Linear and Nonlinear Pricing Linear Pricing – expenditures increase proportionately with consumption E.g., Beer: P = $5 per beer Nonlinear Pricing – expenditures rise disproportionately with consumption E.g. Redskins tickets: Exp = Personal Seat License + X per game
Two-part Tariffs Two-part Tariff involves a fixed fee plus a per unit price Examples: Restaurants (á la carte v buffet) Nightclubs: cover plus drinks Country clubs: monthly charge plus greens fees Important Features of nonlinear pricing Requires ability to prevent resale Creates vehicle for extracting consumer surplus that is otherwise unattainable
Single-type consumers P/Q Q MC = m Optimal linear price: p m pmpm qmqm Optimal two-part tariff: A B C = (A+B+C) + m*q
Multiple-type consumers P/Q Q MC = m pmpm qmqm
Multiple (optional) two-part tariffs P/Q Q MC = m pmpm qmqm If knew customer types and can prevent resale, then charge two tariffs, But suppose that all you know is that there are different customers, Not their identity?
Multiple (optional) two-part tariffs Q Exp. F1F1 F2F2 Consumers will tend To minimize expenditures (absent insurance considerations) Receipts will tend to be Defined by the lower Envelope of the curves
Optional Two-part Tariffs in Practice: Telephone Pricing in the United States Unlimited (Flat-rate) service $17.01/month Limited Per Call Service $ * Calls (for calls > 65/month) Economy Call Service $ *Calls Source: Verizon, Montgomery County White pages
Telephone Expenditures with Nonlinear Pricing $ Calls $ $5.92 $10.16 What is the logical consumer response? What is the actual consumer distribution among the calling plans ? 42
Nonlinear pricing in practice Is the pricing of electricity in Basel (Washington) (elsewhere) linear or nonlinear? What are the economic and societal implications of such pricing? Why would such a firm ever set a price to encourage conservation? What is the structure of mobile telephone pricing? What competitive and economic dynamics have led to this pricing structure?
Discussion: Paying by the Gig What is the current pricing model for Internet usage? What is being trialed by Time Warner Cable? What are the business drivers of the pricing scheme?
Minimum quantity pricing Consider a good or service with a highly fluctuating intertemporal demand The demand for hotel rooms in Washington during the Inauguration activities versus a normal demand The demand for hotel rooms in Basel during Fachnacht Option one: Charge the linear price consistent with the extent of market power or impose minimum stay
Minimum Quantity Pricing 12 A B C DE F Days $/Day mc ProfitConsumer Surplus Monopoly Pricing B+EA Minimum StayE+F+DA + B +C - D NetF+D>B?B+C>D? Pm Pstay
Price Discrimination Price discrimination – practice of charging consumers prices that differ by more than differences in the cost to produce the good (P i /mc i ) (P j /mc j ) [George Stigler] (cost-based differences are not considered price discrimination)
MC(Q) $ Q Profit Maximization with Market Power P* D=Q(P)=P(Q) MR(Q) Q* Is Q*, P* profit max? Why not sell these units?
MC(Q) $ Q Market Power and Price Discrimination P D=Q(P)=P(Q) MR(Q) Consumer Surplus Unrealized Sales What would be ideal for the firm?
MC(Q) $ Q Market Power and Price Discrimination P D=Q(P)=P(Q) MR(Q) Consumer Surplus Unrealized Sales Is this a violation of our MR=MC rule?
Effects of price discrimination Producer increases revenue and profits Low willingness-to-pay consumers typically gain as they would be under-served otherwise High willingness-to-pay consumers typically worse off
Forms of Price Discrimination First Degree – practice of charging each consumer her individual reservation price Second Degree – Practice of charging consumers a volume-sensitive price that is noncommensurate with cost charges Third Degree – practice of sorting consumers into different groups based on observable characteristics and charging different prices
Price Discrimination D mc mr pmpm qm Q $/Q First Degree Price Discrimination Allows firms to extract all consumer surplus
First-Degree (Perfect) Price Discrimination Hard to achieve in reality, but some strategies come close Examples ? Amazon.com dynamic pricing (more later) Used car dealers, mechanics, contractors, any negotiated price Haggling in the bazaar Capital One 1990s - Pricing long-distance telephone calls
First-degree price discrimination Advantages: Extracts the most consumer surplus Disadvantages: Difficult (costly) to do - Determining willingness to pay is exceedingly hard Risk consumer backlash (Amazon.com)
Second-Degree Price Discrimination Practice of charging consumers a volume- sensitive price that is noncommensurate with cost charges M&Ms 1.74 oz. P =.89 or $8.18/lb M&Ms 14 oz P=$2.50 or $2.85/lb
Second Degree Price Discrimination Example: Electricity Pricing Electricity pricing First 1000kwh P=.10 Next kwh P =.08 Kwh > 11,000, p=.07 $/kwh kwh1,00011,
Second-degree price discrimination Advantages: Can target consumers with particular volume preferences Can encourage or discourage consumption by pricing for marginal customers Disadvantages: Lower total revenue than 1 st degree Risk confusing consumers
Third Degree Price Discrimination Occurs when firm charges different consumers different prices for the same good Consider a firm selling to two distinct customer groups, so…
Third Degree Price Discrimination π = P 1 Q 1 + P 2 Q 2 – C (Q) mr 1 = p 1 (1 + 1/ε 1 ) and mr 2 = p 2 (1 + 1/ε 2 ) And profit maximization requires: mr 1 = mc and mr 2 = mc, so p 1 (1 + 1/ ε 1 ) = p 2 (1 + 1/ ε 2 ) = mc, or p 1 /p 2 = (1 + 1/ ε 2 ) / (1 + 1/ ε 1 ) So, say ε 1 =-6 and ε 2 = -4
Third-Degree Price Discrimination Practice of sorting consumers into groups based on observable characteristics associated with willingness to pay and charging different prices (a.k.a. group pricing) Examples of 3 rd degree p.d.: Senior/student discounts Drycleaners and haircuts AAA and AARP discounts Spatial groupings (Canadians at DisneyWorld)
Implications If it is possible to identify separate elasticities, it is desirable to set different prices. How might firms identify elasticities? Travelling tomorrow? Number of substitutes Self-identify (coupons)
Third-degree price discrimination Advantages: Generally produces higher total revenue than a one price constraint Sorting mechanism is observable/verifiable Disadvantages: Lower total revenue than 1 st degree Risk consumer backlash
The Policy of Price Discrimiation Price Discrimination [Clayton Act, Sec. 2] It shall be unlawful for any person engaged in commerce, … to discriminate in price between different purchasers of commodities of like grade and quality, …where the effect of such discrimination may be substantially to lessen competition or tend to create a monopoly in any line of commerce, or to injure, destroy, or prevent competition with any person who either grants or knowingly receives the benefit of such discrimination, or with customers of either of them: Provided that nothing herein contained shall prevent differentials which make only due allowance for differences in the cost of manufacture, sale, or delivery resulting from the differing methods or quantities in which such commodities are to such purchasers sold or delivered: Section 2(b) permits good faith meeting of competition
Peak Load Pricing Suppose that demand is predictably volatile Variation may be daily, seasonal Pricing response?
Intertemporal Price Discrimination: Peak Load Pricing P mc D1 mr1 D2 mr2 q1 p1 p2 q2
Pizza for $2.99???
Examples of Peak-load pricing Pricing power by the hour Average rate = $.11/kwh Peak rate = $.81/kwh Off Peak =$.09/kwh Reservations? How is this different than paying by the gig for Internet downloads?
Necessary conditions for Price discrimination 1. Monopoly power 2. Ability to identify different customers 3. Ability to prevent arbitrage
European Commission Finds against Topps Facts? Should government concern itself with something as trivial as trading cards? Is Topps pricing policy consistent with the establishment of the EU?
The Economics of Price Discrimination Finland Portugal mrd PFPF QFQF P QPQP Q P Combined Market /Q Q Q Q mr d D MR With linear demand and costs, price discrimination fails to benefit consumers mc
Dynamic Pricing Dynamic pricing is sometimes meant to connote price changes over time for the same commodity or service E.g., Caps pricing within a season Coca-cola vending machines that adjust price depnding on temperature Is sometimes meant to connote third degree price discrimination E.g., Amazon.com (setting different prices to different consumners for the same commodity (e.g. book or CD) Orbitz has discovered that Mac users pay on average 30 % more for hotel rooms per night than PC users – modify showing 41
Orbitz Pricing : PC Search (July 6, 2012) 42 1:PC: $103 2:PC: $134 3:PC:$129 4:PC:$159 But if Mac-based search???
43 Hyatt Regency Crystal City October 19- Oct 21 $103 per night October 26- Oct 28 $169 per night
Takeaways When firms have market power, simple pricing can leave a lot of value on the table Price discrimination strategies can help firms increase profits Extract consumer surplus from existing high willingness-to-pay customers Make additional profitable sales to low willingness-to- pay consumers Be aware of legal restrictions