. Problems
(1) [Regression analysis: 6 pts]
- ln(W) = 2.42.
- Yes, significant, because estimated coefficient of S is more than twice its standard error. Specifically 0.10/0.03 = 3.333 > 2.
- Wage increases by about 10 percent.
(2) [Measuring the labor force: 8 pts]
- 238.2 million.
- 9.7 percent.
- 58.5 percent.
- 64.7 percent.
(3) [Budget constraint: 6 pts]
- Endowment point is at L=16 hours and C=$0.
- Kink point is at L=14 hours and C=$0.
- Intercept on consumption axis is at C=$140.
(4) [Optimal choice: 8 pts]
- MRS = (C-100)/(L-10). The reservation wage equals the MRS at the endowment bundle. Inserting nonlabor income for C and total available time for L gives reservation wage = $1.
- C = 150 + (60-L) 25 = 1650 - 25 L.
- Tangency condition is MRS = wage, or (C-100)/(L-10) = $10. Solve this equation jointly with the budget constraint found in part (b), to get L*= 36 hours, C*= $750.
- h*= total available time - L* = 24 hours.
(5) [Individual labor supply - income and substitution effects: 22 pts]
- 80 hours.
- $100.
- $30 per hour.
- $10 per hour.
- income effect: work more.
- +15 hours.
- substitution effect: work less.
- -25 hours.
- total effect: work less.
- -10 hours.
- (w,h) = ($30, 50 hours), ($10, 40 hours).
(6) [SR labor demand: 9 pts]
- Set VMP_{E} = wage, insert given values, and solve to get E* = 144.
- Using production function, q* = 216 units of output.
- profit = Revenue - Total Cost = $540.
(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 -2/5.
We are given that r = $20, so w = $8 on isocost line #1.
- Similarly, the slope of isocost line #2 is - 6/5, so w = $24 on isocost line #2.
- substitution effect: use less labor.
- -40 units of labor.
- scale effect: use less labor.
- -30 units of labor.
- total effect: use less labor.
- 70 units of labor.
(8) [LR labor demand: 8 pts] Same as Version A.
III. Critical thinking
Same as Version A.
[end of answer key]