Question

Coca is a monopolist for a new drug that makes people feel thinner. The total cost function is C(Q) = 200 + 10Q + Q 2(read as Q SQUARED or Q to the power of 2) . The inverse demand function is p(Q) = 82 − Q.

(a) What are the efficiency losses of the monopoly pricing compared to competitive prices?

(b) Coca argues that other firms should not be allowed to enter the market, since it is a natural monopoly. A potential competitor argues that it is not a natural monopoly. Show why both are right at the same time.

Answer 1

a) Total Cost function is,

C(Q) = 200+10Q+Q2 ................(i)

Therefore, marginal cost is, d(C(Q))/dQ=10+2Q

and

Inverse demand function is P(Q) = 82-Q.............(ii)

Therefore, total Revenue is P(Q).Q = 82Q-Q2

or, marginal revenue is, d(P(Q).Q)/dQ= 82-2Q

Under monopolistic competition, Marginal Revenue = 0

or, 82-2Q=0 or, Q=41, Therefore, monopoly price is P(Q) = 82-41=41

Also, under equilibrium market condition,

Marginal Revenue= Marginal Cost

                               82-2Q= 10+2Q

or, 4Q=72 or, Q=18

Therefore, competitive price under equilibrium condition is,

                                            P(Q) = 82-18= 64

It is clear that competitive price is higher than monopoly price of the drug and the efficiency loss = $64-$41=$23

b) The cost of producing good under natural monopoly is very low due to high scale of production of goods by a monopoly firm. The coca is a monopolist drug manufacturer and as shown in a) its monopoly price is $41/unit for producing 41 units of drugs compared to competitive price $64/unit for producing just 18 units of drugs. Therefore, coca is a case of natural monopoly.

If a potential competitor enter the market, it will bring competitive technology and other inputs into the production prrocess that will reduce the total cost of production and also increase the volume of drug production, which will result decrease in the drug price in the market.