Question

The regular demand curve a monopoly faces is Qx= 65 – 1/2Px The​ firm's cost curve...

The regular demand curve a monopoly faces is Qx= 65 – 1/2Px

The​ firm's cost curve is C (Q) = 10 + 6Q

What is the​ profit-maximizing solution?

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Answer #1

Answer : Given,

Demand : Q = 65 - 1/2 P

=> 1/2 P = 65 - Q

=> P = (65 - Q) * 2

=> P = 130 - 2Q

TR (Total Revenue) = P * Q = (130 - 2Q) * Q

=> TR = 130Q - 2Q^2

MR (Marginal Revenue) = TR / Q

=> MR = 130 - 4Q

Given, C(Q) = 10 + 6Q

MC (Marginal Cost) = C(Q) / Q

=> MC = 6

At monopoly equilibrium, MR = MC.

=> 130 - 4Q = 6

=> 130 - 6 = 4Q

=> 124 = 4Q

=> Q = 124 / 4

=> Q = 31

Now, P = 130 - 2Q = 130 - (2 * 31) = 130 - 62

=> P = $68

Therefore, the monopoly firm's profit maximizing price is, P = $68 and quantity is, Q = 31 units.

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