Suppose there are a large number of potential firms that could operate in a particular industry. Each firm has an identical cost function given by C(q) = 1 + q + q2, where q denotes output. The market demand curve is p = 5-Q/12, where p denotes the market price and Q the quantity demanded.

(a) If the industry were competitive, what would be the equilibrium number of firms? Let x denote this number.

(b) Suppose now that these x firms form a cartel that maximises their joint profit. What price will the cartel set and what will be the quota (output) of each firm? How much profit will each firm
make?

(c) Suppose a new firm enters the market but does not join the cartel. If the firm assumes it can sell as much as it wants to at the cartel price, how much profit would it expect to make?

(d) Suppose the cartel is now given legal rights to force any firm in the industry to join the cartel. Assuming there is free entry into the industry, how many firms will eventually be members of the
cartel?

(e) Suppose a new government comes into power and prohibits cartels, thus restoring competitive conditions to the industry. What is the consequence for the original x firms?

a题很简单，x求出等于24。。b题也很简单，利用mr=mc可以求解出。。

想请教c小题怎么解。。。

d小题说假如卡特尔是合法的，而且所用企业必须都假如卡特尔，并且假设进入市场是自由的，求解最终卡特尔会有多少成员。。是否利用p=ac，单个企业利润为零的条件求解？？

e小题说假如现在新的政府进行干预，卡特尔现在禁止，市场恢复为竞争性的，那么最初的x个企业会有什么样的结果。。。
求解出d题的答案等于36，大于竞争市场中企业的均衡数量，那么最初的x个企业会怎样？？

求好心人解答。。c,d,e三小题