Review Demand-oriented Pricing Strategies Consumer Surplus

Lecture 15 Two-parts Pricing What is two parts pricing? Why do we use two parts pricing? How to design two parts pricing?

Motivation Questions Most of the jazz bars charge two parts pricing. You pay the entry fee and every drink. Why is it optimal to do so? How do you determine how much to charge for entry and drinks ?

Two-parts pricing (two-parts tariff) two separate charges for consuming a single product. Services: Jazz bar, Disney Theme Parks, Visa, museum … Products: Bell South, Rental Cars, Costco … When do we use two parts pricing? There are two separate benefits of consuming a single product There are two separate costs of offering the product: fixed cost and variable cost Why do we use two parts pricing? significant difference in the incremental cost of serving different segment ATT WorldNet for industries with high fixed costs Golf Course spur competitive innovation Bell South DSL

Graphical Illustration of Two-Parts Pricing Price ($) c Individual Demand Curve q

A Single Price is Inefficient Price ($) c= Profit (p*-c)q* p* No trade – deadweight loss Money left on the table q

Solving for Optimal Two-Parts Pricing with Homogeneous Customers Step 0: Start with the inverse demand function p = a – b*q Step 1: Set the per-unit price to equal marginal cost, that is p* = c Step 2: From the demand equation, compute the quantity demanded at this price q*(p*), so that q*(c) = (a-c)/b Step 3: Compute the consumer surplus CS* at p* = c and set the fixed fee as equal to CS*: (a-c)*(a-c)/(2*b)

Example: Two-parts pricing A new health club needs to decide how much they should charge for each visit of their patron. They know that individual demand function for weekly usage is P=10-2T, where T is the number of hours spent in the club. The marginal cost for providing an hour usage is $2, and there is no capacity limit. 1). Assuming they are facing a homogeneous population, the management is planning to charge homogeneous price (linear pricing). Design the optimal linear price which only charges a usage fee.

2). Since the club is brand new, the management is eager to cover all the fixed cost involved in building the facilities in addition to the variable cost related to each visit. A two parts pricing will help management solve the problem by better extracting consumer surplus. Design the optimal two-part price with an entry fee plus a usage fee. Will two-part price improve profitability?

3). However, consumers are heterogeneous and it is impossible for you to distinguish them. You need to make a decision on whether you want to lower your price to serve both types of consumers or keep the price high and focus on only Type A consumers who can bring in more profit. Assume there are two types of customers, A and B,  % of the customers are of type A and 40% of the customers are of type B. They have following individual demand function: Type A: P=10-2T Type B: P= 8-2T Price strategy I: two-part price under which both types use the club Price strategy II: two-part price which excludes type B Design the optimal two-part tariffs for both strategies

Take-aways from this example Two parts pricing is a price discrimination technique to differentiate (unobservable) heavy users from light users. For homogeneous consumers, optimal variable fee should be the same as variable cost. For heterogeneous consumers, we need to solve for optimal variable fee and fixed fee.

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