# Marginal cost analysis

18. If the production function is Q = K^5L^5 and capital is fixed at 4 units, then the average product of labor when L = 25 is (hint: raising a variable to the 0.5 power is the same as taking the square root):

a) 2/5.

b) 1/5.

c) 10.

d) none of the above.

20. The change in total revenue attributable to the last unit of an input is the:

a) Marginal product.

b) Average price.

c) Marginal revenue.

d) Marginal return.

22. You are a manager in a perfectly competitive market. The price in your market is $14. Your total cost curve is C(Q) = 10 + 4Q + 0.5 Q^2. What price should you charge in the short-run?

a) $12.

b) $14.

c) $16.

d) $18.

23. You are the manager of a firm that sells its product in a competitive market at a price of $40. Your firm's cost function is C = 60 + 4Q^2. Your firm's maximum profits are

a) 36.

b) 60.

c) 40.

d) 80.

24. For the production function Q = 5.2K + 3.8L, if K = 16 and L = 12, we know that MPL is:

a) 16.

b) 5.2.

c) 3.8.

d) 12.

https://brainmass.com/economics/perfect-competition/marginal-cost-analysis-124517

#### Solution Preview

Answer 18: (A)

Q=K^0.5L^0.5

Putting K=4 and L=25 we get

Q = 2x5 = 10

Average Product of Labor = 10/25 = 2/5

Answer 20: ...

#### Solution Summary

The solution answers a number of economics questions related to marginal analysis.

High-low methods, accounting analysis, CVP, and leverage

EXERCISE4-5. High-Low Method

Campus Copy & Printing wants to predict copy machine repair expense at different levels of copying activity (number of copies made). The following data have been gathered: (see attached)

Required

Determine the fixed and variable components of repair expense using the high-low

method. Use copies made as the measure of activity.

EXERCISE 4-8. Account Analysis

Reef Office Supplies is interested in estimating

the cost involved in hiring new employees. The following information is available regarding

the costs of operating the Human Resource department at Reef Office Supplies

in May when there were 50 new hires.

Human Resource Department

May

Staff salaries $25,000

Manager salary 7,000

Office supplies 200

Depreciation of office equipment 300

Share of building cost (based

on square feet occupied by

Human Resources) 1,500

Total $34,000

Required

a. Use account analysis to determine fixed cost per month and variable cost per new

hire.

b. The company is planning to hire 60 employees in June. Estimate the total cost of

Human Resources for June..

c. What is the expected incremental cost associated with hiring 10 more employees

than were hired in May?

EXERCISE 4-12. CVP Analysis, Profit Equation

Clyde's Marina has estimated that fixed costs per month

are $240,000 and variable cost per dollar of sales is $0.60.

Required

a. What is the break-even point per month in sales?

b. What level of sales is needed for a monthly profit of $60,000?

c. For the month of July, the marina anticipates sales of $1,200,000: What is the expected level of profit?

EXERCISE 4-17. Operating Leverage

(see attached for data)

Required

a. Calculate profit as a percent of sales in the prior year.

b. Suppose sales in the current year increase by 20 percent. Calculate profit as a percent

of sales for the new level of sales and explain why the percent is greater than the

one calculated in Part a.

EXERCISE 4-18. Constraints

Dvorak Music produces two durable music stands:

Stand A Stand B

Selling price $80 $70

Less variable costs 20 40

Contribution margin $60 $30

Stand Arequires 5 labor hours and standB requires 2 labor hours. The company has

only 320 available labor hours per week. Further, the company can sell all it can produce

of either product.

Required

a. Which stand(s) should the company produce?

b. What would be the incremental benefit of obtaining 10 additional labor hours?

PROBLEM 4-12. Multiproduct CVP

Fidelity Multimedia sells audio and video equipment

and car stereo products. After performing a study of fixed and variable costs in the

prior year, the company prepared a product-line profit statement as follows:

Fidelity Multimedia

Profitability Analysis

For the Year Ended December 31,2007

Audio Video Car Total

Sales $3,000,000 $1,800,000 $1,200,000 $6,000,000

Less variable costs:

Cost of merchandise 1,800,000 1,260,000 600,000 3,660,000

Salary part-time staff 120,000 80,000 30,000 230,000

Total variable costs 1,920,000 1,340,000 630,000 3,890,000

Contribution margin 1,080,000 460,000 570,000 2,110,000

Less direct fixed costs:

Salary, full-time staff 300,000 250,000 210,000 760,000

Less common fixed costs:

Advertising 110,000

Utilities 20,000

Other administrative costs 560,000

Total common fixed costs 690,000

Profit $660,000

Required

a. Calculate the contribution margin ratios for the audio, video, and car product lines.

b. What would be the effect on profit of a $100,000 increase in sales of audio equipment

compared with a $100,000 increase in sales of video equipment, or a $100,000

increase in sales of car equipment? Based on this limited information, which product

line would you recommend expanding?

c. Calculate the break-even level of sales for the company as a whole.

d. Calculate sales needed to achieve a profit of $1,500,000 assuming the current mix.

e. Determine the sales of audio, video, and car products in the total sales amount calculated

for Part d.