Question

Consider a situation where the monopolist is considering price discrimination by selling in two different countries, a high income country (1) and a low income country (2). In country 1, it faces the demand curve P1=120-7Q1 and in country 2, P2=60-2Q2. Its total cost function is still the same, TC=8Q^2+5.

1. Derive the MC function for the monopolist.

2. Derive the MR function in each country

3. Determine the price it should charge and the quantity of output that it should sell in each country.

4. Calculate the profit the monopolist would make in each country.

5. As one of the top management personnel in your organization, how will you advise your CEO regarding the merger and the potential price discrimination?

Answer 1

1. MC = d(TC)/dQ = d[8Q² +5]/dQ = 16Q

2. In country 1,

Demand: P1 = 120 - 7Q1

Multiplying both sides by Q1 we get,

P1Q1 = TR1 = 120Q1 - 7Q1²

Or, MR1 = d(TR1)/dQ1 = 120 - 14Q1

In country 2,

Demand: P2 = 60 - 2Q2

Multiplying both sides by Q2 we get,

P2Q2 = TR2 = 60Q2 - 2Q2²

Or, MR2 = d(TR2)/dQ2 = 60 - 4Q2

3. A profit maximizing monoply produces at the point where MR = MC and sets it's profit maximizing price at the point where the profit maximizing quantity lies on the demand curve.

Therefore, in country 1, setting MR1 = MC1,

120 - 14Q1 = 16Q

Or, 30Q = 120

Or, Q = 4

When Q = 4, from country 1 demand equation we get, P1 = 120 - (7*4) = $92

In country 1, the monopoly should sell 4 units and charge $92.

In country 2, setting 60 - 4Q2 = 16Q

Or, 20Q = 60

Or, Q = 3

When Q = 3, P2 = 60 - (2*3) = $54

In country 2, the monopoly should sell 3 units and charge a price of $54.

4.in country 1, Total revenue = price * quantity = $(4*92) = $368. Total cost = 8(4)² + 5 = 133. Therefore, profit = $(368 - 133) = $235.

In country 2, TR = $(3*54) = $162 and TC = 8(3)² + 5 = $77

Profit in country 2 = TR - TC = $(162 - 77) = $ 85