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
