There are two players, a buyer and a seller. In period 1, the seller chooses his investment level I 0 at cost I. In period 2, the buyer observes the investment I and makes a take-itor-leave-it price offer to the seller for one unit of the good. If the offer is accepted by the seller, it will produce one unit at cost c(I). Assume that c 0 < 0 (higher was the investment I earlier, lower is the cost of production; and also assume that c 00 > 0 and c(0) < v, where v is the buyers utility from consuming the good.

(a) Model this interaction as a game.

(b) Find subgame perfect equilibria/equilibrium of this game.

(c) What is the socially optimal level of investment? (d) Is it possible for the buyer and the seller to agree on a contract (before period 1) which delivers the socially optimal investment? Note that contracts can not be written on the level of I, because such contracts are not verifiable.