A monopolist\'s inverse demand function P D(Q) is described as follows: D(1)-64,

Question

A monopolist's inverse demand function P D(Q) is described as follows: D(1)-64, D(2)-45, D(3)-26, D(4)-17, D(5)-8. Answer the following: a) What is the infra-marginal effect of this monopolist at Q-1? b) What is the volume effect of this monopolist at Q-1? c) What is the marginal revenue of this monopolist at Q-3? d) Suppose the marginal cost is not constant and increases with production in the following way: MC(1)-1, MC(2)-6, MC(3)-12, MC(4)-21, MC(5)-33. How many units should this monopolist sell to maximise profit?

Explanation / Answer

Answer

a) Inframarginal effect at Q = 1 = absolute value of D(2) - D(1) = 45-64 = 19

Hence Inframarginal effect at Q = 1 = 19

b) We can see from above question that D(1) = 64.

Hence Volume effect at Q (= 1) = 64

c) At Q = 3 Total Revenue = Q*D(Q) = 3*26 = 78

At Q = 2 Total Revenue = 2*45 = 90. Hence Marginal Revenue at Q = 3 is 78 - 90 = -12

d) A monopolist have to sell that quantity at which MR = MC. But in this casr MR is not equal to MC at any Q. Hence in order to maximize the Profit. He will have to produce quantity whose MR is greater and closest to MC. In this case that Q = 2. Hence he should Producee 2 units in order to maximize profit. Note that Total revenue at Q = 3 is lesser than at Q = 2. Hence he will not produce more than 2 in order to maximize profit.

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