Consider an industry where firms compete by setting output levels. Market demand
ID: 1132674 • Letter: C
Question
Consider an industry where firms compete by setting output levels. Market demand is givevn by D(P)-150-P, and each potential firm has the cost function C(q)-150 + 50q a) Show that profits per firm are given by 961, 475, and 250 as the number of firms equals 2, 3 or 4 Suppose that any merger would lead to a new firm with the same fixed costs and the same marginal cost b) Suppose that initially there are four firms. Show that a merger between only two firms is unprofitable. c) Suppose now that there are three firms in the market. Show that a merger between two firms is profitable.Explanation / Answer
Answer:
a) For n firms, cournot competition has each firm producing q = (a - m)/(b(n + 1)) where demand is p = a - bQ (Q is the market quantity). Price is P = (a + nm)/(n + 1) where m is the marginal cost
Case 1 (n = 2)
q = (150 - 50)/3 = 100/3
Price p = (150 + 100)/3 = 250/3
Profit per firm = TR - TC = (100/3)*(250/3) - (150 + 50*(100/3)) = 961.11
Case 2 (n = 3)
q = (150 - 50)/4 = 25
Price p = (150 + 150)/4 = 75
Profit per firm = TR - TC = (25*75) - (150 + 50*(25)) = 475
Case 3 (n = 4)
q = (150 - 50)/5 = 20
Price p = (150 + 200)/5 = 70
Profit per firm = TR - TC = (20*70) - (150 + 50*(20)) = 250
b) When there are four firms, each firm earns a profit of 250. Now when 1 and 2 merge, there are 3 firms each earning 475. But 1 and 2 are cumulatively earning 475 and separately they are splitting the profit at 237.50 each. Hence merger has reduced their profits from 250 to 237.50
c) When there are four firms, each firm earns a profit of 250. Firm 3 and 4 merge so that now each of the three firms earn 475. Now 1 and 2 also merge so there are two firms, each earning 961.11. Separately, all of them are earning 240. This merger between 1 and 2 is profitable because without merger their profits are 237.50 (when 3 and 4 have merged). This shows that of 3 and 4 merge, 1 and 2 will have to merge to increase their profits.