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