Principles of Economics, 7th Edition (MindTap Course List)
Principles of Economics, 7th Edition (MindTap Course List)
7th Edition
ISBN: 9781285165875
Author: N. Gregory Mankiw
Publisher: Cengage Learning
Question
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Chapter 18, Problem 5PA

Subpart (a):

To determine

Wage rate.

Subpart (a):

Expert Solution
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Explanation of Solution

Daily wage can be derived as follows.

Wage=VMP×PriceApple=(1002L)×2=2004L

Wage is 2004L .

Rearrange the wage equation in terms of labor L=500.25W . Market demand function can be derived as follows.

Demand=L×Number of firms=(500.25W)×20=1,0005W

Labor demand is 1,0005W .

Subpart (b):

To determine

Calculate wage rate, profit and income.

Subpart (b):

Expert Solution
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Explanation of Solution

Wage level with 200 labors can be calculated as follows.

Supply of labor=Demand for labor200=1,0005W5W=1,000200W=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)=((100LL2)×2)(160×10)=((100(10)(10)2)×2)(160×10)=1,8001,600=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):

To determine

Calculate wage rate and income.

Subpart (c):

Expert Solution
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Explanation of Solution

New daily wage can be derived as follows.

Wage=VMP×PriceApple=(1002L)×4=4008L

Wage is 4008L .

Rearrange the wage equation in terms of labor L=500.125W . Market demand function can be derived as follows.

Demand=L×Number of firms=(500.125W)×20=1,0002.5W

Labor demand is 1,0002.5W .

Wage level with 200 labors can be calculated as follows.

Supply of labor=Demand for labor200=1,0002.5W2.5W=1,000200W=8002.5=320

Wage is 320.

Profit can be calculated as follows.

Profit=(Q×Price)(Wage×Labor)=((100LL2)×4)(320×10)=((100(10)(10)2)×4)(320×10)=3,6003,200=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):

To determine

Calculate profit and income.

Subpart (d):

Expert Solution
Check Mark

Explanation of Solution

Market demand function after the destruction can be derived as follows.

Demand=L×Number of firms=(500.25W)×10=5002.5W

Labor demand is 5002.5W .

Wage level with 200 labors can be calculated as follows.

Supply of labor=Demand for labor200=5002.5W2.5W=500200W=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)=((100LL2)×2)(160×20)=((100(20)(20)2)×2)(120×20)=3,2002,400=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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The nation of Ectenia has 20 competitive apple orchards, all of which sell apples at the world price of $2 per apple. The following equations describe the production function and the marginal product of labor in each orchard: Q=100 L-L2 MPL = 100-2L Where Q is the number of apples produced in a day, L is the number of workers, and MPL is the marginal product of labor a. What is each orchard's labor demand as a function of the daily wage W? What is the market's labor demand? b.Ectenia has 200 workers who suply their labor inelastically. Solve for the wage W How many workers does each orchard hire ? How much profit does each orchard owner make? c.Calculate what happens to the income of workers and orchard owners if the world price doubles to $4per apple. d. Now suppose the price is back at $2 per apple, but a hurricane destroys half the orchards. Calculate how the hurricane affects the income of each worker and of each remaining orchard owner. What happens to the income of Ectenia as a…
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