EXAM 1 ANSWER KEY
Version A
I. Multiple choice
(1)b. (2)b. (3)a. (4)c. (5)c. (6)c. (7)a. (8)b. (9)c. (10)a.
(11)b. (12)c. (13)b. (14)b.
II. Problems
(1) [Regression analysis: 6 pts]
- log(W) = 2.70.
- Yes, significant, because estimated coefficient of S is more than twice its standard error.
- Wage increases by 13 percent.
(2) [Measuring the labor force: 8 pts]
- 226.1 million.
- 5.0 percent.
- 62.8 percent.
- 66.1 percent.
(3) [Budget constraint: 6 pts]
- Endowment point is at L=80 and C=$100.
- Kink point is at L=40 and C=$900.
- Intercept on consumption axis is at C=$2100.
(4) [Labor supply: 12 pts]
- $2.
- C = 150 + (75-L) 15 = 1275 - 15 L.
- L*= 49 hours, C*= $540.
- h*= 26 hours.
(5) [SR labor demand: 12 pts]
- E* = 1600.
- q* = 2400.
- profit = $15,000.
(6) [LR labor demand: 12 pts]
- Substitution effect causes company to use less capital and more labor, because the relative price of labor (w/r) has decreased from 0.5 to 0.25.
- Scale effect causes company to use less capital and less labor, because input prices have increased so it will "scale down" output and inputs.
- Total effect causes company to use less capital because substitution and scale effects work in the same direction. Total effect for labor cannot be determined because substitution and scale effects work in opposite directions.
(7) [LR labor demand: 4 pts]
Industry B has more elastic demand for labor because its elasticity of substitution in production is greater (Hicks-Marshall rules).
(8) [Elasticities, minimum wage: 12 pts]
- We are given that the elasticity of demand for workers = -0.8
= (percent chg E) / (percent change w).
Substituting (percent change w) = 10 percent yields
(percent change E) = -8 percent.
Thus 8 percent fewer people would be employed. (100-8)percent x 200 million = 184 million people would now be employed.
- We are given that the elasticity of supply = 0.01
= (percent chg E) / (percent change w).
Substituting (percent change w) = 10 percent yields
(percent change E) = 1 percent.
Thus 1 percent more people would want jobs. (101)percent x 200 million = 202 million people would want jobs. 202-184 = 18 million people would want to work but would be unable to find jobs.
- Unemployment rate = 18/202 = 8.9 percent.
Version B
I. Multiple choice
(1)a. (2)c. (3)a. (4)a. (5)b. (6)b. (7)a. (8)a. (9)b. (10)b.
(11)c. (12)d. (13)a. (14)d.
II. Problems
(1) [Regression analysis: 6 pts]
- log(W) = 2.22.
- Yes, significant, because estimated coefficient of S is more than twice its standard error.
- Wage increases by 10 percent.
(2) [Measuring the labor force: 8 pts]
- 237.8 million.
- 9.5 percent.
- 58.4 percent.
- 64.6 percent.
(3) [Budget constraint: 6 pts]
- Endowment point is at L=60 and C=$100.
- Kink point is at L=40 and C=$500.
- Intercept on consumption axis is at C=$1100.
(4) [Labor supply: 12 pts]
- $3.
- C = 200 + (60-L) 10 = 800 - 10 L.
- L*= 39 hours, C*= $410.
- h*= 21 hours.
(5) [SR labor demand: 12 pts]
- E* = 900.
- q* = 600.
- profit = $1,000.
(6) [LR labor demand: 12 pts]
- Substitution effect causes company to use more capital and less labor, because the relative price of labor (w/r) has increased from 0.5 to 0.8.
- Scale effect causes company to use less capital and less labor, because input prices have increased so it will "scale down" output and inputs.
- Total effect causes company to use less labor because substitution and scale effects work in the same direction. Total effect for capital cannot be determined because substitution and scale effects work in opposite directions.
(7) [LR labor demand: 4 pts]
Industry A has more elastic demand for labor because its elasticity of demand for output is greater (Hicks-Marshall rules).
(8) [Elasticities, minimum wage: 12 pts]
- We are given that the elasticity of demand for workers = -0.6
= (percent chg E) / (percent change w).
Substituting (percent change w) = 10 percent yields
(percent change E) = -6 percent.
Thus 6 percent fewer people would be employed. (100-6)percent x 150 million = 141 million people would now be employed.
- We are given that the elasticity of supply = 0.02
= (percent chg E) / (percent change w).
Substituting (percent change w) = 10 percent yields
(percent change E) = 2 percent.
Thus 2 percent more people would want jobs. (102)percent x 150 million = 153 million people would want jobs. 153-141 = 12 million people would want to work but would be unable to find jobs.
- Unemployment rate = 12/153 = 7.8 percent.
Version C
I. Multiple choice
(1)a. (2)c. (3)b. (4)a. (5)d. (6)a. (7)b. (8)a. (9)b. (10)c.
(11)d. (12)d. (13)a. (14)b.
II. Problems
(1) [Regression analysis: 6 pts]
- log(W) = 3.08.
- Yes, significant, because estimated coefficient of S is more than twice its standard error.
- Wage increases by 15 percent.
(2) [Measuring the labor force: 8 pts]
- 232.2 million.
- 4.6 percent.
- 62.7 percent.
- 65.8 percent.
(3) [Budget constraint: 6 pts]
- Endowment point is at L=60 and C=$200.
- Kink point is at L=40 and C=$1000.
- Intercept on consumption axis is at C=$2200.
(4) [Labor supply: 12 pts]
- $0.50.
- C = 50 + (80-L) 20 = 1650 - 20 L.
- L*= 41 hours, C*= $830.
- h*= 39 hours.
(5) [SR labor demand: 12 pts]
- E* = 100.
- q* = 300.
- profit = $500.
(6) [LR labor demand: 12 pts]
- Substitution effect causes company to use more capital and less labor, because the relative price of labor (w/r) has increased from 0.5 to 0.75.
- Scale effect causes company to use more capital and more labor, because input prices have decreased so it will "scale up" output and inputs.
- Total effect causes company to use more capital because substitution and scale effects work in the same direction. Total effect for labor cannot be determined because substitution and scale effects work in opposite directions.
(7) [LR labor demand: 4 pts]
Industry B has more elastic demand for labor because its elasticity of demand for output is greater (Hicks-Marshall rules).
(8) [Elasticities, minimum wage: 12 pts]
- We are given that the elasticity of demand for workers = -0.6
= (percent chg E) / (percent change w).
Substituting (percent change w) = 10 percent yields
(percent change E) = -6 percent.
Thus 6 percent fewer people would be employed. (100-6)percent x 250 million = 235 million people would now be employed.
- We are given that the elasticity of supply = 0.02
= (percent chg E) / (percent change w).
Substituting (percent change w) = 10 percent yields
(percent change E) = 2 percent.
Thus 2 percent more people would want jobs. (102)percent x 250 million = 255 million people would want jobs. 255-235 = 20 million people would want to work but would be unable to find jobs.
- Unemployment rate = 20/255 = 7.8 percent.
Version D
I. Multiple choice
(1)b. (2)b. (3)b. (4)c. (5)c. (6)d. (7)a. (8)c. (9)c. (10)c.
(11)a. (12)b. (13)b. (14)d.
II. Problems
(1) [Regression analysis: 6 pts]
- log(W) = 2.97.
- Yes, significant, because estimated coefficient of S is more than twice its standard error.
- Wage increases by 11 percent.
(2) [Measuring the labor force: 8 pts]
- 236.0 million.
- 9.7 percent.
- 59.1 percent.
- 65.4 percent.
(3) [Budget constraint: 6 pts]
- Endowment point is at L=80 and C=$200.
- Kink point is at L=40 and C=$600.
- Intercept on consumption axis is at C=$1200.
(4) [Labor supply: 12 pts]
- $3.
- C = 1300 + (70-L) 15 = 1300 - 15 L.
- L*= 42 hours, C*= $670.
- h*= 28 hours.
(5) [SR labor demand: 12 pts]
- E* = 400.
- q* = 2000.
- profit = $5000.
(6) [LR labor demand: 12 pts]
- Substitution effect causes company to use less capital and more labor, because the relative price of labor (w/r) has decreased from 0.5 to 0.333.
- Scale effect causes company to use more capital and more labor, because input prices have decreased so it will "scale up" output and inputs.
- Total effect causes company to use more labor because substitution and scale effects work in the same direction. Total effect for capital cannot be determined because substitution and scale effects work in opposite directions.
(7) [LR labor demand: 4 pts]
Industry A has more elastic demand for labor because its elasticity of substitution in production is greater (Hicks-Marshall rules).
(8) [Elasticities, minimum wage: 12 pts]
- We are given that the elasticity of demand for workers = -0.8
= (percent chg E) / (percent change w).
Substituting (percent change w) = 10 percent yields
(percent change E) = -8 percent.
Thus 8 percent fewer people would be employed. (100-8)percent x 225 million = 207 million people would now be employed.
- We are given that the elasticity of supply = 0.01
= (percent chg E) / (percent change w).
Substituting (percent change w) = 10 percent yields
(percent change E) = 1 percent.
Thus 1 percent more people would want jobs. (101)percent x 225 million = 227.25 million people would want jobs. 227.25-207 = 20.25 million people would want to work but would be unable to find jobs.
- Unemployment rate = 20.25/227.25 = 8.9 percent.
[end of answer key]