Question

Consider a market that is served by a single producer. Suppose you are told that the producer has the following cost curves where TC is total cost measured in dollars, Q is the quantity, and P is the price of Q in dollars: Total Cost: TC = Q 2 Marginal Cost: MC = 2 Q Suppose you also know that the market demand curve is given by the following equation: Market Demand: Q = 96 – P

1. Determine the price and quantity that maximize the producer profit. Explain the steps of your answer. (2 points)

2. Calculate the level of profit in the short- run for this producer. (2 points)

3. Is there any deadweight loss (DWL) that results from this market? If your answer is “yes”, compute this DWL and provide a graph that is well labeled to illustrate your answer. (2 points)

4. Is there any way to regulate this market in order to achieve productive efficient in long run? Explain. (2 points) Hint: Answer shouldn’t exceed two lines.

5. Is there any way to regulate this market so that the market output is equal to 60 units? Explain. (2 points) Hint: Answer shouldn’t exceed two lines.

Answer 1

Single producer shall charge a monopoly price by equating Marginal Revenue with Marginal Cost

MR = dP*Q/dQ

     = d(96-Q)*Q/dQ

    = 96 – 2Q

Marginal cost 2Q

= > MR = MC

= > 96-2Q = 2Q

= > Q* = 96/4 = 24        

P* = 96 -24 = 72

Profit in short run = revenue – total cost

                            = 72*24- 24*24

                            = 1152           

Yes since the pricing is at monopoly level instead of competitive market level the producer is charging a higher price than the marginal cost which is effectively the price level in a competitive market.

Dead weight loss is the loss in economic surplus post the implementation of monopoly instead of competitive market

From the figure we see that the red region is the loss in consumer surplus as well as producer surplus. Although the producer do extract a share of surplus from the consumer and thus increase its profit more than it would have earned under monopoly , however the loss to the consumers and the loss of efficiency due to reduced output creates a DWL

Under competitive market :-

P=MC

= > 96-Q = 2Q

= >96/3=Qc = 32

P = 64

Hence the DWL = area of red region = ½ * (72-48)*(32-24)

                                                          = ½ * 24*8

                                                          = 96

The only way to regulate this market to achieve efficient output in the long run is to introduce competition by allowing other firms to enter the makrte.

Note that one cannot make the market produce 60 units of output because at 60; MC = 120 while P = 26 , Since price received exceeds the marginal cost hence firms shall never produce this level of output by incurriing loss