Econ 555 Homework #4 Answer Key

Economics for Decision Making T. Donley

1) A firm’s marginal product of capital is twice its marginal product of labor; the price of labor is $6, and the price of capital is $3. Is the firm minimizing costs? If not, how can it reduce its costs? Profit maximization (or cost minimization) requires that: condition is not being satisfied since:
MPL MPK = . This PL PK

1 2 ≠ . To equate these ratios you would need to 6 3 substitute more capital for less labor. Which would act to decrease the MRP of capital and increase the MRP of labor. (Remember the law of diminishing marginal product).

2) The Miracle Manufacturing Company’s short-run average cost function in 1996 is: AC = 3 + 4Q Where: AC: Average cost in dollars per pound of product Q: Output a) Obtain the equation for the firm’s short-run total cost function. Since, AC = TC , it follows that TC = AC * Q . TC = 3Q + 4Q 2 Q

b) Does the firm have any fixed costs? No, since every term in the total cost function is multiplicative in Q. c) If the price of the product (per pound) is $2, is the firm maximizing profits or losses? Explain your answer.
Π = TR − TC

Note: Π = 2 * Q − (3Q + 4Q 2 )
Π = − Q − 4Q 2 If the firm produces any positive amount of output they are experiencing a loss.. Their best solution is to produce nothing and close down.

3) The Suffern Company’s total cost function is: C = 100 + 3Q − 2Q 2 + 3Q 3 where: C: Total Cost Q: output per day a) What is the equation for the firm’s average cost curve?
TC Q 100 AC = + 3 − 2Q + 3Q 2 Q b) What is the equation for the firm’s marginal cost curve? AC =

MC =

∂TC ∂Q

MC = 3 − 4Q + 9Q 2 c) At what output is the marginal cost a minimum? Set the first derivative of MC wrt Q equal to zero and solve for Q. −4 + 18Q = 0 18Q = 4 2 Q= 9 4) Suppose you are a consultant to Harper & Row, the book publisher. Suppose