Question

1. Suppose in a market, for the typical firm P = 20 - q - b(n - 1)q and TC = 2q, where P is the price of output q, b is a parameter determining how sensitive a firm’s output price is to the output of its (n - 1) competitors/rivals, where n is the number of firms in the market, TC is the total cost of production, and q=Q=industry/market output. a. Suppose n = 1 and this market was occupied by a single profit-maximizing Monopolist (e.g. Q = q), how much output would be produced? What price would be charged? How much profit would be earned? b. Suppose b = 0 and this market was occupied by a very large number of profit-maximizing Perfectly Competitive Firms (e.g. Q = q for the industry), how much output would be produced? What price would be charged? How much profit would be earned?

2. Refer back to #1 and suppose that the industry consists of Monopolistically Competitive firms that face (n-1) = 2 other competitor/rivals, where b = 1/2 and q = Q. a. How much output would be produced by a typical firm? What price would be charged? How much profit would be earned? How much output would the industry/market produce? b. What, theoretically, explains the differences in the pricing/output decisions across the three market structures considered in questions 1 - 2?

Answer #1

Answer : 1) a) Given,

P = 20 - q - b (n-1) ; TC = 2q

When n = 1 ,

P = 20 - q - b (1 - 1) = 20 - q - b*0

=> P = 20 - q

TR (Total Revenue) = P*q = (20 - q)*q = 20q - q^2

MR (Marginal Revenue) = TR/q = 20 - 2q

MC = TC/q = 2

In case of single monopolist at equilibrium condition,

MR = MC

=> 20 - 2q = 2

=> 20 - 2 = 2q

=> 18/2 = q

=> q = 9

Now, P= 20 - 9 = 11

TR = P*q = 11*9 = 99

TC = 2*9 = 18

Profit = TR - TC = 99 - 18 = 81

Therefore, the output level is q = 9.

Price level is P = 11 and profit level is 81.

b) when b=0 ; P = 20 - q - 0 (n - 1) => P = 20 - q

In case of perfectly competitive market at equilibrium,

P = MC

=> 20 - q = 2

=> 20 - 2 = q

=> q = 18

Now, P = 20 - 18 = 2

TR = P*q = 2*18 = 36

TC = 2q = 2*18 = 36

Profit = TR - TC = 36 - 36 = 0

Therefore, the output level is q = 18 ; price level is P= 2 profit level = 0 (zero).

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