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

Motives for Advance Purchase Discounts 1)Traditional Price Discrimination Courty and Li, 2000, Deneckere and McAfee,1996, Anderson and Dana, )Reducing Monopoly Distortion - Homogeneization Courty, 2003, Shugan and Xie, 2001, Gale and Holmes 1992, )Information and Customization of Capacity (or Price) Tang, et. al., 2000, Arrow-Debreu 4)Screening and Capacity Utilization Dana, 1998, 1999, Gale and Holmes 1992, 1993

Advance Purchase Discounts = Damaged Goods? Purchasing in advance is an inconvenience –If consumers who are more inconvenienced also have higher valuations, then advance purchases requirements can segment high and low value consumers Analogy seems good

Yet Advance Purchase Discounts are Quite Different Consumers are learning over time about their own preferences –The inconvenience is (at least in part) derived from uncertainty about future preferences –Consumer’s behavior is changing over time Aggregate uncertainty –Capacity must be planned in advance –Market prices must be planned in advance –Consumers face greater expected costs of stockouts (which are especially costly for high value consumers)

A Simple Model of Price Discrimination A model in which the inconvenience of advance purchase is due to uncertainty about preferences (e.g., departure time or destination) Two Types: Business and Leisure Time 0 (advance) and time 1 (spot) Consumers forecast their preferred product with probability  i Ex post valuations are V(i,0) = v i for the preferred and v i – x i Ex ante valuations for the preferred product are Ex ante valuations for the alternative

Three Pricing Options Sell to the business travelers only in the spot market at the business traveler ’ s valuation Sell to both leisure travelers and business travelers in the spot market at the leisure travelers valuation Sell to leisure travelers in advance at their valuation and sell to business travelers in the spot market at the highest possible price.

The Advance Purchase Option Advance purchase discounts are optimal when or If V(B,0) < V(L,0), advance purchase discounts are clearly profitable. But if V(B,0) < V(L,0) this is not automatically satisfied.

The Advance Purchase Option Note that is not sufficient. That is, correlation between v and the expected cost of consuming the wrong product is not sufficient for advance purchases to be profitable.

A General Model Assume a continuum of consumers with uncertain valuations and a single firm with unit costs of capacity k, and usage costs c, but who must produce in advance. Notation –Let  denote the aggregate state with pdf g(  ) –Let  denote a consumer ’ s type with distribution f( ,  ) –Let v 1 denote a consumer ’ s valuation for product 1 with distribution  1 (v, ,  ).  1 is increasing in . –Let v 2 denote a consumer ’ s valuation for product 2 with distribution  2 (v, ,  ).  2 is increasing in . –Let h(  ) denote the distribution of  given . f, g, h, and  are common knowledge

The General Timing The firm make an initial production decision The firm offers its products at the advance purchase price –Offers may or may not include a refund option Consumers learn their types  –And update their beliefs, h(  ), about the aggregate state Consumers make purchase decisions The firm update its beliefs about the aggregate state The firm revises its capacity/inventory decision The firm offers its products at the spot price Consumers learn their realized valuations Consumers make purchase decisions Consumers exercise their return options, if available

Special Cases Ex ante homogeneous consumers –No aggregate uncertainty, k = c = 0 The firm will sell in advance at p = E[v] (Courty, 2003 and Shugan and Xie, 2001) –No aggregate uncertainty, E[v] < c + k The firm will sell in the spot market at the monopoly price (Courty 2003 and Shugan and Xie, 2001) –Aggregate uncertainty, k > 0, no consumer learning (v =  =  ) The firm will sell a limited amount in advance to learn  and then adjust its inventory for the spot market (Tang, et. al. 2000)

Special Cases Ex ante heterogeneous consumers and no aggregate uncertainty –Two products, x =  v 1 – v 2 , max {v 1, v 2 } = v(  ), min {v 1, v 2 } = v(  ) – x, k > 0. This is the example we solved above. –Refunds feasible, k = 0, c > 0. The firm will segment consumers with a menu of advance- purchase, partially-refundable contracts (Courty and Li, 2000) –Two products,  =  v 1 – v 2 , max {v 1, v 2 } = constant, refunds not feasible, k > 0, same capacity is used for both products. If more consumer will prefer product 1 to product 2, advance purchase discounts is the cheapest way to move low  consumers to product 2 (Gale and Holmes, 1993).

Research Agenda Ex ante heterogeneous consumers with aggregate uncertainty –Related work by Gale and Holmes, 1992, Dana, ??

Four Effects 1)A firm with market power may find it profitable to extract more surplus from high value consumers by making its lower priced products available only in advance, an option which is less attractive to high value consumers. 2)A firm with market power may be able to extract more surplus from consumers by selling in advance; particularly if consumers are more homogeneous in advance. 3)A firm can use consumers’ advance purchases as information to economize on capacity or inventory in the spot market and to adjust prices in the spot market. 4)A firm can use advance purchases to improve capacity or inventory utilization and better allocate capacity, particularly when the spot market is not a “perfect” market. Firms With Market Power All Firms