jnu question

[sohini]

sir, pl give the detailed solution for the question below-

A monopolist faces 2 distinct and separate mkts-1 and 2; in one mkt the dd curve is given by Q1=10/P1; in the other mkt, the dd curve is given by Q2=1000-P2. The monopolist can produce any amt. at a constant marginal cost of 20 per unit. how much does the monopolist sell in each mkt and at what price?

[Amit Goyal]

A monopolist faces 2 distinct and separate mkts-1 and 2; in one mkt the dd curve is given by Q1=10/P1; in the other mkt, the dd curve is given by Q2=1000-P2. The monopolist can produce any amt. at a constant marginal cost of 20 per unit. how much does the monopolist sell in each mkt and at what price?

Assuming that the monopolist can charge two different prices in two markets:
For the first market, there is no solution.
For the second market, P=510, Q=490

[prakriti]

how?

[Ankur]

@Prakriti

In a monopoly MR=MC
Market 1  
             1) Q1=10/P1
                MC=20
                MR=(dP/dQ) + P
               P1=10/Q1 from 1
               dP1/dQ1=-10/Q1^2

             MR=(-10/Q1^2)Q1 + (10/Q1)=0
              Hence no solution

Similarly for market 2 Q2=1000-P2
MR=1000-2Q2
MC=20
MR=MC
Q2=490,P=510

[Ankur]

@Prakriti

In a monopoly MR=MC
Market 1  
             1) Q1=10/P1
                MC=20
                MR=(dP/dQ) + P
               P1=10/Q1 from 1
               dP1/dQ1=-10/Q1^2

             MR=(-10/Q1^2)Q1 + (10/Q1)=0
              Hence no solution

Similarly for market 2 Q2=1000-P2
MR=1000-2Q2
MC=20
MR=MC
Q2=490,P=510

[Ankur]

MR=(dP/dQ)Q+P...