In: Economics
Use the work-leisure choice diagram to illustrate the following cases where an individual is: A) Unwilling to go on welfare because the welfare payment is too low. B) Indifferent between welfare and work. C) Induced to move off welfare because of an increase in her wage. D) Induced to move off welfare because of a change in preferences between income and leisure. E) Induced to move off welfare by a reduction of 100 percent implicit tax on earnings.
2 The UK O±ce of Fair Trading has recently unveiled a plan that will o®er
immunity from prosecution to ¯rms who blow the whistle on their co-cartel conspirators. In the U.S., this tactic has proven extremely successful: since its introduction in
1993, the total amount of ¯nes for anti-competitive behavior has increased twentyfold.
Show how the tactic initiated by the U.S. Department of Justice and soon to be
followed by the O±ce of Fair Trading changes the rules of the game played between
¯rms in a secret cartel.
Solution: Prior to the introduction of the plan, each cartel ¯rm would have two options:
(a) to stick by the agreement or (b) to deviate and set lower prices. With the introduction of
the plan, the ¯rm has a third option: (c) to blow the whistle. Let ® be the probability that
the DOJ discovers the price conspiracy. High values of ® imply a low expected value from
(a). The same is true of (b), though probably to a lesser extent. Finally, (c) is invariant to
the value of ®. We would thus expect that, for high values of ®, (c) is the best strategy.
With the introduction of the plan, the ¯rms now play a second prisoner's dilemma type
of game. Before, it was whether to price high or price low. Now, it's whether to blow the
whistle or not. Firm would be better o® if neither of them blew the whistle. However, if ®
is high, the bblowing the whistle is a dominat strategy.
4.3 Figure 1 represents a series of two-player games which illustrate the rivalry between Time magazine and Newsweek. Each magazine's strategy consists of
choosing a cover story: \Impeachment" or \Financial crisis" are the two choices.10
The ¯rst version of the game corresponds to the case when the game is symmetric
(Time and Newsweek are equally well positioned). As the payo® matrix suggests,
\Impeachment" is a better story but payo®s are lower when both magazines choose
the same story. The second version of the game corresponds to the assumption
that Time is a more popular magazine (Time's payo® is greater then Newsweek's
when both magazines cover the same story). Finally, the third version of the game
illustrates the case when the magazines are su±ciently di®erent that some readers
will buy both magazines even if they cover the same story.
For each of the three versions of the game,
(a) Determine whether the game can be solved by dominant strategies.
(b) Determine all Nash equilibria.
(c) Indicate clearly which assumptions regarding rationality are required in order
to reach the solutions in (a) and (b).
Solution:
(i) Impeachment is a dominat strategy for both players. It follows that (Impeachment, Impeachment) is the unique Nash equilibrium. All we need to assume to reach this conclusion
is that players are rational and know their own payo®s.
10In each cell, the ¯rst number is the payo® for the row player (Time).