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Vitek1552 [10]
4 years ago
15

We can use the Cournot model to derive an equilibrium industry structure. For this purpose, we will define an equilibrium as tha

t 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?
Business
1 answer:
Nina [5.8K]4 years ago
5 0

Answer:

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

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Answer not in the given option, please recheck for error.

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