Question

A monopolist can practice third-degree price discrimination. If demand in the United States is given by y1 = 7,200 – 100p1, where p1 is the price in the United States, and if the demand in England is given by y2 = 3,600 – 200p2, where p2 is the price in England, then the difference between the monopolistic price charged in England and the monopolistic price charged in the United States will be:__________.

Answer 1

The difference between the monopolistic price charged in England and the monopolistic price charged in the United States will be = 27

Step-by-step explanation:

Y1 = 7200 -100p1 = > p1 = 72 – y1/100

Y2 = 3600 – 200p2 = > p2 = 18 – y2/200

The cost of monopolist (since it’s the same firm and uses same technology) shall be same in both countries, hence let us assume marginal cost to be say c

Now the first order condition for Profit Maximisation of a monopolist yields

Marginal Revenue = Marginal cost

= > Marginal Rev US = c = Marginal RevEngland…………………..i

Now, Revenue in US = p1y1 = y1(72 – y1/100)

MR US = dRev/dy1 = 72 – y1/100 -y1/100 = 72 – y1/50

Similarly MR­Eng = 18 – y2/100

Hence putting the above derivations in i:-

72 – y1/50 = 18 – y2/100

Now putting values for y1 and y2 again the above equation becomes:-

72 – (7200 -100p1)/50 = 18 – (3600 – 200p2)/100

= > 54 – 144 + 2p1 = -36 + 2p2

= > 2(p1 – p2) = -36 + 90 = 54

= > p1 – p2 = 27