Question 3: Monopoly [7 marks; 3,2,2]

Suppose a monopoly drug manufacturer faces the following inverse demand curves for its product in two different countries 1 and 2.

Inverse demand curve in country 1:p₁ = 200 - Q₁

Inverse demand curve in country 2: p₂ = 180 - 0.5Q₂

where p_i and Q_i denote price and quantity sold in country i respectively and i = 1, 2. The monopolist's cost function is given by

c(Q) = 0.25Q²

where Q = Q₁ + Q₂. Assume thatresale between the countries is not possible and the monopolist maximizes profits.

(a) (3 marks) Find p₁ and p₂ that maximizes monopolist's profits.

(b) (2 marks) Suppose the monopoly drug manufacturer in (a) faces a capacity constraint of 130 units. That is, Q₁ + Q₂ = 130. What price will the monopolist charge in country 1? What price will the monopolist charge in country 2?

1. (2 marks) Suppose there are no capacity constraints, but unlike in parts (a) and (b), price discrimination is not allowed. That is, the monopolist cannot charge two different prices in countries 1 and 2. Find the unique price that maximizes monopolist's joint profits (i.e., the sum of profits in the two countries).