
Subpart (a):
Wage rate.
Subpart (a):

Explanation of Solution
Daily wage can be derived as follows.
Wage=VMP×Unknown node type: x-custom-btb-meApple=(100−2L)×2=200−4L
Wage is 200−4L.
Rearrange the wage equation in terms of labor
L=50−0.25W .
Demand=L×Number of firms=(50−0.25W)×20=1,000−5W
Labor demand is 1,000−5W.
Subpart (b):
Calculate wage rate, profit and income.
Subpart (b):

Explanation of Solution
Wage level with 200 labors can be calculated as follows.
Supply of labor=Unknown node type: x-custom-btb-me for labor200=1,000−5W5W=1,000−200W=8005=160
Wage is 160.
Number of labor demanded by each firm can be calculated as follows.
Demand for labor=Total laborTotal nuber of firms=20020=10
Each firm employs 10 labors.
Profit can be calculated as follows.
Profit=(Q×Price)−(Wage×Labor)=((100L−L2)×2)−(160×10)=((100(10)−(10)2)×2)−(160×10)=1,800−1,600=200
Total profit for each firm is 200.
Total income can be calculated as follows.
Total income=(Profit×Number of firm)+(Wage×Number of labor)=(200×20)+(160×200)=36,000
Total income is $36,000.
Subpart (c):
Calculate wage rate and income.
Subpart (c):

Explanation of Solution
New daily wage can be derived as follows.
Wage=VMP×PriceApple=(100−2L)×4=400−8L
Wage is 400−8L.
Rearrange the wage equation in terms of labor L=50−0.125W . Market demand function can be derived as follows.
Demand=L×Number of firms=(50−0.125W)×20=1,000−2.5W
Labor demand is 1,000−2.5W.
Wage level with 200 labors can be calculated as follows.
Supply of labor=Demand for labor200=1,000−2.5W2.5W=1,000−200W=8002.5=320
Wage is 320.
Profit can be calculated as follows.
Profit=(Q×Price)−(Wage×Labor)=((100L−L2)×4)−(320×10)=((100(10)−(10)2)×4)−(320×10)=3,600−3,200=400
Total profit for each firm is 400.
Total income can be calculated as follows.
Total income=(Profit×Number of firm)+(Wage×Number of labor)=(400×20)+(320×200)=72,000
Total income is $36,000.
Subpart (d):
Calculate profit and income.
Subpart (d):

Explanation of Solution
Market demand function after the destruction can be derived as follows.
Demand=L×Number of firms=(50−0.25W)×10=500−2.5W
Labor demand is 500−2.5W.
Wage level with 200 labors can be calculated as follows.
Supply of labor=Demand for labor200=500−2.5W2.5W=500−200W=3002.5=120
Wage is 120.
Number of labor demanded by each firm can be calculated as follows.
Demand for labor=Total laborTotal nuber of firms=20010=20
Each firm employs 20 labors.
Profit can be calculated as follows.
Profit=(Q×Price)−(Wage×Labor)=((100L−L2)×2)−(160×20)=((100(20)−(20)2)×2)−(120×20)=3,200−2,400=800
Total profit for each firm is 800.
Total income can be calculated as follows.
Total income=(Profit×Number of firm)+(Wage×Number of labor)=(800×10)+(120×200)=32,000
Total income is $32,000. The total income decreased.
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Chapter 18 Solutions
Study Guide for Mankiw's Principles of Microeconomics, 7th
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