Question

In: Economics

A monopolist faces a demand of P = -3Q + 400. The monopolist’s marginal cost is...

A monopolist faces a demand of P = -3Q + 400. The monopolist’s marginal cost is MC = 2Q + 80. The total cost for the monopolist is TC = Q² + 80Q + 6000

a) Find the profit-maximizing quantity, price, and profit of the monopolist.

b) A regulatory agency tries to force the monopoly to produce the same quantity as a competitive firm. Show what this price and quantity is and why the firm will eventually shut down rather than submit to this regulation.

Solutions

Expert Solution

a. The profit-maximizing condition for the monopoly firm is:

MR=MC

As given,

Demand function:

Total revenue of the firm will be:

The marginal revenue of the firm will be:

As,

Putting MR=MC we get:

Putting the value of Q in demand function e get the profit-maximizing price.

Profit = TR-TC

Putting the Q=4

TR=1552

TC=6336

b. If the firm produces competitive quantity then the profit maximizing condition for the firm will become:

P=MC

Q=64

Profit=TR-TC

TC=15216

Average total cost of the firm =TC/Q = 15216/64=237.75

This implies,

As if the firm produces competitive output, then the price of the firm will be less than the average total cost of the firm. Thus, the firm will shut down.

Rahul Sunny answered 1 year ago

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