A monopolist faces a market demand: P = 200 – Q. The monopolist has cost function...

A monopolist faces a market demand: P = 200 – Q. The monopolist has cost function as C = 1000 + Q2, and marginal cost MC = 2Q. (

1) Solve for Marginal Revenue (MR) function.

(2) Find the profit-maximizing quantity? Profit?

(3) Suppose the monopolist decides to practice 3rd degree price discrimination. Without solving for the 3rd degree price discrimination, can you compare the new profit earned by the monopolist with the old profit?

Solutions

Expert Solution

1 )

P = 200 - Q

TR = P*Q

= (200 - Q)*Q

=200Q - Q^2

TR is differentiated to get MR:

MR = 200 - 2Q

Profit Maximizing Quantity is achieved where MR = MC

200 - 2Q = 2Q

200 = 4Q

Q = 50

P = 200 -Q

= 200 - 50

= 150

Profit = TR - TC

= 150*50 -1000 - (50)^2

= 4000

Price discrimination is practised based on the age, group etc. or elasticities of demand varied for different age groups. Thus, under the price discrimination , prices can be set according to the elasticities of demand prevailing in market. So profits in third degree price discrimination market tends to be larger.

Rahul Sunny answered 1 year ago

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