# Managerial Economics: Cost Function

1. An economist estimated that the cost function of a single product is

C(Q)= 50 +25Q+30Q SQUARED+5Q CUBED

Based on this information determine:

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.

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#### Solution Preview

Please refer to the attached file for the computation guide provided.

Cost Function Computation Guide

1. An economist estimated that the cost function of a single product is

C (Q) = 50 +25Q+30Q SQUARED+5Q CUBED

Based on this information determine:

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

Fixed cost is the cost that does not change with the change in output. Hence, even though the production (Q) is zero, the amount is still the same. Referring to the cost function at hand, the fixed cost is 50. Even with the assumption that Q is zero, it is still the same.

b. The variable cost of producing 10 ...

#### Solution Summary

Managerial economics cost functions for a single product is examined. The fixed cost of producing 10 units of output are determined.

3551-Managerial Economics-03

7. (9-6) The Deering Manufacturing Company's short run average cost function in 1999 is AC=3+4Q, where AC is the firm's average cost (in dollars per pound of the product), and Q is its output rate.

a. Obtain an equation for firm's short run total cost function.

b. Does the firm have any fixed costs? Explain?

c. If the price of Deering Manufacturing Company's product (per pound) is $ 3, is the firm making profits or losses? Explain.

d. Derive an equation for the firm's marginal cost function.

8. (10-2) In 2001, the box industry is perfectly competitive. The lowest price point on the long-run average cost curve of each of the identical box producers is $4, and this minimum point occurs at an output of 1,000 boxes per month. The market demand curve for boxes is QD=140,000-10,000P where P is the price of a box (in dollars per box) and QD is the quantity of boxes demanded per month. The market supply curve for boxes is Qs=80,000+5,000P, where Qs is the quantity of boxes supplied per month.

a. What is the equilibrium price of a box? Is this the long-run equilibrium price?

b. How many firms are in this industry when it is in long-run equilibrium?

9. (11-2) The can industry is composed of two firms. Suppose that demand curve for cans is P=100-Q, where P is the price (in cents) of a can, and Q is the quantity demanded (in millions per month) of cans. Suppose that the total cost function of each firm is TC=2+15q where TC is total cost (in tens of thousand of dollars) per month, and q is the quantity produced (in tens of thousands of dollars) per month, and q is the quantity produced (in millions) per month by the firm.

a. What are the price and output if the firms set price equal to marginal cost?

b. What are the profit-maximizing price and output if the firms collude and act like a monopolist?

c. Do the firms make a higher combined profit if they collude than they would if the set price equal to marginal cost? If so, how much higher is their combined profit?