Question

2. Suppose that you run the only movie theater in a small town – it is a monopoly in your area. On occasion you have given discounts to students from a nearby college (they have to show their college ID to get the discount and to enter the theater). From analyzing your sales data over time, you realize that your customers have differing price elasticities of demand – movie goers who are not students have a price elasticity of demand of -1.3, while students have a price elasticity of demand of -1.7. You have a constant marginal cost of $3 per movie goer. You decide to price discriminate between students and non-students.

a) What is your profit maximizing ticket price for non-students and what is your profit maximizing ticket price for students? Show your work.

b) For the group that has the higher ticket cost in (a), thoroughly explain the economic logic behind charging that group a higher price (Don’t go through the math, just explain the reasoning).

Answer 1

While non students movie goers have a price elasticity of demand of -1.3, students movie goers have a price elasticity of demand of -1.7. You have a constant marginal cost of $3 per movie goer. Use the rule for price setting, P = MC * (ED)/(ED + 1)

a) Then, profit maximizing ticket price for non-students = 3 * (-1.3)/(-0.3) = $13. And, profit maximizing ticket price for students = 3 * (-1.7)/(-0.7) = $7.29

b) The economic logic is related to elasticity and revenue relationship. In case of students demand is more elastic. This implies that a lower price would generate a higher revenue while a higher price will generate a lower revenue. In contrast, when demand is less elastic, as it is with non students, a higher price would generate a higher revenue while a lower price will generate a lower revenue. Hence, non students are charged a higher price (as their demand is less elastic) while students are charged a lower price (as their demand is more elastic)