A firm faces the demand curve Q 20 08P and marginal cost M

A firm faces the demand curve Q = 20 - 0.8P and marginal cost MC = 2.5Q. If the firm cannot price-discriminate, what is the profit-maximizing price and quantity? If the firm can practice perfect price discrimination, how many units will it sell?

Solution

a. since firms cannot price discriminate price and quantity will be

Q=20-0.8P HERE P=MC

MC=2.5Q

NOW,

Q=20-0.8(2.5Q)

SOLVING THIS Q=20/3

PUT Q=20/3 IN Q=20-0.8P TO GET THE PRICE

PRICE =16.66

b. since price discrimination is followed so price will be greater than the cost . so when p=mc quantity was 20/3

but here quantity will be more than 20/3.