Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

252 PRICE AND OUTPUT UNDER MONOPOLISTIC COMPETITION AND OLIGOPOLY [CHAP. 10
firm A enters the market first, (b) what happens when firm B subsequently enters the market, (c) A’s
reaction, and (d) the final result. Is the result stable? Why?
Fig. 10-14
(a)
IfA enters the market first, A will sell 300 units at the price of $3 and thus maximize its TR and total profits at
the level of $900. This is the monopoly solution for duopolist A.
(b) Now B enters the market, and assumes that A will continue to charge the price of $3, Since we are dealing
with a homogeneous product, by selling at a price slightly below $3, B can sell its maximum output of 500
units and thus capture most of A’s market. Thus B’s TR and total profits will be almost $1500 (see
Fig. 10-14).
(c) Firm A now reacts, and assuming that B will keep its price constant, A can sell its maximum output of 500
units (and capture most of B’s market) by setting its price slightly below B’s price.
(d ) This process will continue until each firm will sell its maximum output of 500 units at the price of $1 (and
thus make $500 of profit). The above result is not stable, however. For example, suppose firm A is the first
to take stock of the situation and notes that if firm B maintains the price of $1, A could increase its total
profits to $900 by selling 300 units of output at the price of $3 (the original monopoly solution for firm A).
But then firm B realizes that by raising its price from $1 to slightly below $3, it can sell its maximum
output of 500 units and thus increase its total profits to almost $1500. Having lost most of its market,
A reacts by lowering its price, and the process goes on indefinitely with the price fluctuating between
the monopoly price of $3 and the maximum output price of $1 for each firm. The above is an illustration
of the Edgeworth model.
10.13 Assume that (1) there are only two firms, A and B, selling a homogeneous commodity produced at zero
cost; (2) the total market demand function is QD ¼ 240 – 10P and is divided equally between A and B;
(3) each firm can produce no more than 100 units of output; and (4) firm A enters the market first, followed
by B, but each always assumes, in determining its best level of output, that the other holds its
price constant. (a) With the aid of a figure, explain what happens when A enters the market first;
when B enters the market; and A’s and B’s reaction pattern and (b) explain why and how the price
of the commodity will fluctuate indefinitely. (c) What do the Cournot, the Bertrand and the Edgeworth
models have in common?
(a)
The assumption above define the Edgeworth model. From Fig. 10-15, we see that if A enters the market first, A
will sell 60 units at $6 each and make the monopoly profit of $360. Since the commodity is homogeneous, by
selling at a price slightly below $6, B can enter the market, capture 2/3 of A’s market, and sell its maximum
output of 100 units. A reacts and the process will continue until A and B both sell their maximum output of 100
units at the price of $2, and so each makes a profit of $200.