TwoTierPricing

# TwoTierPricing - Industrial Organization: EC460 Spring 2009...

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Industrial Organization: EC460 Spring 2009 Notes on 2nd Degree Price Discrimination—Example from class A ski resort has two types of customers: hard-core and leisurely. The demand curve for skiing—as measured by how many lift rides up the mountain a skier would like to have given diﬀerent prices—is given by P h = 5 - . 5 Q h for hard-core skiers; and P l = 9 - 2 Q l for leisurely skiers. Suppose once the lift is in operation the marginal cost of taking a skier up the mountain is zero, i.e., MC = 0. 1. Calculate the proﬁt maximizing prices per single-trip lift-ticket if hard-core skiers can be distinguished and charged separately from leisure skiers. What is the ﬁrm’s overall proﬁt when there is exactly one skier of each type? 2. Calculate the optimal two-part tariﬀs, that is, suppose that the resort decides to sell day-passes (tier 1) in conjunction with a marginal price per lift ride (tier 2). When distinguishing hard-core and leisure skiers, what price should it charge for a day pass for each type of skier and what is the optimal marginal price to be charged? What is the ﬁrm’s proﬁt when there is exactly one skier of each type? 3. Can the plan calculated under 2 be modiﬁed in such a way that it can be implemented if the resort cannot distinguish between the two types of skiers? That is, which modiﬁcation to the plan will make it incentive compatible so that skiers self-select into the plans designed for them? Explain. Answer: 1. The solution to this question gives the standard third-degree price discrimination scenario for uniform pricing across the two groups. Consider the two groups sepa- rately: For hard-core skiers: Rev h = 5 Q h - . 5( Q h ) 2 , so MR h = 5 - Q h . Setting MR h = MC (= 0) yields Q h * = 5, hence P h * = 2 . 50 and the ﬁrm obtains Q h * × P h * = 12 . 50 from the hard-core skier.

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## This note was uploaded on 03/29/2009 for the course ECON 460 taught by Professor Boyer during the Spring '08 term at Michigan State University.

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TwoTierPricing - Industrial Organization: EC460 Spring 2009...

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