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1. A market with 2 identical firms lasts for 10 periods. The market demand is p=80-q in each period. The cost function of each firm is c(q)=q2 in each period. Each firm chooses its output in each period to maximize its total profit from 10 periods.

 

Find the market equilibrium and each firm’s profit in the 7th period.

 

 

2. Consider a market with n identical firms. Each firm has a cost function c(q)=24q. The market demand has a constant price elasticity e. Firms choose output simultaneously and non-cooperatively.

(a) Find the profit margin when

(i) n=1, e=-1.3

(ii) n=1, e=-1.8

(iii) n=2, e=-1.3

(b) Explain the differences in the profit margins in (a).

 

 

3. There are two types of firms in a competitive market. The aggregate supply of type 1 firms and type 2 firms are S1(p)=70p and S2(p)=50p, resepectively. The market demand is D(p)=3200-80p.

(a) Find the equilibrium.

(b) Find the equilibrium if all firms merge.

(c) Explain the differences in prices, outputs, and welfare between (a) and (b).

 

4. There are three firms in a market: firm 1, firm 2, and firm 3. They have same cost function c(q)= and choose output simultaneously and non-cooperatively. The market demand is p=65-q.

(a) Find the market price, each firm’s output and profit, consumers’ surplus, and welfare.

(b) Find the market price, each firm’s output and profit, consumers’ surplus, and welfare if firm 2 and firm 3 merge.

(c) Explain the differences in prices, each firm’s outputs and profits, consumers’ surplus and welfare between (a) and (b).

 

 

 

5. (a) Customers are uniformly located along a street with unit length (the left end is 0 and the right end is 1). Each of them either buys one unit of a good or does not buy. The benefit to each customer from consumption of the good is c dollars. The transportation cost of customers is c dollars per unit length. Firms have zero production cost and the market price is fixed at .

(i) Find the equilibrium locations of firms if there are three firms in the market.

(ii) Is the equilibrium in (i) efficient?

 

(b) Customers are uniformly located along a street with unit length (the left end is 0 and the right end is 1). Each of them wants to buy one unit of a good. The transportation cost of customers is c dollars per unit length. Three identical firms with cost function c(q)=mq are located at 0, 0.5, and 1. Find the price and profit of the firm located at 0.5 if the other two firms set their prices at m+0.5c.

 

希望能有思路和大概的解题过程，中英文都可以，谢谢大家了

 

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关键词：微观经济 SIMULTANEOUS equilibrium differences Cooperative 微观经济

1,两个同样的企业，进行10个阶段的竞争，应该采取古诺竞争，还是其他方式？

有限博弈，和一次博士的结果是一样的。同时决定产量的话，应该是古诺竞争，又先后次序的话，要进行斯塔克博格竞争。或伯特兰德竞争。

2，n个相同的企业竞争，市场的需求弹性给定，各个企业的成本函数相同。进行同时的非合作的博弈。古诺模型是合作博弈，

非合作博弈是伯特兰德模型或其他。一个企业就是垄断，两个企业就是垄断竞争。

用公式可以求出来的。

3,两个供给函数不同的企业，进行竞争。因为是供给函数，不知道是否可以推出边际成本，如果可以就可以进行正常的分析了。把供给函数写成反供给函数，能够确定其边际成本呢？好像应该可以的。MR1=MC1。

4，三个成本相同的企业进行竞争，同时选择产量和进行非合作竞争。产量选择在这里应该就是古诺竞争。

5，三个企业好像没有均衡点。或者说是无效的。

楼主的问题，我很感兴趣，但是我的水平有限，期待高手继续指点。

很感谢楼上的回答，虽然没有具体的解释，但是给了我思路，谢谢了。

这些题是去年我学的一门课的半期考的题目，快要半期考了，希望能够做出来能对考试有帮助。可惜水平有限，所以只能在这里求助了。

说句实在话，楼主的这些题目，我基本上没有见过，毕竟是原版的英语试题啊。

但是这些题目将丰富我的题库，我不会让它沉下去的，这些题有一定的研究价值。

谁救救我啊，考试危在旦夕~