A monopolist is deciding how to allocate ouput between two geographically separa

Question

A monopolist is deciding how to allocate ouput between two geographically separated markets. Demand and marginal revenue for the two markets are:

P1 = 20 - Q1 MR1 = 20 - 2Q1

P2 = 35 - 2Q2 MR2 = 35 - 4Q2

The monopolist's total cost is C = 5 + 5 (Q1 + Q2)

What are price, output, profits, marginal revenues, and deadweight loss if the monopolist can price discriminate? (all answers rounded to 2 decimal places).

In market 1, the price is $12.50 and the quantity is 7.5. In market 2, the price is$20 and the quantity is 7.5. The monopolist's profit is $163.75 and the deadweight loss is $84.38.

If the law prohibits charging different prices in the two regions, the market price is$___, the quantity in market 1 is ___ and the quantity in market 2 is ___. The profit is $___ and the deadweight loss is $___.

Explanation / Answer

This is a case of third degree price discrimination.

Equilibrium condition is MR1=MR2=MC

In case of MR1=MC we have

20-2Q1=5 as TC=5+5(Q1+Q2)

or, Q1=7.5

Similarly, 35-4Q2=5

or, Q2=7.5

Hence, P1=20-7.5=12.5

P2=35-2Q2=35-2x7.5=20

(Q1,Q2)=(7.5,7.5)

MR1=20-2x7.5=5

MR2=35-4x7.5=5

Profit=P1.Q1+P2.Q2-TC=12.5x7.5+20x7.5-(5+5x15)=93.75+150-80=163.75

For deadweight loss it is=1/2x(35-12.5)x(7.5-0)=84.38

When Q2=0 then, P2=35 and price floor =12.5 and minimum quantity consumption=0 and at P1=12.5, Q1=7.5

All the prices, outputs, profits, deadweight losses are derived above.

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