Suppose that a monopoly can price discriminate between two markets: market 1, wh

Question

Suppose that a monopoly can price discriminate between two markets: market 1, where the demand curve is given by q1 = 1-p1 and market 2 where demand is given by q2 = 4-3p2. Assume that arbitrage between the two markets is impossible and that production unit costs are c=1/2.

• Calculate the profit-maximizing output level that the monopoly sells in each market. Calculate the price charged in each market.

• Calculate the monopoly’s profit

• Suppose now that arbitrage is possible and therefore the monopoly is forced to charge a uniform price p1 =p2 =p. Find p that maximizes profits

Explanation / Answer

A monopoly can price discriminate between two markets: market 1, where the demand curve is given by q1 = 1 - p1 or p1 = 1 - q1. In market 2, demand is given by q2 = 4 - 3p2 or p2 = 4/3 - (1/3)q2. The production unit costs are c = 1/2.

• Calculate the profit-maximizing output level that the monopoly sells in each market. Calculate the price charged in each market.

Find marginal revenues in each market. MR1 = 1 - 2q1 and MR2 = 4/3 - (2/3)q2.

MR1 = MC MR2 = MC

1 - 2q1 = 1/2 4/3 - (2/3)q2 = 1/2

q1 = 0.25 q2 = 1.25

p1 = 1 - 0.25 = 0.75 and p2 = 4/3 - (1/3)*1.25 = 0.916

• Calculate the monopoly’s profit

Profit = (0.75 - 0.5)*0.25 + (0.916 - 0.5)*1.25 = 0.5825

• Suppose now that arbitrage is possible and therefore the monopoly is forced to charge a uniform price p1 =p2 =p. Find p that maximizes profits

For a single price we have a single market and single demand

q1 + q2 = 1 - p + 4 - 3p

q = 5 - 4p

p = 5/4 - (1/4)q

MR = 1.25 - 0.5q

MR = MC

1.25 - 0.5q = 0.5

0.5q = 0.75

q = 1.5 and p = 1.25 - 0.25*1.5 = 0.875

Profits = (0.875 - 0.5)*1.5 = 0.5625.

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