Suppose a monopolist sells in two distinct markets. The demand and marginal revenue for the first market are given by P1 = 240 - 2Q1 and MR1 = 240 - 4Q1, respectively, where Q1 is the quantity demanded and P1 is the price paid by the first group. The demand and marginal revenue for the second market are given by P2 = 120 - Q2 and MR2 = 120 - 2Q2, respectively, where Q2 is the quantity demanded and P2 is the price paid by the second group. The monopoly's marginal cost is given by MC = 4/9 Q, where Q is the total output produced by the monopoly.
(i) How much does the monopoly supply in each market and what price does it charge?
(ii) What is the common equilibrium value of marginal revenue and marginal cost?
(iii) Use your answers to parts i and ii to calculate the elasticity of demand for each market.
(i) Use the equations MR1 = MR2 = MC and Q1 + Q2 = Q to show that Q 1 = 50 units and Q2 = 40 units. Substitute these values into the demand formulas to show that P1 = $140 per unit and P2 = $80 per unit.
(ii) MR1, MR2, and MC all equal $40 per unit.
(iii) The formula MR = P • (1 - 1/n|) shows that the elasticity of demand equals -1.4 in the first market and -2 in the second market.
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