Please include step by step working and derivation of any methods in the following question: 1. (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. 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. Explain if your answer above is as expected by calculating the elasticities of demand in each country.
Please include step by step working and derivation of any methods in the following question:
1. (a) A monopolist has discovered that the inverse
(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.
- 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. - Explain if your answer above is as expected by calculating the
elasticities of demand in each country.
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