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Average Product of Capital and Average Product of Labor

A firm’s product sells for $4 per unit in a highly competitive market. The firm produces output using capital (which it rents at $25 per hour) and labor (which is paid a wage of $30 per hour under a contract for 20 hours of labor services). Complete the following table and use that information to answer the questions that follow.

Instruction: Round your answers for Average Product of Capital and Average Product of Labor to 2 decimal places.

(1) (2) (3) (4) (5) (6) (7)
Capital Labor Output Marginal Product of Capital MPK Average Product of Capital APK Average Product of Labor APL Value Marginal Product of Capital ;VMPK
0 20 0
1 20 50
2 20 150
3 20 300
4 20 400
5 20 450
6 20 475
7 20 475
8 20 450
9 20 400
10 20 300
11 20 150
; ; ; ; ; ; ;
; ; ; ; ; ; ;

. Identify the fixed and variable inputs.

Capital and labor are fixed inputs.
Capital is the fixed input and labor is the variable input.
Capital and labor are variable inputs.
Labor is the fixed input and capital is the variable input.
What are the firm’s fixed costs?


c. What is the variable cost of producing 475 units of output?


d. How many units of the variable input should be used to maximize profits?

e. What are the maximum profits this firm can earn?


f. Over what range of the variable input usage do increasing marginal returns exist?

From to

g. Over what range of the variable input usage do decreasing marginal returns exist?

From to

h. Over what range of input usage do negative marignal returns exist?

From to ; ; 2. An economist estimated that the cost function of a single-product firm is:

C(Q) = 100 + 20Q + 15Q2 + 10Q3.

Based on this information, determine the following:

a. The fixed cost of producing 10 units of output.


b. The variable cost of producing 10 units of output.


c. The total cost of producing 10 units of output.


d. The average fixed cost of producing 10 units of output.


e. The average variable cost of producing 10 units of output.

$ f. The average total cost of producing 10 units of output.


g. The marginal cost when Q = 10. ; ; ; A manager hires labor and rents capital equipment in a very competitive market. Currently the wage rate is $15 per hour and capital is rented at $8 per hour. If the marginal product of labor is 45 units of output per hour and the marginal product of capital is 65 units of output per hour, should the firm increase, decrease, or leave unchanged ;the amount of capital used in its production process? The firm should increase capital. The firm should leave capital unchanged. The firm should decrease capital. ; ; The World of Videos operates a retail store that rents movie videos. For each of the last 10 years, World of Videos has consistently earned profits exceeding $37,000 per year. The store is located on prime real estate in a college town. World of Videos pays $2,100 per month in rent for its building, but it uses only 50 percent of the square footage rented for video rental purposes. The other portion of rented space is essentially vacant. Noticing that World of Videos only occupies a portion of the building, a real estate agent told the owner of World of Videos that she could add $1,650 per month to her firm’s profits by renting out the unused portion of the store. While the prospect of adding an additional $1,650 to World of Videos’s bottom line was enticing, the owner was also contemplating using the additional space to rent video games. What is the opportunity cost of using the unused portion of the building for video game rentals?

$ ; ; Hyundai Heavy Industries Co. is one of Korea’s largest industrial producers. According to an article in BusinessWeek Online, the company is not only the world’s largest shipbuilder but also manufactures other industrial goods ranging from construction equipment and marine engines to building power plants and oil refineries worldwide. Despite being a major industrial force in Korea, several of the company’s divisions are unprofitable, or “bleeding red ink” in the words of the article. Indeed, last year the power plant and oil refineries building division recorded a $105 million loss, or 19 percent of its sales. Hyundai Heavy Industries recently hired a new CEO who is charged with the mission of bringing the unprofitable divisions back to profitability. According to BusinessWeek, Hyundai’s profit-driven CEO has provided division heads with the following ultimatum: “…hive off money-losing ;businesses and deliver profits within a year—or else resign.”

Suppose you are the head of the marine engine division and that it has been unprofitable for 7 of the last 10 years. While you build and sell in the competitive marine engines industry, your primary customer is Hyundai’s profitable ship-building division. This tight relationship is due, in large part, to the technical specifications of building ships around engines. Suppose that in our end-of-year report to the CEO you must disclose that while your division reduced costs by 10 percent, it still remains unprofitable. Which of the following, if true, would be valid arguments you could make to the ;CEO when explaining why your division should not be shut down. There are cost complementarities and diseconomies of scale. There are constant returns to scale and economies of scope. There are cost complementarities and constant returns to scale. There are cost complementarities and economies of scope.

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