Answer to Question #87334 in Microeconomics for SARATHLAL

Question #87334
1. A monopolist faces the demand curve Q = 60-P/2. The cost function is C=Q2
. Find
the output that maximises this monopolist’s profits. What are the prices at profits
and that output? Find the elasticity of demand at the profit maximising output.
1
Expert's answer
2019-04-02T10:18:01-0400

Q = 60 - P/2 or P = 120 - 2Q.

Monopolist profit-maximizing quantity is produced, when MR = MC.

"MR = TR' = (P*Q)' = (120Q - 2Q^{2})' = 120 - 4Q,"

"MC = C' = (Q^{2})' = 2Q."

120 - 4Q = 2Q,

Q = 20 units.

P = 120 - 2*20 = 80.

"Ed = -b*P\/Q = -0.5*80\/20 = -2,"

so the demand is elastic.


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