(a) A monopolist has discovered that the inverse demand function of a person with income Y for the monopolist's product is P = 0.002Y-Q where P is the price, Y the income, and Q is the output. The monopolist can observe the incomes of its consumers and hence vary its price accordingly. The monopolist has a total cost function C(Q) = 100Q. Calculate the profit maximising price as a function of the consumer's income Y carefully explaining all the steps in the derivation of the formula.

(b) A monopolist has a constant marginal cost of 2 per unit and no fixed costs. He faces two separate markets in the United States and in the UK. The goods sold in one market are never resold in the other. He sets one price P₁ for the US market and another price P₂ for the UK market (both measured in ). The demand in the United States is given by Q₁=7,000-700P₁ and the demand in the UK is given by Q₂=1,200-200P₁.

i

i. Calculate the profit maximising output produced and price charged in each country by the price-discriminating monopolist and comment in which country the price charged is higher and by how much.

ii. Explain if your answer above is as expected by calculating the elasticities of demand in each country.