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# The Marginal Product

Question 5

Suppose that the marginal product of the last worker employed by the Delicious Ice Cream Company is 300 units of output per day & the daily wage of the firm must pay is \$50, while the marginal product of the last ice cream machine that the firm rents is 200 units of output per day and the daily rental price of the machine is \$25.

a. Is the firm maximizing output or minimizing costs?

The condition for maximizing output is the same as the condition for minimizing costs: (MPk/Pk)=(MPL/PL) That is, the Marginal Product of Capital divided by the Price of Capital is equal to the Marginal Product of Labor divided by the Price of Labor. This makes sense because if they are not equal, then we could save money by adding more of the cheaper input and using less of the more expensive input. This also makes sense for maximizing output over a budget constraint, because if we can get more output for our money, we should choose that factor of production until we are indifferent between the two factors.

How can the firm maximize output or minimize costs?

In order to minimize costs/maximize quantity, we should find the level of output where (MPk/Pk)=(MPL/PL).

Question 12

With respect to the given data of problem 11*,

*Total fixed costs:

Copyediting \$10,000
Typesetting \$70,000

Selling and promotion \$20,000

Total fixed costs \$100,000

Average variable costs:

Printing and binding \$6

Sales commissions 1

Bookstore discounts 7

Author’s royalties 4

Average variable costs \$20

Project selling price \$30

Find the publisher’s break even output and the output that would lead to a total profit of \$60,000 if, as a result of a technological breakthrough in printing, the publisher was able to lower its TFC to \$40,000. Draw a chart showing your answer.

b. Find the publishers breakeven output and the output that would lead to a total profit of \$60,000 if total fixed costs remained at \$100,000 but average variable costs declined to \$10. Draw a chart to show your answer.

Find the breakeven output at which the publisher earns a profit of \$60,000 if the publisher’s total fixed costs remained at \$100,000 and its average variable costs at \$20 but the publisher charged a price of \$40. Draw a chart showing your answer.

Question 14

Microsoft wants to estimate the average variable cost function of producing computer diskettes. The firm believes that AVC varies with the level of output and wages. Alan Anderson, the economist in the research department of the firm, collects monthly data on output (the number of diskettes produced), average variable costs, and wage rates paid by the firm over the past two years. He deflates costs and wages by their respective price indexes in order to eliminate inflationary influences. He then regresses total variable costs (TVC) on output (Q) and wages (W) and obtains the following result (where the numbers in parentheses are t values):

TVC = 0.14 + 0.80Q + 0.036W

(2.8) (3.8) (3.3)

R2 = 0.92 D – W = 1.9

a.If W = \$10, derive the AVC and MC functions of the firm

What are the shapes of the AVC and MC curves of the firm?

Why did Anderson fit a linear rather than a quadratic or cubic TVC function?