Question

A circus knows that their typical customer has an inverse demand function for shows at the circus equal to p(y) = 216 - 9y, where p is the per unit price of a show. The marginal cost of a show is £72 and we assume there is no fixed cost. The circus is a monopolist in the market and can choose among the following pricing options: A: sell tickets for shows at a price p1 per ticket. B: sell tickets for shows at a price p2 per ticket AND charge and entrance fee of Y, C: practice first degree price discrimination The circus wants to maximise its profits. Which of the following statements is true? Note: that a pricing strategy must be feasible, and customers must be willing to pay the price charged by the circus. Select one: a. The circus would be indifferent between C and B with p2 =72 and Y = 1152, b. The circus would be strictly better off under A, with p1 = 72, c. The circus would be strictly better off under B, with p2 = 144 and Y = 288, d. The circus would be strictly better off under A, with p1 = 144, e. The circus would be strictly better off under B, with p2 =72 and Y = 1157 f. The circus would be strictly better off under C.

Note: Show your workings and explanations clearly.

Answer 1

The inverse demand function is p(y) = 216 - 9y

TR = 216y -9y²

MR = 216 -18y

Marginal Cost is given as 72 and there is no fixed cost.

We know, that for a Monopolist firm, Profit maximizing equilibrium is at MR = MC

=> 216 -18y = 72

=>18y = 216 - 72

=> 18y = 144

=> y = 144/ 18 = 8

p = 216 - 9(8) = 216 - 72 = 144

Therefore, the correct option will be A: sell tickets for shows at a price p1 per ticket and d. The circus would be strictly better off under A, with p1 = 144.