We can use the Cournot model to derive an equilibrium industry structure. For this purpose, we will define an equilibrium as that structure in which no firm has an incentive to leave or enter the industry. If a firm leaves the industry, it enters an alternative competitive market in which case it earns zero (economic) profit. If an additional firm enters the industry when there are already n firms in it, the new firm's profit is determined by the Cournot equilibrium with n + 1 firms. For this problem, assume that each firm has the cost function: C (q) = 256 + 20_q. Assume further that market demand is described by: P = 100 - Q. a. Find the long-run equilibrium number of firms in this industry. b. What industry output, price, and firm profit levels will characterize the long-run equilibrium?

a. long run equilibrium numbers of firms in the industry are 4

b. Output of each firm will be 16

Explanation:

Under cournot's equilibrium, the cost function of an individual firm is written as:

C (q) = F + cq

In our case, C (q) is given as

C (q) = 256 + 20q

Therefore, F = 256 and c = 20

At the same time, the demand function is written as:

P (Q) = a - bQ

In our case, P is given as

P = 100 - Q

Therefore, a = 100, b = 1

a. Long run equilibrium number of firms in the industry

N = ((a-c) / (bF) ^0.5) - 1

N = ((100-20) / (1*256) ^0.5) - 1

N = (80/16) - 1 = 4

Therefore, long run equilibrium numbers of firms in the industry are 4

b. Output of each firm will be q = (a-c) / b * (1+N) = (100-20) / 1 * (1+4) = 80/5 = 16

Therefore, total output of industry is 16*4 = 64

Price = 100-64 = 36

Profit = Revenue - Cost

Revenue of each firm = Price * Output = 36*16 = 576

Cost = 256+20*16 = 576

Therefore, profit = 0