3. Suppose a firm has a constant marginal cost of $10. The current price of the

Question

3. Suppose a firm has a constant marginal cost of
$10. The current price of the product is $25, and at
that price, it is estimated that the price elasticity of
demand is 3.0.
a. Is the firm charging the optimal price for the
product? Demonstrate how you know.
b. Should the price be changed? If so, how?

7. A monopolist sells in two geographically divided
markets, the East and the West. Marginal cost is
constant at $50 in both markets. Demand and marginal
revenue in each market are as follows:
QE = 900 - 2PE
MRE = 450 - QE
QW = 700 - PW
MRW = 700 - 2QW
a. Find the profit-maximizing price and quantity in
each market.
b. In which market is demand more elastic?

Explanation / Answer

The profit maximising condition for a monopolist is given by MR = MC. Now MR for a monompolist is given by

MR = P(1 - 1/e).Now at profit maximising level MR = MC .Thus our profit maximising condition becomes MC = P(1 - 1/e)

Given MC = $10 we get 10 = P(1 - 1/3)

Solving we get P =$15.

Thus the profit maximising price level is $15.The price charged by the monopolist currently of $25 is not the profit maximising price .Rather he must reduce the price charged by $10.

7)A monopolist under price discrimination charges different prices to different consumers for the same good depending on their respective elasticities.His profit maximising condition in case of price discrimination is

MRE = MC = MRW.

For market east

450 - QE = 50

Solving we get QE = 400.

Substituting this in the demand function we get

400 = 900 - 2PE

Solving we get PE = 250.

In western market 700 - 2QW = 50

Solving we get QW = 325

Substituting this in demand function we get PW = 375.

b) Clearly a monopolist sells a lesser quantity and charges higher price in the market with inelastic demand while he has to sell a larger amount at a lower price in an elastic market.This is because demand would not fluctuate so much in an inelastic market in response to a change in price as it would do in an elastic market.Thus EASTERN market is more elastic than WESTERN market.

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