Changes

3. The Board of Directors does not approve of Carol's wasteful money burning scheme. Fortunately, Carol knows that her employees all have CARA preferences with an identical risk-aversion parameter, <math>\rho</math>. She proposes a clever new scheme to get all the Yahoos to work. What is it?

Consider a buyer-seller transaction in which the buyer makes a relationship specific investment x in period 1. This investment costs the buyer <math>x^2</math>, and it only pays off if the buyer is supplied with a “widget” by the seller in period 2. The return from investment (assuming the widget is supplied) is x + v, where v is a random variable uniformly distributed on <math>[– h,h]</math>. Assume that <math>h\in[0.25,0.5]</math>. Neither x nor v is observed by the seller, and the buyer only learns v in period 2 so that investment x is made prior to learning v. The seller's cost of producing the widget is zero.

(c) Compare your solution in (b) to the first-best level obtained in part (a). How does the buyer’s investment vary with the amount of noise, h?

In many political and business settings, control over the agenda of policy changes is a

1. Suppose a setting like that in Barro (1973), where an infinite pool of identical politicians is available. A voter appoints a politician in period 1, and must decide whether to reelect her in each period or appoint a new one. The politician has discretion over a $1 budget each period and must decide an amount x to steal, leaving 1-x to the voter. The voter commits to a retrospective voting rule {X1,X2,X3,...} such that if in period t the politician steals at most Xt then she is to be reappointed. Voter and politicians have the same discount rate δ and their utility for money is the identity function.

a. Characterize the optimal retrospective voting rule. Is it important that the voter can commit to a voting rule?

2. Suppose the same setting, but now a piece of legislation has mandated a term limit whereby the politician can be reelected only once.

a. Does this help the voter?

b. Is the voter better off, worse off, or the same if we assume he cannot commit to a voting rule?

3. (for bonus points) Would it help to extend term limits so that the politician can be reelected twice rather than just once? How does this answer depend on the voter being able to commit?