我们用的书是 tirole
theory of industrial organization

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. Hence, there is a possibility that the good is useless with the new technology. The probability that the good is useful to the buyer is "x" if the buyer invests x2(平方)/2. 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
这个地方 用x(v-c)-x2/2 FOC 即可得出来。

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 and when the power to decide on price and quality is given to the seller.


题目里有点绕。第一题我解出来了，但是觉得不对。
而我也奇怪 为什么 x*=v-c 不能用到第一问题里。
再请大牛帮忙解释一下， ex-ante 和 ex-post 前后的价格设定 差别  等等和 其他的所造成的不同影响。


拜托了。。。。。