【正文】 激勵(lì)相容約束 例：參考價(jià)格對(duì)高價(jià)位產(chǎn)品的影響 微波爐型號(hào) 選擇率（ %） 第一組（ 60人） 第二組（ 60人） 松下 Ⅱ 型 13 松下 Ⅰ 型 43 60 愛默生 57 27 Indirect price discrimination based on quantity ? quantity discount. ? taxi fee ? electric power use ? Package strategy（ quantity—price portfolio） （ P、 F）組合類型 One2one銅服務(wù)價(jià)格 One2one金服務(wù)價(jià)格 月租費(fèi) 工作日白天通話費(fèi) 29便士 18便士 英國移動(dòng)通信公司的二部定價(jià)套餐 此外還有，移動(dòng)的動(dòng)感地帶短信套餐等。 Comparision among several methods in nonlinear pricing ? Twopart tariff (T(q)= A+ pq) provides a menu of consume bundles in a line. Generally the line does not pass origin. ? Simplicity is its primary attraction, and sometimes it depends on possibility of limited arbitrage. ? Full arbitrage is prevented, namely only one buyer pays for fixed fee A, and then resale goods to other consumers. ? Notice： actually twopart tariff corresponds to quantity discount, average price decrease with increase of consume quantity. Profit and welfare ? Assumption： consumers reference as below ? U= ? V(0)=0,V’(q)0,V’’(q)0. θ is a constant of taste, different in person. V(*) is uniform to everyone. ? Also these can be explained in the same preference of consumers but with different ine level. ? Compare among case of perfect discrimination, monopoly pricing and twopart tariff. θV(q) – T if they pay T and consume q 0 if they do not buy A simple model ? Two kinds of consumers, proportion of taste parameter beingθ1 is λ, proportion of taste parameter beingθ2 is 1λ. Assume that θ2 θ1 ,monopoly produce in fixed cost c, and c θ1 θ2 . ? for simplicity, assume so V’(q)=1q 21 (1 q )V (q )= 2??Utility function ? Notice： fixed cost only influence the decision of buying or not. Once consumers decide to buy, it is out of consider. ? Consumer utility maximization： U=θiV(q) pq ? Firstorder condition： θiV’(q) = p ? According to assumption before,θi(1q) = p ? So , demand function is educed as q = Di(p) = 1p/ θi ? Net consumer surplus is i i i iS ( p ) V ( D ( p ) ) pD ( p )???General demand function ? In this case, consumer surplus is ? Notice that ,and θ2 type consumers always hold higher surplus. ? Make θas harmonic mean of θ1 and θ2 ? Then general demand in price p is 2iii( p )S ( p )2????iiS ( ) 0? ?1211??? ? ????12D ( p ) = D ( p ) (1 ) D ( p ) 1 p /? ? ?? ? ? ?θ2 θ1 p P1=c D1 D2 S2(p) S1(p) Case1： perfect price discrimination ? Assume that monopoly can observe θi directly. Then it can set marginal price as p1=c, and set personal fixed fee ? Manufacturer’s monopolistic profit is ? Leave distribution question out of account, welfare here is optimal. 2iiii( c)A S ( c)2?????2212112( c) ( c)(1 )22??? ? ?????? ? ?Case2： Monopoly pricing ? Assume that consumers have plete arbitrage, so that monopoly can only set uniform price： T(q) = pq ? Profit is (pc)D(p), and D(p) =1 p/θ ? Monopoly price is ? Monopolistic profit is ? Here we assume that monopoly decides to provide goods to two kinds of consumers. It need (c+θ2)/2≤θ1, or λ is large enough. m2cpp2????22( c )4?????Case3： Twopart tariff ? Assume also that monopoly provides goods to two kinds of consumers. ?