Chapter 8

Production and Cost in the Short Run

Duplicate Technical Problems

1. “When a manager fails to employ an economically efficient input combination, then the firm cannot be producing in a technically efficient manner.” Evaluate this statement.

2. A firm plans to produce 500 units per day of good Z. The firm’s production engineer finds two technically efficient processes (i.e., input combinations of labor and capital) to produce 500 units per day:

Process Alpha Process Beta

 

625

250

 

45

125

Labor

Capital

a. If the production function for the existing technology is Q = f ( L, K ) , where Q is the maximum possible output, L is the amount of labor used, and K is the amount of capital used, then f (625, 45) = and f (250, 125) = .

b. If the firm must pay $350 per day for a unit of labor and $1,500 per day for a unit of capital, which process is economically efficient, Alpha or Beta?

c. If the price of labor falls to $300 per day for a unit of labor and the price of capital remains

$1,500 per day, which process is now economically efficient, Alpha or Beta?

d. Holding the price of capital constant at $1,500 per unit, Process Alpha will never be economically efficient if a unit of labor costs (less, more) than $ per day

e. “The process that turns out to be economically efficient will depend on the prices the firm must pay for labor and capital inputs.” Evaluate this statement.

3. Water Works Plumbing Company is a small owner-managed plumbing services company that  serves the greater Miami metropolitan area. Identify each of the following costs as either a variable, a fixed, or a quasi-fixed cost:

a. Gasoline expense for the service van.

b. Cost of a complete set of tools needed to be a plumber.

c. Labor expense for an assistant plumber who is hired on an hourly basis and works with the owner-manager of the firm when the owner needs a helper.

d. Monthly lease payment for a drain-line auger, which contractually binds WW Plumbing to pay

$75 per month for the next 12 months, regardless of how much or how little the company uses the leased piece of plumbing equipment. Subleasing is prohibited and there will be no refund if the machine is returned before the 12 month period expires.

e. Cost of the owner’s time to run the plumbing business.

f. Expense for plumbing service consumables: plumbers’ putty, Teflon tape, pipe lubricant, sandpaper, PVC glue, butane for torch, etc.

Chapter 8

2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

 

4. For each of the following situations, determine whether the manager is concerned with a short-run or a long-run production decision. Explain briefly in each case.

a. The Global Operations Chief Executive at Adidas AG wishes to acquire Glad Foot Inc. in order to expand the company’s sport shoe line to include specialty shoes designed for table tennis, a type of shoe for which Glad Foot is the global leader.

b. The vice president of Wal-Mart decides not to build another distribution center in Virginia, instead choosing to extend hours of operation by 7 percent at each one of the 14 distribution centers in the greater Richmond, Virginia area.

c. GemCon Direct, a diamond brokerage firm in Beirut, lays off five of its brokers in response to declining demand for its services.

d. Tampa International Airport announced that it will add a fifth concourse in order to meet the growing demand for air travel in west-central Florida.

5. Frito-Lay, a division of PepsiCo, manufactures, markets and distributes a variety of snack foods, including Fritos corn chips, Lay’s potato chips, Cheetos cheese snacks, Doritos tortilla chips, and Quaker Chewy granola bars, just to name the most familiar products. Identify the following costs for Frito-Lay as either sunk or avoidable costs:

a. Commission payments to Frito-Lay sales representatives.

b. All the costs associated with winning approval by the FDA to advertise Frito-Lay’s new cheese popcorn snack as a probiotic nutritional supplement.

c. Labor cost for installing two new plasma baking ovens at the St. Louis production plant.

d. Legal fees incurred in winning an antitrust law suit filed by rival company R. W. Garcia, who sued Frito-Lay for illegal price fixing of flax seed chips.

6. Fill in the blanks in the following table:

Units of labor Total product Average product Marginal product

 

1

2

3 2,000

4

5

6 2,970

7

8

 

500

625

415

 

700

300

–81

 

 

7. Refer to your answer to Technical Problem 6 and explain precisely why using 7 units of labor is technically efficient but not economically efficient.

Chapter 8

2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

 

8. The following table shows the amount of total output produced from various combinations of labor and capital:

Units of capital

 

Units of labor

1

2

3

4

 

1

200.00

300.00

400.00

500.00

 

2

230.00

345.00

460.00

575.00

 

3

253.00

380.00

506.00

632.00

 

4

288.00

435.00

575.00

720.00

 

5

317.00

475.00

635.00

795.00

a. Calculate the marginal product and average product of labor when capital is held constant at 2 units. When the average product of labor is increasing, what is the relation between the average product and the marginal product? What about when the average product of labor is  decreasing?

b. Calculate the marginal product of labor for each level of the capital stock. How does the marginal product of the second unit of labor change as the capital stock increases? Why?

9. Fill in the blanks in the following table:

 

Output

Total cost

Total fixed cost

Total variable cost

Average fixed cost

Average variable cost

Average total cost

Marginal cost

 

100

1,000

 

200

9

 

300

9.50

 

400

7,300

 

500

16.78

 

600

6,000

 

700

5

12.50

 

800

12,150

Chapter 8

2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

 

10. Total variable costs over the output range 20,000 to 30,000 units are given in the table below. Fill in the missing values and then answer the following questions.

 

Total variable

Q cost

 

Average variable cost

 

Marginal cost

 

20,000 $37,400

25,000 46,750

30,000 56,100

a. Are average variable costs rising, falling or constant over the output range 20,000 to 30,000 units?

b. Describe the relation between average variable cost and marginal cost over this output range.

11. Suppose your business is currently employing 750 workers, the only variable input, at a wage rate of $48. The average product of labor is 96, the last worker added 6 units to total output, and total fixed cost is $12,000.

a. What is marginal cost?

b. What is average variable cost?

c. How much output is being produced?

d. What is average total cost?

e. Is average variable cost increasing, constant, or decreasing? What about average total cost?

12. The first two columns in the following table give a firm’s short-run production function when the only variable input is labor, and capital (the fixed input) is held constant at 15 units. The price of capital is $800 per unit, and the price of labor is $200 per unit.

Total cost Average cost

 

Units of labor

Units of output

Average product

Marginal product

Fixed

Variable

Total

Fixed

Variable

Total

Marginal cost

 

0

0

xx

xx

xx

xx

xx

xx

 

25

3,600

 

50

9,000

 

75

13,500

 

100

15,000

 

125

16,400

a. Complete the table.

b. Do your numbers in the table illustrate the expected relation between average variable cost and marginal cost? Between average total cost and marginal cost?

c. Does the expected relation between average product and average variable cost reveal itself in this table? Explain. And between marginal product and marginal cost?

Chapter 8

2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

 

13. A firm produces in the short run with a single variable input, labor. The panel below on the left shows the firm’s total product curve. Point I is the inflexion point where total product goes from increasing at an increasing rate to increasing at a decreasing rate.  This firm faces a wage rate of $50 per unit of labor, and the firm’s short-run marginal cost curve reaches its minimum value of $4 at 360 units of output.

a. On the axes to the right of total product, sketch the marginal product curve. The average product curve is already sketched for you. Label the marginal product curves MP, and show the maximum values for MP and AP on the vertical axis.

b. Find the firm’s minimum average variable cost and determine the output level where AVC reaches its minimum level.

Chapter 8

2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.