a. Fill in the profit entries in the payoff table.
b. If the firms act independently, what advertising level should each
choose? Explain. Is a prisoner’s dilemma present?
c. Could the firms profit by entering into an industry-wide agreement
concerning the extent of advertising? Explain.- In each of the following cases, provide a brief explanation of whether a
prisoner’s dilemma is present. If so, suggest ways the dilemma can be
overcome.
a. When there is a bumper crop (a large supply and, therefore, low
prices), farmers incur losses.
b. Individual work effort has been observed to suffer when managers are
grouped in teams with all team members receiving comparable
compensation based on the overall performance of the group. - Economists Orley Ashenfelter and David Bloom studied disputes that were
brought to arbitration between management and workers’ unions. They
found that being represented by a lawyer increased that side’s chance of
winning its arbitration case. The payoff table (listing the union’s chance of
winning the arbitration case) summarizes their empirical findings.
Management
W/O Lawyer Lawyer
W/O Lawyer .56 .27
Union
Lawyer .77 .54For instance, according to the upper-left entry, if neither side uses a
lawyer, the union is expected to prevail in the arbitration case 56 percent
of the time.
a. Determine each side’s optimal action and the resulting outcome.
b. Does this situation constitute a prisoner’s dilemma? Explain briefly.- Two firms produce differentiated products. Firm 1 faces the demand
curve Q 1 75 P 1 .5P 2. (Note that a lower competing price robs the
firm of some, but not all, sales. Thus, price competition is not as extreme
as in the Bertrand model.) Firm 2 faces the analogous demand curve Q 2
75 P 2 .5P 1. For each firm, AC MC 30.
a. Confirm that firm 1’s optimal price depends on P 2 according to P 1
52.5 .25P 2. (Hint:Set up the profit expression 1 (P 1 30)Q 1
(P 1 30)(75 P 1 .5P 2 ) and set M 1 / P 1 0 to solve for P 1
in terms of P 2. Alternatively, set MR 1 MC and solve for Q 1 and then
P 1 in terms of P 2.
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