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. (Lerner Index)

A. If the firm\'s marginal cost is constant at $2, what is the profit-maximizing price and quantity?

B. If the firm\'s marginal cost increases to a constant $3, what is the profit-maximizing price and quantity?

Solution

Lerner\'s index measures market power.Lerner\'s index is equal to inverse of absolute value of elasticity .

Another way to calculate Lerner\'s index is that it is difference between price and marginal cost expressed as a percentage of price.

L=(P-MC) /P=1/absolute value of elasticity

L=1/2

MC=2

L=(P-MC)/P

1/2=(P-2)/P

P=4

Constant elasticity of demand function is of form=

Q=P^{(- e)}

where e is elasticity

Q=4⁽²⁾=16

B.) MC=3

L=(P-MC)/P

1/2=(P-3)/P

P=6

Q=P^-e

Q=6²=36

L=