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

256 PRICE AND OUTPUT UNDER MONOPOLISTIC COMPETITION AND OLIGOPOLY [CHAP. 10
In other more complicated and realistic cases, it may not be so easy to decide on how the cartel’s profits should
be shared. The bargaining strength of each firm then becomes important.
(d ) Even if cartels are illegal in the U.S., cartel models give some indication of how a tightly organized oligopolistic
industry might operate. The best known international cartel today is OPEC (Organization of Petroleum
Exporting Countries). Note that the greater the number of firms in the cartel, the easier it is for members to
“cheat” on others and thus cause the collapse of the collusive agreement.
10.18 Assume that (1) the two identical firms in a purely oligopolistic industry agree to share the
market equally, (2) the total market demand function for the commodity is QD ¼ 240 2 10P and
P is given in dollars, and (3) the cost schedules of each firm are as given by the figures in
Table 10.2 and factor prices remain constant. Show that this market-sharing cartel also reaches the
monopoly solution. What are the total profits of the cartel? Is this solution likely to occur in the
real world?
Table 10.2
q 40 60 80
SMC ($) 8 12 16
SAC ($) 13 12 13
In Fig. l0-19, each duopolist is in equilibrium at point C (where mr ¼ SMC) and sells 40 units of output at the
price of $16 on d, the half-share demand curve. The market as a whole will produce 80 units (given by point E,
where MR ¼ P MC) and the price is $16 on D. This is the monopoly solution. Each duopolist makes a profit
of $3 per unit and $120 in total. So this market-sharing cartel as a whole will make profits of $240. However, in
the real world, the market need not be shared equally and we may have more than two firms, each facing different
cost curves. So the solution is not likely to be the neat monopoly solution found in Fig. 10-19.
Fig. 10-19
10.19 Suppose that there are only one low-cost firm and one high-cost firm selling a homogeneous commodity,
and they tacitly agree to share the market equally. If D in Fig. 10-20 is the total market demand curve for
the commodity, then d is the half-share curve for each firm and mr is the corresponding marginal
revenue curve. If the subscripts 2 and 1 refer, respectively, to the low-cost and the high-cost firms, determine
what each firm would like to do and what it actually does.