Suppose a firm faces the demand curve which gives a constant

Suppose a firm faces the demand curve which gives a constant price elasticity of demand of -2. (recall the Lerner index) 1. If the firm\'s marginal cost is constant at $2, what is the profic-maximizing price and quantity? 2. If the firm\'s marginal cost increases to a constant $3, what is the profit-maximizing price and quantity?

Solution

Lerner\'s index is given by (P - MC / P).At profit maximising condition MR = MC Thus we have MR = MC = P(1 - 1/e)

Substituting the same in lerner\'s index we have (P - MC / P) = 1/e.

Therefore for 1st case when marginal cost is $2 we have (P - 2) / P = 1/2

P = 4.Thus profit maximising price is equal to 4.

2nd case when MC = 3

(P - 3) / P = 1/2

P = 6.Thus equilibrium price in this scenario is equal to 6.