Question

Monopoly: Consider a monopoly firm facing a demand curve Q = 100 – P. The marginal revenue curve is therefore MR= 100 – 2Q. This firm has fixed costs =$1000 and constant marginal cost =$20. Total costs are $1000 + $20Q and average costs are $1000/Q + $20. a. What is the firm’s profit maximizing level of output? What price does it charge to sell this amount of output? How much profit does it make? Show your work. b. Suppose this firm is regulated by the government, and that the regulation requires that the firm charge a price equal to marginal cost. Calculate the number of units demanded and profit at this level of output. Is this policy sustainable in the long run? Why or why not? c. As an alternative, consider a regulation that is meant to allow the firm to earn a “reasonable rate of return” for operating. After analyzing the firm’s costs, the regulator allows the firm to charge $36 per unit produced. Calculate quantity demanded and profit under this policy. Is this a sustainable price in the long run? Why or why not?

Answer 1

[A]

Given MR= 100 – 2Q

MC = 20

Thus, equilibrium point where profit is maximum is where MR= MC

Thus, 100-2Q= 20

80=2Q

Q=80/2=40

At this point of equilibrium output , Q=40

P= 100 - Q = 100- 40 = $60

Thus, profit = TR-TC = {P*Q} - {1000 +20Q}

={60*40} - {1000 +20(40)}

={2400}-{1000 + 800}

=2400-1800 =$600

[B]

If polic is applied according to which price = MC= $20

Then quantity demanded, Q= 100 - P = 100 -20 = 80

Then profit at Q= 80,

Profit = TR-TC = {P*Q} - {1000 +20Q}

= {20*80}-{1000+20*80}

=1600 - 2600 = -$1000

Thus there will be loss of 1000.

No, this policy is not sustainable in long run as in long run this will only cause losses and forces the firm to shut down. As in this variable cost is only covered in short run .

[C]

Under policy regulation firm is allowed to charge $36 per unit.

Then qunatity demanded will be , Q = 100 - P = 100-36 = 64

So, under this policy Profit = TR-TC = {P*Q} - {1000 +20Q}

={36*64}-{1000+20*64}

=2304 - 2280 = $24

This policy can be sustainable but profit is maximized at MR=MC.

Thus , this can be sustainable but in long run firm will try to achieve maximum profit that firm will require to maximize thus would like to shift to above level.