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
Chapter 18, Problem 5PA

Subpart (a):

To determine

Wage rate.

Subpart (a):

Expert Solution
Check Mark

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
Check Mark

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
Check Mark

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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
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…
Suppose that Zamboni Enterprises is the only company that sells zambonis (ice resurfacing machines). To produce the machines, the company hires assembly workers. Since these workers can work in many different companies, Zamboni Enterprises must pay them the market wage, which is equal to $6. The number of zambonis that the company produces, which is denoted by y, is proportional to the number of assembly workers that it hires, which are denoted by N; in particular, the production function is given by y=0.76N. The economywide demand for zambonis is given by the following demand function: y=2191-219p, where y is the number of zambonis that consumers are willing to purchase at price p.  Given this market structure, how many assembly workers will Zamboni Enterprises choose to hire? How many zambonis will Zamboni Enterprises produce and sell?
Suppose that Zamboni Enterprises is the only company that sells zambonis (ice resurfacing machines). To produce the machines, the company hires assembly workers. Since these workers can work in many different companies, Zamboni Enterprises must pay them the market wage, which is equal to $6. The number of zambonis that the company produces, which is denoted by y, is proportional to the number of assembly workers that it hires, which are denoted by N; in particular, the production function is given by y=0.76N. The economywide demand for zambonis is given by the following demand function: y=2191-219p, where y is the number of zambonis that consumers are willing to purchase at price p.  Given this market structure, how many assembly workers will Zamboni Enterprises choose to hire? How many zambonis will Zamboni Enterprises produce and sell? What will be the price of a zamboni? If the market for zambonis were competitive, how many zambonis would be produced? If the market for…
Knowledge Booster
Similar questions
  • Suppose that Zamboni Enterprises is the only company that sells zambonis (ice resurfacing machines). To produce the machines, the company hires assembly workers. Since these workers can work in many different companies, Zamboni Enterprises must pay them the market wage, which is equal to $6. The number of zambonis that the company produces, which is denoted by y, is proportional to the number of assembly workers that it hires, which are denoted by N; in particular, the production function is given by y=0.76N. The economywide demand for zambonis is given by the following demand function: y=2191-219p, where y is the number of zambonis that consumers are willing to purchase at price p.  If the market for zambonis were competitive, how many zambonis would be produced? If the market for zambonis were competitive, how many assembly workers would be hired? If the market for zambonis were competitive, at what price would zambonis be sold?
    Suppose a competitive firm can sell its output for $7 per unit. The following table gives the firm’s short run production function. Labor Output 0 0 1 15 2 40 3 70 4 86 5 94 6 98 In the table below, you will determine several points on the firm’s demand curve for labor. To do this, you must determine how many workers the firm should hire for different values of the wage rate in order to maximize profit. Complete the table below: Wage Rate Per Worker Quantity Demanded of Workers $30 $50 $70 $100 Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
    Consider a firm that produces widgets according to the following Cobb-Douglas production function: Q = A * L^α * K^β where: Q is the quantity of output, L is the quantity of labor, K is the quantity of capital, A is a scale parameter (total factor productivity), α and β are the output elasticities of labor and capital respectively. Given that A = 1, α = 0.6, β = 0.4, L = 16 and K = 9, a) Calculate the quantity of output Q. b) If the firm increases the quantity of labor (L) to 20 while keeping the quantity of capital (K) constant, what will be the new quantity of output?
  • Hannah and Sam run Moretown Makeovers, a home remodeling business. The number of square feet they can remodel in a week is described by the Cobb-Douglas production function             Q=F(L,K)              Q=10L^0.25 K^0.25             where L is their number of workers and K is units of capital. The wage rate is $500 per week and a unit of capital costs $500 per week. Suppose that when initially producing 10 square feet a week, they use 1 unit of capital.a. What is their short-run cost of remodeling 80 square feet per week?    Instructions: Round your answer to the nearest whole number.    $ b. What is their short-run average cost of remodeling 80 square feet per week?    Instructions: Round your answer to the nearest whole number.    $ c. What is their long-run cost of remodeling 80 square feet per week?    Instructions: Round your answer to the nearest whole number.    $ d. What is their long-run average cost of remodeling 80 square feet per week?    Instructions: Round your answer…
    The production engineers at Impact Industries have derived the optimal combinations of labor and capital.  These are the only two inputs used by Impact.  The following chart shows the combinations of labor and capital for three levels of output. Q is the output level.  L* is the optimal amount of labor.  K* is the optimal amount of capital.  The price of labor is $90 per unit.  The price of capital is $15 per unit. Q L* K* 120 5 20 180 7 7 240 12 24     a)  If the manager of Impact Industries decides to produce 120 units, what will the long-run total cost and long-run average cost of producing 120 units? Show all calculations.   b)  If the manager of Impact Industries decides to produce 180 units, what will the long-run total cost and long-run average cost of producing 180 units? Show all calculations.   c)  If the manager of Impact Industries decides to produce 240 units, what will the long-run total cost and long-run average cost of producing 240…
    The production engineers at Impact Industries have derived the optimal combinations of labor and capital.  These are the only two inputs used by Impact.  The following chart shows the combinations of labor and capital for three levels of output. Q is the output level.  L* is the optimal amount of labor.  K* is the optimal amount of capital.  The price of labor is $90 per unit.  The price of capital is $15 per unit. Q L* K* 120 5 20 180 7 7 240 12 24     a)  If the manager of Impact Industries decides to produce 120 units, what will the long-run total cost and long-run average cost of producing 120 units? Show all calculations.   b)  If the manager of Impact Industries decides to produce 180 units, what will the long-run total cost and long-run average cost of producing 180 units? Show all calculations.   c)  If the manager of Impact Industries decides to produce 240 units, what will the long-run total cost and long-run average cost of producing 240…
  • The production engineers at Impact Industries have derived the optimal combinations of labor and capital.  These are the only two inputs used by Impact.  The following chart shows the combinations of labor and capital for three levels of output. Q is the output level.  L* is the optimal amount of labor.  K* is the optimal amount of capital.  The price of labor is $90 per unit.  The price of capital is $15 per unit. Q L* K* 120 5 20 180 7 7 240 12 24     a)  If the manager of Impact Industries decides to produce 120 units, what will the long-run total cost and long-run average cost of producing 120 units? Show all calculations.   b)  If the manager of Impact Industries decides to produce 180 units, what will the long-run total cost and long-run average cost of producing 180 units? Show all calculations.
    Hannah and Sam run Moretown Makeovers, a home remodeling business. The number of square feet they can remodel in a week is described by the Cobb-Douglas production function             Q=F(L,K)             Q=10L^0.5K^0.5,where L is their number of workers and K is units of capital. The wage rate is $250 per week and a unit of capital costs $250 per week. Suppose that when initially producing 100 square feet a week, they use 10 units of capital.a. What is their short-run cost of remodeling 1,000 square feet per week?    Instructions: Enter your answer as a whole number.    $ b. What is their long-run cost of remodeling 1,000 square feet per week?    Instructions: Enter your answer as a whole number.    $
    Widget factory Inc. in Wisconsin has the following production function: F(L,K) = 2L1/2 K1/2  L represent the number of labour hours. Workers at this factory are paid an hourly wage of $30 and they rent capital at $25/hour. Since this is a competitive market, the factory output the factory gets per is output is $50 per unit. Let's pretend the firm operates in the short run with capital fixed at 900, how many factory workers would Widget Factory Inc employ? What is their profit rate?
  • Suppose the long-run production function for a competitive firm is f(x1,x2)= min {x1,2x2}. The cost per unit of the first input is w1 and the cost of the second input is w2. .a. Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y. .b. Draw the conditional input demand functions for labor and capital in the x1-y and x2- y spaces. .c. Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs? .d. Write down the formula and draw the graph of the average cost function, as a function of y. .e. Write down the formula and draw the graph of the marginal cost function, as a function of y.
    Jess owns a firm that uses labour (L) and capital (C) to sell widgets (X), according to the following production function: X = F(L,C) = ln(L) + ln(C) Jesse buys her factors and sells her output in perfectly competitive markets. The market prices for L, C and W are a, r and p, respectively.  What is the firm’s profit function.  What is the  firm's marginal product of labour , marginal product of capital  and marginal rate of technical substitution  Does the firm exhibit a diminishing marginal product of capital? What is the firms demand functions for labour and capital.  Say the central bank decides to increase interest rates, causing ? to go up. What effect will this have on the firm’s use of L and C? What effect will it have on output (X) and profits?
    We often work with production technologies that give rise to initially increasing marginal product of labor that eventually decreases. Are the following statements then True or False? Explain.A negative marginal product of labor necessarily implies a downward sloping production frontier at that level of labor input.
    • SEE MORE QUESTIONS
    Recommended textbooks for you
  • Principles of Economics (MindTap Course List)
    Economics
    ISBN:9781305585126
    Author:N. Gregory Mankiw
    Publisher:Cengage Learning
    Principles of Economics, 7th Edition (MindTap Cou...
    Economics
    ISBN:9781285165875
    Author:N. Gregory Mankiw
    Publisher:Cengage Learning
    Microeconomic Theory
    Economics
    ISBN:9781337517942
    Author:NICHOLSON
    Publisher:Cengage
  • Principles of Economics (MindTap Course List)
    Economics
    ISBN:9781305585126
    Author:N. Gregory Mankiw
    Publisher:Cengage Learning
    Principles of Economics, 7th Edition (MindTap Cou...
    Economics
    ISBN:9781285165875
    Author:N. Gregory Mankiw
    Publisher:Cengage Learning
    Microeconomic Theory
    Economics
    ISBN:9781337517942
    Author:NICHOLSON
    Publisher:Cengage