Question

Suppose we are studying the market for beer; the market for candy is perfectly competitive. There are two types of firms that produce beer, Type A firms and Type B firms. The cost curve of type A firm is represented by CA(y) = y^2 + 5, and the cost curve of a type B firm is represented by CB(y) = ((y^2) / 2 ) + 10. In the short-run, there are 10 Type A firms in the market, and 15 Type B firms in the market. The market demand for beer is given by: D(p) = 180 - 10p.

a. Solve for the short-run market equilibrium quantity and price.

b. Would type A firms enter the market in the long-run? Explain.

c. Briefly explain why the market price can’t be less than min (ATC) at the long-run competitive equilibrium.

Answer 1

A)

D = 180 - 10 P

MCa = 2 y

MCB = y

In the short run, the marginal cost curve is the supply curve of a firm (in a perfectly competitive market)

=> P = 2 ya    => ya =

=> p = yb    => yb =

total output supplied by both firms A and B is equal ya + yb

=>

at equilibrium quantity demamnded = quantity supplied

therefore,

substituting this value in demand equation we get market equiloibrium quantity as

B) In the long run type A firms would not enter the market becuase it has higher marginal cost than type B firms.  In fact the marginal cost of type A firms is double that of type B firms. In the long run type B firms will out compete type A firms because it has less marginal cost compared to type A firms. Hence will drive type A firms out of business.

C)

From the standard microeconomic theory of perfectly competitive markets we know that if firms are earning positive economic profits, more firms will enter the market, thus shifting the supply curve to the right. As the supply curve shifts to the right, the equilibrium price will go down. As the price goes down, economic profits will decrease until they become zero.

When price is less than average total cost, firms are making a loss. Over the long-run, if firms in a perfectly competitive market are earning negative economic profits, more firms will leave the market, which will shift the supply curve left. As the supply curve shifts left, the price will go up. As the price goes up, economic profits will increase until they become zero.

To summarize, in the long-run, firms in a perfectly competitive market earn zero economic profits. The long-run equilibrium point for a perfectly competitive market occurs where the price intersects the marginal cost curve and the minimum point of the average total cost (ATC) curve.