Problems and Applications

Price
and
Costs

Firm

Market



MC





ATC



P=$8

P=$8

S



q=4


Figure 7

11. a. Each firm’s fixed cost, the portion of total cost that does not vary with changes in q, is $50. Each firm’s variable cost, the portion of total cost that varies with changes in q, is . The equation for average total cost is: .

b. See Figure 8 for the graph of the average-total-cost curve and the marginal-cost curve for q from 5 to 15. The average-total-cost curve is minimized when the quantity is 10. The average total cost and marginal cost are both $10 at that quantity.

Price



MC



ATC



$10



Quantity

15

10

5


Figure 8

c. The supply curve for each firm is the segment of the marginal-cost curve that lies above the intersection of the average-total-cost curve and the marginal-cost curve, so the supply curve for each firm is:

d. In the short run, the supply curve for each firm is the segment of the marginal-cost curve that lies above the intersection of the average-variable-cost curve ( ) and the marginal-cost curve. The average-variable-cost curve and the marginal-cost curve intersect where q=0, so the short-run supply curve for each firm is . Because the number of firms is fixed at 9 in the short run, the short-run market supply curve is .

e. Setting the market demand and market supply curves equal to each other, , adding P to both sides of the equation, , and solving for P, the equilibrium price is $12. Substituting the price into either the demand function or the supply function yields the equilibrium quantity, 108.

f. In this equilibrium, each of the 9 firms produces (108/9 = 12) 12 units. Profit is total revenue minus total cost. Total revenue is and total cost is , so each firm’s profit is $144 - $122 = $22. Because the profit is greater than zero, there is an incentive for firms to enter the market.

g. In the long run with free entry and exit, all firms will earn zero economic profit so the price will be equal to the minimum of the average-total-cost curve. The equilibrium price will be $10. When the price is $10, the equilibrium quantity is 110 units.

h. In this long run equilibrium, , so each firm produces 10 units and there are 110/10 = 11 firms.

Chapter 15