Question

1. A monopolistic firm has costs C = 160 + 16Q + .1Q² and has the price equation P = 48 - .4Q .
2. 1. Find the firm's profit-maximizing price.
   2. Find the firm's profit-maximizing quantity.
   3. What is the firm's profit?
   4. What is the firm's efficient scale of output?
   5. Why doesn't the firm produce at its efficient levels?

Answer 1

A)

The firm maximizes profit at MR=MC

Marginal revenue is the change in total revenue, and it is found by differentiation

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MC is the change in total cost, and it is found by the differentiation of the total cost

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equating the MC=MR

16+0.2Q=48-0.8Q

Q=32

the profit is maximum at the output level of 32 units.

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B)

The price is found by using the demand curve

P=48-0.4Q

P=48-0.4*32

P=35.2

the price is $35.2

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C)

Profit =TR-TC

TR=P*Q=35.2*32

TR=1126.4

TC=160+16*32+0.1*(32^2)

TC=774.4

Profit=1126.4-774.4

=352

The profit is $352

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D)

The efficient level of output is at MC=ATC

equating with MC

Q=40

the efficient level of output is 40 units

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E)

The firm produces at MR=MC where Profit is maximum, and the efficient level of output is MC=ATC which is higher than it where

MC>MR

Q=40

MC=16+0.2*40

MC=$24

MR=48-0.8Q

Q=40

MR=48-0.8*40

MR=16

the marginal profit at an efficient level of output is

Marginal profit =MR-MC

=16-24

=-$8

the firm will lose $8 per unit if the firm produces at the efficient level of output.