0 2 Inverse demand function for a good supplied by a monopol

0 2. Inverse demand function for a good supplied by a monopolist is P 64-This monopolist has three plants whose marginal cost functions are given as: MC,(02 ) = 2 + 202 MC,(L) = 6 +0) Find the monopolists profit maximizing price and output at each plant.

Solution

Inverse demand Function: P= 64-(Q/7)

Total Revenue(TR)= 64Q-(Q²/7)

Marginal Revenue(MR)= 64-(2Q/7)

In monopoly market , the monopolist\'s maximising output occurs where marginal revenue equals marginal cost

Profit maximisation for Firm 1,

64-(2Q₁/7)=4Q₁

Q₁=14.9

P₁= 64.87

Profit maximisation for Firm 2,

64-(2Q₂/7)=2+2Q₂

Q₂=27.13

P₂=60.12

Profit maximisation for Firm 3,

64-(2Q₃/7)=6+Q₃

Q₃=45.11

P₃=57.56