At the point when is Price Discrimination Profitable

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At the point when is Price Discrimination Profitable? Eric T. Anderson Kellogg School of Management James Dana Kellogg School of Management

Motivation Price Discrimination by a Monopolist Offer different results of varying qualities Distort quality sold to low esteem customers (Mussa and Rosen, 1978) But, value segregation is not generally ideal, and positively not generally utilized Stokey (1979) Salant (1989)

Research Agenda Develop prescriptive apparatuses to assess when value separation is gainful. Applications Advance Purchase Discounts Screening utilizing decreased adaptability Intertemporal Price Discrimination Screening utilizing utilization delays "Harmed" Goods Screening utilizing lessened elements Versioning Information Goods Coupons

Key Assumption: Quality is Constrained Commonly Made Assumption Explicit Salant (1989) Usually verifiable and underemphasized Coupons (Anderson and Song, 2004) Intertemporal Price Discrimination (Stokey, 1978) Damaged Goods (Deneckere and McAfee, 1996) Versioning (Bhargava and Choudhary)

Case 1: Two Types Assumptions Two buyer sorts, i  {H,L}, with mass n i Utility: V i (q) Cost: c(q) Unconstrained Quality Constrained Quality Upper Bound is q=1

Three Options Sell only one item to only the high esteem customers Set the cost at high sort's ability to pay Sell only one item, however value it to offer to both the high and the low esteem shoppers Set the cost at low sort's eagerness to pay Sell one item intended for the high sorts and second item intended for the low sorts. Value the low sort's item at their readiness to pay Price the high sort's item at their eagerness to pay or where they are quite recently unconcerned between their item and the low sort's item, whichever is higher. Bring down the nature of the low sort's item to "screen" the high esteem shoppers

Unconstrained Quality c'(q) V' H (q) V' L (q) q L q * L q * H

D c'(q) B V' H (q) A C V' L (q) q * L q * H Constrained Quality Bn H > A L Cn L > Dn H

Result Conditions for Price Discrimination Rewrite these as An essential condition may be

D c'(q) B V' H (q) A C V' L (q) q * L q * H Constrained Quality

Log Supermodularity A twice differentiable capacity F ( q , q ) is wherever log supermodular if and just if or equally

Case 1: Two Types, Two Products

Results Claim 1

Figure

Case 2: Continuum of Types and Qualities

Results Proposition: If V(q, q ) – c(q) is log submodular then the firm offers a solitary quality If V(q, q ) – c(q) is log supermodular then the firm offers numerous qualities

Results Corollary: If V ( q, q ) = h ( q ) g ( q ) and c ( q ) > 0 then the firm offers various items if for all q, and the firm offers a solitary item if

Applications Intertemporal Price Discrimination Damaged Goods Coupons Versioning Information Goods Advance Purchase Discounts

Intertemporal Price Discrimination Stokey (1979), Salant (1989) U ( t, q ) = qd t Product Cost: k ( t ) = c d t Transformation q = d t This gives us: V ( q, q ) – c ( q ) = q – cq Results This is not log supermodular

Intertemporal Price Discrimination More broad utility capacity – Stokey (1979) U ( t, q ) = q g ( t ) Price separation is attainable if g  ( t ) < 0 But is log submodular, if g  ( t ) ≤ 0 and c ≥ 0 , so value segregation never ideal.

Intertemporal Price Discrimination More broad cost work: c(q) The surplus capacity is log supermodular if and just if or minor cost > normal cost

Damaged Goods Model from Deneckere and McAfee (1996) Continuum of sorts with unit requests Two exogenous quality levels: q L and q H V( q H , q ) = q , V( q L , q ) = l ( q ) V(q, q ) - c(q) is log supermodular if With some extra changes, we recuperate the fundamental and adequate state of Deneckere and McAfee.

Coupons Model from Anderson and Song (2004) Consumers consistently dispersed on No Coupon Used: V( q ,N) = a + q b Coupon Used: V( q ,C) = a + q b – H( q ) Product Cost: c Coupon Cost: l V(q, q ) – c(q), q  {C,N} is log supermodular if

Versioning Information Goods Information Goods  No Marginal Cost Literature Shapiro and Varian (1998) Varian (1995, 2001) Bhargava and Choudhary (2001, 2004) Versioning beneficial just if

When are Advance Purchase Discounts Profitable? James Dana Kellogg School of Management