1. GMG, a cinema complex, is considering charging a different price for the afternoon showings of its films compared with the evening ticket price for the same films. It has estimated its afternoon and evening demand functions to be:
PA = 8.5 – 0.25QA
PE = 12.5 – 0.4QE
where PA and PE are ticket prices (in £) and QA and QE are number of customers per week (in hundreds). GMG has estimated that its fixed costs are £2,000 per week, and that its variable costs are 50 pence per customer.
a. Calculate the price that GMG should charge if it does not use price discrimination, assuming its objective is to maximize profit.
b. Calculate the prices that GMG should charge if it does use price discrimination.
c. Calculate the price elasticities of demand in the case of price discrimination.
d. How much difference does price discrimination make to profit?
2. TT Products produces two items, bibs and bobs, in a process that makes them joint products. For every bib produced two bobs are produced. The demand functions for the two products are:
Bibs: P = 40 4Q
Bobs: P = 60 3Q
where P is price in £ and Q is units of each product. The total cost function is:
C = 80 + 20Q + 4Q 2
where Q represents a product bundle consisting of one bib and two bobs.
a. Calculate the prices and outputs of bibs and bobs that maximizes profit.
b. Calculate the size of the above profit.