Answer Happy

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.