Question

Question 8: Viewers of the movie Zootopia' often want to see it again. Suppose individual demand of all viewers is identical and given by P = 16-20, and that the local (monopolist) movie theatre has a marginal cost of $2 per ticket. The theatre manager wants to sell a A dollars to buy B tickets for Zootopia. (for example, if a bundle of four tickets would sell for pay $18, then we would have A-18 and B-4). Derive the optimal Zootopia package' (ile, the profit- maximizing values of A and B). (Hint: as so often, there are multiple ways to tackle this question. Explain your steps clearly. If you cannot answer this question, then explain how you would price the tickets if you were the monopolist)

Answer 1

In order to find out the optimal zootopia package, we first need to know the profit maximisation condition of the theatre monopolist. For profits to maximise, the basic condition is that Marginal costs must equal marginal reveue. Here, Marginal cost is given which is equal to $2 per ticket. To calculate Maginal Revenue, we will follow the bellow steps:

Total Revenue = Price * Quantity

= (16 - 2Q)*Q

=16Q - 2Q2 .......(1)

Marginal Revenue is the first derivative of total revenue. Derivating Equation 1 with respect to Q,

we get

MR = 16 - 4Q

Since MR = MC for maximising profit,

16 - 4Q = 2

Q = 3.5

and P = 16 - 2Q

= 16 - 2(3.5)

= 9

Hence, the monopolist will sell approximately 4 tickets for $9 each

A = 9 and B = 4.