Assume that there are one buyer and one seller. Both parties can trade 1 unit of a good ex-post. The cost to the seller to supply 1 unit of the good is (c+s) where "c" is the marginal cost and "s" is quality. The gross surplus to the buyer if trade occurs is (v+s), where 1 ≥ v-c ≥ 0. (Assume that v and c are known ex-ante). The buyer must invest in a new technology ex-ante for the good to be useful. The probability that the good is useful to the buyer is "x" if the buyer invests x 2 /2. Hence, there is a possibility that the good is useless with the new technology. Both the buyer and seller will only know whether the good is useful only after the investment is made but before the good is produced. Bargaining will produce the Nash equilibrium.
a)Show that if price and quality can be determined through a contract ex-ante, the chosen level of investment is efficient. Also show that if price can be determined through a contract ex-ante (while investment cannot be determined through a contract), the chosen level of investment is not efficient.
b)Assume that quality is exogenous and price cannot be determined through a contract ex-ante.
(i) Show that the efficient level of investment is x* = v-c.
(x* is the efficient level of investment).
(ii) Show that if the power to determine price and quality is given to the seller, then the outcome is the same as when there is no integration
(the buyer and the seller do not merge as a single firm).
(iii) Show that the outcome depends on the parameters of the model for no-integration scenario and when the power to decide on price and quality is given to the seller.
c) Further assume that quality is exogenous and price cannot be determined through a contract. Also assume that there are 2 identical sellers that simultaneously determine price ex-post.
(i) Show that the level of investment is efficient.
(ii) Based on your answer in (i), suggest one implication on a firm’s behavior when it licenses other firms to produce its good.