咱想要详细的过程，因为是要交的
大家别怪咱这样作弊，实在因为老师用英文上课听不懂，而上课的都是大三的师兄师姐，他们都是学过高级微观课的，老师都讲给他们听啊，我刚过完大一，悔只在我选错课...
那些式子没法显示，所以把作业PDF也附在下面了，大家麻烦下...
拜托了，学分绩啊~~~~

A cartel of 16 firms is lobbying for a bill that will bring a tax break of $100,000
to firm 1 and $90,000 to each of the other firms. They are in competition
with another interest group lobbying against the proposed bill. This other
group has invested $40,000 in its lobbying campaign. It is estimated that the
probability of adoption of the bill is proportional to the budgets of the two
competing campaigns. Thus, if the industry gathers x thousands of dollars,
the probability of adoption of the bill is x/(x + 40). The expected profit of
firm i contributing xi (thousands of dollars) to the campaign is
u1(x1, ..., x16) = 100 ·
x
x + 40
− x1,
ui(x1, ..., x16) = 90 ·
x
x + 40
− xi, i = 2, ..., 16
where x =
P
i xi.
a) Calculate each firm’s equilibrium contribution and the total lobbying
investment (approximate
p
10 by 3.15).
b) Show that there is only one firm contributing to the lobbying investment
and all other firms free-ride, and that the contributing firm has the
smallest expected profit (work hard and get less).
1