Free Shipping and Repeat Buying on the Internet: Theory and Evidence

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1 Free Sipping and Repeat Buying on te Internet: eory and Evidence Yingui Yang, Skander Essegaier and David R. Bell 1 June 13, Graduate Scool of Management, University of California at Davis (yiyang@ucdavis.edu) and te Warton Scool, University of Pennsylvania (skander@warton.upenn.edu; davidb@warton.upenn.edu). e autors tank seminar participants at Arizona State University, INSEAD, Koc University, UC Davis and Fall 2004 INFORMS Meetings for elpful comments. ey are grateful to Eitan Gerstner, Cristope Van den Bulte and Jon Zang for detailed suggestions and to comscore for providing data. A separate ecnical Appendix is available from te autors. e autors are listed in reverse-alpabetical order.

2 Free Sippping and Repeat Buying on te Internet: eory and Evidence Abstract Free sipping is widely regarded as te most effective marketing tool in e-tailing. We model a rational, cost-minimizing sopper wo responds to prices and sipping policies set by te e-tailer. A base scenario compares te optimal sopping policy under free and fixed fee sipping. A more complex case of value-contingent free sipping (e.g. sipping is free for orders over $X) explores ow prices and te free sipping tresold interact to affect te optimal policy. Compared to free sipping, sipping fees increase te rational sopper s optimal purcase quantities per visit, and te optimal elapsed time between visits. Contingent free sipping induces an iso-cost curve were different combinations of price and tresold keep long run average sopping costs constant for te rational sopper. Furtermore, te price-tresold relationsip is sown be inverted-u saped. is implies (1) te initial price level dictates weter prices sould be raised or lowered wen a site lowers te tresold for free sipping, and (2) price dispersion for omogenous goods increases wen te tresold is lowered. Key Words: Free Sipping, Internet, Retailing, Sopping Beavior

3 1 1 Introduction Internet-based sopping is te fastest growing sector in US retailing wit sales exceeding $110 billion for 2004 (Forrester Researc). E-tailers ave a number of marketing tools at teir disposal and in many instances specific tactics (suc as price cuts or coupons) and teir consequences are largely analogous to tose in offline settings. Free sipping, owever, represents an aspect of e-tailing for wic tere is often no clear correspondence wit offline practice. One may argue tat sipping costs substitute for costs of time and travel, yet it is unclear tat consumers view tem in tis way. 1 Sipping discounts appear vital for attracting customers and generating sales as approximately sixty percent of online retailers cite free sipping wit conditions as teir most successful marketing tool for driving business. 2 is well-documented success of free sipping and te relative paucity of researc on te topic motivates our study. We model a rational cost-minimizing sopper s response to price and sipping policies to develop insigts into ow tey affect sopping beavior. Model implications are tested using comscore data on repeat purcase beavior. Sipping Fees and Sopping Beavior. e beavioral mecanism is unclear, yet managers are confident tat sipping scedules ave a substantial impact on consumer beavior. Bizrate.com CEO Cuck Davis noted tat... (free sipping) wit conditions turned out to be te defining caracteristic of te 2002 oliday season adding is is not surprising considering tat te majority of online buyers said tat sipping costs prevent tem from buying more online. A January 2004 survey by NetIQ Corp concurs:... sipping and andling costs trigger 52% of te abandonment of online sopping carts. (DMA 2004). Clearly, anecdotal evidence suggests tat: (a) consumers are igly responsive to sipping policies, (b) tere is room for improvement in ow policies are crafted, and (c) little is known about consumer trade-offs tat lead to te observed beaviors. As te e-tailing sector grows, sipping fee structures will receive more attention (Cox 2002; Miller and Franco 2002). Absent formal researc insigt into ow free sipping works, many e-tailers including Amazon.com experiment wit different sipping policies. 3 A tangi- 1 ravel costs are incurred prior to product selection, wereas sipping fees are incurred at te conclusion of te site visit. 2 ere are a variety of sources for tis figure including sop.org/bizrate.com (2002 and 2003 Online Holiday Mood Study). e data on wic tis estimate is based is provided directly from online retailers. 3 Amazon.com began experimenting wit free sipping in 2002 and made it available for customers wo

4 2 ble illustration and point of motivation for our study is provided by Lewis, Sing and Fay (2005). ey estimate empirical coice and demand models on te order value and purcase incidence decisions of soppers at an online retailer selling non-perisable grocery and drugstore items. able 1 reproduces data from able 2 in Lewis et al (2005). [able 1 About Here ] e rows of able 1 distinguis two different kinds of fee structure free sipping and contingent free sipping. e first tree columns indicate te sipping fee attaced to orders falling in different size classes. e final column sows te average order value under te corresponding sipping fee regime. e data are consistent wit te idea tat consumers seek to ammortize iger sipping fees by purcasing larger quantities per site visit. Of course, data in able 1 do not control directly for selection effects (different regimes attract different kinds of soppers) and we return to tis point later. Contribution and Caveats. We develop a model of a rational cost minimizing sopper, ordering non-durable products from an Internet retailer. Wen te products run out, te sopper returns to te site. Conditional on needs tat trigger te site visit, te consumer makes purcase quantity decisions in response to te price and sipping policies set by te retailer. Analytical expressions for te optimal sopping policy under different sipping fee structures are obtained. We find te following: Consistent wit te empirical work in Lewis et al (2005), imposition of a sipping fee induces iger purcase quantities per visit from te rational sopper. e rational sopper also increases te elapsed time between site visits. Contingent free sipping (use of a free sipping tresold ) creates tension between price and te sipping fee. Specifically, we derive an iso-cost curve of combinations of price and tresold tat impose identical long run average sopping costs on rational consumers. It beaves as follows. As prices are increased, free sipping tresolds sould first increase ten decrease in order to leave a rational consumer equally well place orders above a certain tresold. Initially, tis was $99 (of eligible products) and was subsequently lowered to $49 and ten to $25 (see Jung 2003). In te Discussion section we report Amazon s latest sipping policy experiment Amazon Prime all-you-can-eat express sipping.

5 3 off. 4 ypically, price increases are bad news for consumers, everyting else constant. Wit repeat buying on te Internet owever, a price increase as negative and positive effects. e negative effect of iger prices is tat on average, purcasing costs will increase. e positive effect is tat te average probability of exceeding te free sipping tresold goes up, leading to a reduction in te average sipping fee incurred. Prices and free sipping tresolds interact in a subtle way. Weter or not a reduction in a free sipping tresold sould be accompanied by a price increase or decrease is sown to depend on te existing price level. We extend tis result to sow tat price dispersion for omogenous goods sould be greater wen free sipping tresolds are lowered. An exogenous cange in te free sipping tresold at a leading e-tailer is used to examine tis implication. e paper represents te first attempt (to our knowledge) to derive closed form caracterizations of te optimal sopping policy for consumers facing an e-tailer wo sets price and sipping policies. e contribution terefore lies in an analytical model to explore consumer beavior in tis setting. Under value-contingent sipping, te retail price and free-sipping tresold interact to impact consumers ordering policy in a complex yet predictable way. e model is intended to cover common purcasing contexts were consumers visit, store inventory, and ten repeat visit once te inventory is depleted. us, it is not suited to address all classes of Internet sopping beavior. e model is firmly grounded in te beavior of te consumer; we do not explicitly address wat is optimal for te firm. e model leads to testable implications, some of wic are examined wit exploratory empirical analysis and reference to oter publised work. e remainder of te paper is organized as follows. e next section introduces te model. We compare and contrast a sopping context in wic sipping costs are largely irrelevant (sipping is eiter free or always carged) wit one were tey are contingent: If a certain value tresold is reaced, consumers receive free sipping. Exploratory empirical analysis follows in a separate section and te paper concludes wit a discussion of te findings and avenues for future researc. 4 A grapical representation sows an inverted-u were price is on te x-axis and te free sipping tresold tat olds total cost constant is on te y-axis.

6 4 2 Background and Model We offer a brief review of related work and ten develop te model. Assumptions are motivated wit respect to existing literature and institutional details of Internet sopping. First, we analyze a base case of free sipping and fixed fees. We ten analyze te contingent free sipping case, were te sopper pays a fixed fee wen te total value of te order falls below a certain tresold, and obtains free sipping oterwise. 2.1 Related Work As noted in te Introduction, tere are many anecdotes regarding te effects of free sipping and te difficulty in implementing te rigt scedule, yet formal researc is scarce. Morwitz, Greenleaf and Jonson (1998) study partitioned pricing scemes of te following kind: (1) $82.90 including sipping and andling and (2) $69.95 plus $12.95 sipping and andling. ey find tat wen prices are partitioned as in (2) consumers can ave iger demand. ey are less likely to recall te full total cost but instead more likely to focus on te product cost alone. is migt imply tat E-tailers wo carge for sipping sould position it as an add on cost. Scindler, Morrin and Becwati (2005) explore tis finding furter and sow preference for bundled sipping fees is related to an individual different variable tey label sipping carge skepticism. Skeptics wit access to external reference prices prefer bundled prices. ese articles do not address free sipping tresolds. Hess, Cu and Gerstner (1996) analyze te strategic use of non-refundable sipping fees to mitigate returns by catalog soppers. Consistent wit te teory, empirical analysis suggests tat fees increase wit te value of te mercandise ordered, even wen costs remain constant. Cao and Zao (2004) study customer perceptions of inventory fulfillment but do not address free sipping directly. ey find tat satisfaction wit delivery is moderated by overall satisfaction wit prices. Lewis (2005) estimates ow sipping fees affect order size and site traffic. He finds tat free sipping brings more customers, but lower average order sizes (compared to oter scedules were sipping is not free). Incentives tat offer lower sipping fees on larger orders also increase te order value. Lewis, Sing and Fay (2005) find free sipping policies increase order sizes by approximately 10% on average and up to 35% for te most responsive customer segment.

7 5 2.2 Context and Assumptions We model a risk neutral sopper buying products on te Internet. e sopper first visits a site and ten makes a purcase decision for goods tat are bougt repeatedly over time. us, te model could apply to te purcase of groceries or any oter consumable goods for wic tere is repeat. ese are also goods for wic te sopper incurs positive storage costs for any inventory on and. Repeat visits to te site are trigged by low inventory levels (wic may be set to zero witout loss of generality). e structure is familar as it builds on te classic model of Golabi (1985) and recent extensions (e.g., Ho, ang and Bell 1998). Prior to visiting te website, te sopper plans to purcase some quantity of te product in question. A fixed quantity Q is selected on te basis of te prevailing price p. 5 Wile te price is known deterministically, te actual quantity of goods purcased is a random variable. e randomness expresses te notion tat upon visiting te site, particular marketing initiatives at te point of purcase (e.g., recommendations, pop-ups, etc.) could influence te final quantity bougt. Considering te nt visit by te sopper, te actual quantity purcased is terefore Q n = Q + ɛ n, were ɛ n is a random element tat captures te effect of tese marketing initiatives. e random socks ɛ n,n 1 are iid wit mean zero and variance σ 2. Φ denotes te cumulative distribution function associated wit ɛ n. e sopper as a known consumption rate r for goods under consideration. ese are consumed repeatedly. at is, wen groceries (or oter replenisable products) run out, te consumer returns to te site. 6 ime between successive visits is determined as follows. If te consumer purcases Q n at te nt visit, ten te elapsed time until te next purcase occasion is given by Q n /r. Once at te website, te sopper incurs a visit-specific transaction cost k (searcing for product information, typing in payment details and so fort). Moreover, te sopper incurs inventory olding costs per unit time on all products actually bougt. is implies tat te inventory cost incurred subsequent to te n t visit is given by Q n /2 Q n /r. at is, te olding cost multiplied by te expected inventory 5 Ho, ang and Bell (1998) employ a similar model structure but allow te (stocastic) price to follow a probability distribution wit n mass points. In our model, te price is known by te sopper witout cost since on te Internet tere is no fixed cost of travel to visit a store and learn precise price information. 6 Implicitly, we assume tat sopping at te site is triggered by zero inventory of te product, owever it is straigtforward to alter te model to consider te possibility tat future site visits are triggered by a non-zero tresold. Doing so as no effect on qualitative insigts.

8 6 on and, Q n /2, multiplied by te elapsed time to te next visit, Q n /r. e final element of cost is product expenditures wic are equal to pq n. Given tese assumptions and a context of repeat buying for replenisable items, we can caracterize te optimal sopping policy. We determine te optimal purcase quantity per site visit, te optimal elapsed time between visits and te total long run average cost of sopping. We subsequently augment te basic model set up wit a cost of sipping per trip, S n. Regardless of te particular sipping policy adopted by te site (free sipping, fixed fees, contingent fees, etc.) te objective of te sopper is always to coose te purcase quantity Q suc tat te total long-run average relevant cost per unit time is minimized. 2.3 Model Analysis We analyze two related classes of problem. In te first, sipping costs S n ave rater obvious effects on te optimal ordering policy. is serves as te base case and covers free sipping and fixed carges (independent of purcase value). e second class is value-contingent sipping fees. Many sites (including te one represented in able 1) offer free sipping wen purcases exceed a certain tresold. 7 Free Sipping and Fixed Fees Given we analyze repeat buying, we start wit te long run average cost per unit time to be minimized by te sopper. is as two components: (1) te expected relevant cost per unit time (i.e., te cost incurred on a site visit), and (2) te expected elapsed time between successive visits. e expression for te optimal purcase quantity is ten obtained by straigtforward differentiation. Define C n to be te cost incurred on te n t visit (1) C n = k + S n + pq n + 2r Q2 n. k and S n are te transaction and sipping costs, respectively. pq n are product expenditures and 2r Q2 n is te inventory olding cost. Let X n,n 1 be te random variable corresponding to te elapsed time until te next purcase after te nt visit (2) X n = Q n r = Q + ɛ n. r 7 ere are many variations in practice. Netgrocer.com, for example, carges sipping fees tat vary not only by order value, but also by region of te United States were te order is sipped.

9 7 Lemma 1 Under free sipping and fixed fees, te long run expected average cost per unit time LR(Q) is LR(Q) = k + S + pq + 2r (Q2 + σ 2 ) Q. r Proof: Because ɛ n,n 1 are iid, te time until next purcase, X n,n 1, is iid. Defining N(t) as te counting process tat specifies te number of visits from time 0 to time t, {N(t),t 0} is a renewal process, and te time until te next purcase is terefore a renewal cycle. e total cost incurred at time t is terefore C(t) = N(t) n=1 C n. Using Ross (1980), te long run average cost per unit time is equal to te expected cost in a renewal cycle E(C n ) divided by te expected lengt of a renewal cycle E(X n ). Combining equations (1) and (2) we obtain te stated expression for te long run average cost per unit time LR(Q). e long run average cost per unit time LR(Q) is pseudoconvex in Q since E(C n )is quadratic in Q and E(X n ) is linear in Q (see Avriel 1976). e optimal policy Q is terefore obtained by solving te first-order condition. We now solve for te two base cases: (1) free sipping, and (2) fixed carges. Free Sipping. Wen te retailer does not carge for sipping S n = 0 and te solution to te first order condition yields 2kr Q Free = + σ2. is can be simplified to obtain a familiar expression, akin to tat for te standard inventory model. o see tis let ˆK Free = k + 2r σ2 so tat Q 2r Free = ˆK Free (3). e optimal long run average cost per unit time is given by LR(Q Free )=L Free = 2r ˆK Free + rp = Q Free + pr. Fixed Fees. Starting wit Lemma 1 and solving te first order condition wit S n = K yields 2(k+K)r + σ 2 = 2r ˆK F ixed were ˆKF ixed = k + K + 2r σ2. (4) Q F ixed = Here LR(Q F ixed )=L F ixed = 2r ˆK F ixed + rp = Q F ixed + pr. Comparing tis to te result for free sipping leads to a straigtforward and reassuring conclusion. A fixed fee increases

10 8 te optimal order quantity per site visit, Q, and also increases te elapsed time between visits, Q /r. Furtermore, te addition of a sipping fee necessarily increases te long run overall cost faced by te sopper. Value-Contingent Sipping Fees e cases of free sipping and fixed fees offer straigtforward results. Analysis of valuecontingent sipping fees provides te more interesting and less obvious insigts. e e-tailer now waives te sipping fee wen sopper expenditures exceed a certain level, wic we denote by. If expenditures exceed ten S n = 0, and if not S n = K. e total cost incurred on visit n pivots around te free sipping tresold as follows C n, = k + pq n + 2r C n = Q2 n if pq n, C n,l = k + K + pq n + 2r Q2 n if pq n <. C n, (C n,l ) represents te cost incurred wen te sopper s purcase value is iger tan (lower tan). Substituting Q n = Q + ɛ n in te condition we ave C n, = k + pq n + 2r C n = Q2 n if ɛ n p (5) Q, C n,l = k + K + pq n + 2r Q2 n if ɛ n < Q. p e expected cost incurred on te n t visit is a weigted sum were te weigts are simply te probabilities of exceeding te tresold (and paying no sipping fee), or not. Hence [ ] (6) E(C n )= 1 Φ p Q E(C n, )+Φ p Q E(C n,l ). We ave te following lemma. Lemma 2 Under te value contingent sipping policy, te long run expected average cost per unit time is [ ] (k 1 Φ( p Q) + pq + 2r (Q2 + σ 2 ) ) +Φ( p Q) ( k + K + pq + 2r (Q2 + σ 2 ) ) (7) LR(Q) =. Proof: e argument is te same as in Lemma 1. e total cost incurred at time t is C(t) = N(t) n=1 C n. Combining equations (5) and (6), we get te expected cost in a renewal cycle E(C n ) and divide it by te expected lengt of a renewal cycle E(X n )= Q r per unit time LR(Q). Q r to obtain te stated expression for te long run average cost

11 9 o obtain te probabilities from Φ( ) we assume tat ɛ n is uniform on an interval [α, β]. Because te mean of te distribution is zero, ɛ n is uniform on [ β,β], β > 0. Beaviorally tis says tat random elements of website layout and marketing initiatives ave bot positive and negative effects on quantities purcased, but on average tese effects even out. e value of (/p Q) combines wit te extremes of te uniform distribution to produce one analytical expression and two boundary conditions for te probability tat te free sipping tresold is exceeded and te sopper pays no fee. Specifically, wen (/p Q) lies witin te interval ( β,β) te probability of paying no fee, 1 Φ ( p Q), is equal to β ( p Q). at is, te discrepancy between /p and Q is not 2β too large. In te extreme case were te sopper always its te (low) tresold, (/p Q) is non positive and less tan te lower support of te distribution (i.e., Q β). is p means tat 1 Φ ( p Q) is equal to one. Conversely, wen te free sipping tresold is impossibly ig ( Q β) te sopper pays te sipping fee wit probability one. e p collectively exaustive and mutually exclusive conditions are Φ( Q) = ( p Q)+β and 1 Φ( Q) = β ( p Q), wen Q ( β,β], p 2β p 2β p (8) Φ( Q) =0 and 1 Φ( Q) = 1, wen Q β, p p p Φ( Q) =1 and 1 Φ( Q) = 0, wen Q β. p p p In deriving te sopping policy implications for different combinations of prices p and free sipping tresold we will consider all combinations of cost function tat arise from te tree regions of probability weigt. Combining (7) and (8), we obtain a cost function wit tree brances: LR(Q) = L F ixed (Q) = k+k+pq+ 2r (Q2 +σ 2 ) Q r L Int (Q) = (k+pq+ 2r (Q2 +σ 2 ))+K ( Q r L Free (Q) = k+pq+ 2r (Q2 +σ 2 ) Q r p Q)+β 2β, wen Q p β (Fixed Branc), wen Q ( p β, p + β) (Intermediate Branc), wen Q p + β (Free Branc) Earlier we sowed tat te first order conditions determine Q F ixed and Q Free as te global optimum for L F ixed (Q) and L Free (Q), respectively. Similarly, te global optimum for L Int (Q) obtains troug te first order condition as (9) Q = Q Int = Q Free 2 + β p + β.

12 10 Simple algebra allows us to express te value-contingent sipping fee cost function as ( ) L F ixed (Q) = Q 2 F ixed 2 Q + Q + pr, wen Q p β LR(Q) = L Int (Q) = Q 2 Int (10) 2 Q + Q 2β + pr, wen Q ( p β, p + β) ( ) L Free (Q) = Q 2 Free 2 Q + Q + pr, wen Q p + β e analysis to determine te optimal policy arising from te cost function (10) is sligtly more involved tan tat following Lemma 1. We proceed in two steps. First, we obtain te optimal sopping policy for eac of te tree brances of te cost function (10). is leads to five potential optimal order quantities. Second, we rule out one of tese and focus on te remaining four to determine te range of over wic eac is te optimal sopping policy. p ese steps are detailed in te Appendix. We assume tat < 8β2. Note tat measures te consumer s unit storage cost over 2r te consumption cycle. We assume tis unit storage cost is large enoug relative to te sipping fee (i.e., > 1 K). In te Appendix we sow tat, in te presence of contingent 2r 16β 2 sipping, te global optimal order quantity (Q ) tat results from (10) is defined by Q = Q Free and LR(Q )=L Free = Q Free + pr if p <Q Free β Q = p + β and LR(Q )=L Free ( p + β) if Q Free β p Q Free2 + Q = Q Int and LR(Q )=L Int = Q Int 2β Q + pr if 2 Free + ( 2β Q = Q F ixed and LR(Q )=L F ixed = Q F ixed + pr if p Q F ixed + 4β + β (11) Wit tese expressions in and we can establis Proposition β + 2β β ) 2 + 2β β< p <Q F ixed + 4β + β Proposition 1 ere are closed form solutions for te optimal order quantities in te presence of contingent sipping. e actual optimal order quantity and te associated optimal long run average cost per unit time cange depending on te value of /p. Figure 1 illustrates te optimal solutions wit respect to /p. Wen te sipping tresold is very small relative to p (Region 1 of Figure 1), te optimal optimal order quantity is independent of and equal to Q Free, te optimal order quantity under te free sipping regime. As is very low relative to p, an order quantity of Q Free guarantees tat on any purcase occasion, te sopper always buys

13 11 Figure 1: Optimal Solutions wit respect to /p Q F ixed = p Q F ixed + + β 4β Q Int β p 2 Q Free 1 = Q p Free β + β 2β = p Q Free β p enoug to satisfy te low dollar purcase requirement for free sipping. 8 As increases relative to p and we move beyond Region 1, ordering Q Free no longer guarantees free sipping. wo competing forces are now at work. On te one and te consumer wants to increase te order quantity so as to reac te tresold and avoid te sipping carge K; on te oter and, suc an increase in te order quantity leads to undesirably iger inventory costs. As it turns out, te first force completely dominates in Region 2, wereas bot forces balance eac oter in Region 3 (were te optimal order quantity reflects a compromise solution). In Region 2, te quantity Q Free no longer guarantees free sipping on all purcase visits as p >Q Free β. e sopper optimally increases er order from Q Free to Q = + β, p wic is te minimum order quantity required in order to reac te free sipping tresold (and avoid paying te fee) on all sopping occasions. e consumer increases er order 8 Wen Q = Q Free, tis guarantees tat even for sopping occasions were te actual purcased quantity is at te low end of te support (ɛ n = β and Q n = Q β = p ), te free sipping tresold is reaced: pq n p(q Free β), wic is greater tan te tresold in Region 1.

14 12 quantity and does wat it takes to obtain free sipping, regardless of te associated increase in inventory costs. In Region 2, te incentive to avoid te sipping fee troug increased order quantity completely dominates te disincentive associated wit iger inventory costs. As we move into Region 3, furter increases relative to p. e required increase in order quantity to avoid paying te sipping fee becomes substantial, and so does te associated increase in inventory costs. e disincentive associated wit iger inventory costs starts to bite and te optimal order quantity is no longer + β. e sopper strikes p a compromise between two opposite and competing incentives avoiding te sipping fees versus minimizing inventory costs. e optimal balance is now an intermediate quantity Q = Q Int between Q Free and p +β.9 Wit Q = Q Int, te consumer will avoid te sipping fee on some purcase visits but not on all of tem. Se owever will carry a lower inventory cost tan wat se would if se ordered + β (in a bid to avoid te sipping fee on all p purcase visits). 10 Finally, as we move into Region 4, becomes too large relative to p. e optimal order quantity is independent of and equal to Q F ixed. As is too ig (relative to p), te sopper can never attain it and always pays K. Wit te optimal policy in and, we can start to understand ow p and in combination influence te rational sopper. We can, for example, explore te implications of a decision to decrease prices wile at te same time increasing. Similarly, we can obtain insigt into wat sould appen wen is lowered (from say $49 to $25). Intuitively, lower prices or a lower tresold for free sipping will lead to lower costs for rational soppers. Considering te two variables togeter, owever, produces more nuanced insigts. For a given value of, iger prices make it more likely tat te sopper will exceed (and pay S n = 0) more often over repeated visits. e net effect terefore requires more detailed elaboration. 9 In Region 3, we ave Q = Q Int < p. Also, one can see clearly from equation (9) tat Q Int >Q Free. 10 Our assumption tat < 8β2 insures tat te consumer s unit storage cost over te consumption cycle 2r is large enoug relative to te sipping fee K so tat te disincentive associated wit iger inventory costs as some bite in Region 3. Wen tis condition is not satisfied and te unit storage cost is too small relative to te sipping fee (i.e., 8β2 ), ten te inventory cost disincentive is too small to ever be a concern, and in tat case, even in Region 3, te consumer orders enoug to guarantee free sipping on every purcase visit; i.e., Q = p + β.

15 13 e Relationsip Between Free Sipping resolds and Prices (p) Wen is eiter very large (Region 4) or very small (Region 1) relative to p, te optimal long run average cost per unit time is independent of. We terefore restrict attention to te more interesting situation were bot te and p affect te optimal policy (Regions 3 and 2 in Figure 1). In tese regions te ratio /p is of moderate size. In wat follows, our focus continues to be on te beavior of te consumer expressed troug te optimal sopping policy. Any implications for optimal firm beavior are implicit rater tan explicit, and we will return to tis issue in te concluding section. In order to understand ow and p interact in teir effect on consumer beavior, we define an iso-cost curve. e iso-cost curve is a function of and p suc tat all points (i.e., every combination of and p captured by te curve) impose an identical level of long run average cost per unit time on te rational sopper. We define te iso-cost curve analytically, illustrate it grapically, and ten explore its properties. We begin wit Region 3. Here [ Q p Free β + 2β β,q F ixed + + β] and 4β Q = Q Int. From tis we obtain te optimal long run average cost per unit time and set tat equal to a constant, C L Int = Q Int + rp 2β = C. It is now possible to express as a function of p as follows 11 3 (p) =p C pr β + β ( C pr (12) ) 2 Q Free2 + ( 2β ) 2. Wit tis expression we analyze te properties of te Region 3 iso-cost curve and summarize tem in te following Lemma. Lemma 3 e feasible region for te 3 (p) curve is illustrated in Figure 2. e curve is concave between p =0and p = r 3. Proof: See ecnical Appendix. 11 e constant C sould be greater tan te lowest possible cost tat can be acieved in tis system wic is L Free = Q Free + pr (i.e., te minimum cost tat can be acieved wen tere are no sipping fees). us C pr Q Free.

16 14 [ Figures 2 and 3 About Here ] In Region 2, p [Q Free Q β, 2 Free + 2 2β + β]. Following te same style of 2β analysis, we set te optimal long run average cost per unit time in Region 2 equal to a constant C (recall tat C pr (13) Q Free ) and obtain (C 2 (p) =p C pr ) pr 2 β + Q Free 2. Lemma 4 summarizes te properties of te function in Region 2. Lemma 4 e feasible region for te 2 (p) curve is illustrated in Figure 3. e curve is concave between p =0and p = r 2. Proof: See ecnical Appendix. us, we ave sown tat in Regions 3 and 2 were te ratio /p is moderate suc tat te tresold and te price bot affect te optimal policy, te iso-cost curves defined by 3 (p) and 2 (p) are concave in teir relevant regions. Finally, Lemma 5 describes ow te curves 3 (p) and 2 (p) intersect at te boundary line Q = 2 p Free + 2 2β + β 2β tat separates Regions 2 and 3. Lemma 5 (a) e curves 3 (p) and 2 (p) cross te boundary of Regions 3 and 2 at te same point p, and (b) 2 (p) and 3 (p) are tangent at te point p i.e., 2(p )= 3(p ). Proof: See ecnical Appendix. e iso-cost curve (p) defined by 3 (p) in Region 3 and by 2 (p) in Region 2 is continuous and concave over te Regions 3 and 2. is is sown in Figure 4 and we summarize te result in Proposition 2. [ Figure 4 About Here ] Proposition 2 In Region 3 and 2, te iso-cost curve (p) as an inverted-u sape.

17 15 Along te iso-cost curve te rational sopper incurs te same optimal long run average cost per unit time. e first observation is terefore tat many combinations of price levels and free sipping tresolds can impose te same total cost, leaving te rational sopper indifferent between suc scemes. e inverted-u sape for te iso-cost function also implies te following. Imagine tat two different sites set te same value for. For example, bot sites offer free sipping wen orders exceed $25. Holding constant it is straigtforward to see tat tere are two price points (a low and a ig price) tat impose te same total long run average cost on te rational sopper. 12 e intuition is as follows. Wen price levels are relatively low, it is less likely tat te value of te order will be large enoug to surpass te tresold value. e sopper is terefore more likely to incur te sipping carge K. So, even toug te sopper benefits from lower prices, se seldom gets te benefit of free sipping. Conversely, at te ig price point te sopper pays more and is more likely to exceed and pay no sipping fee. e net effect is tat for te same value of two different price points impose te same expected total long run cost on te consumer. is is illustrated in Figure 5. [ Figure 5 About Here ] 2.4 Model Implications We explore two issues. First, wat do te canges in consumer beavior induced by a cange in suggest a firm sould do wit prices. Second, weter suc canges in ave implications for price dispersion. Proposition 2 provides te basis for te analysis. Free Sipping resold and Retail Price Canges Suppose a firm lowers its free-sipping tresold. If te goal is to alter beavior but leave consumers equally well off in terms of teir total long run average sopping costs 13 sould 12 Recall te conditions (Lemmas 3 and 4) under wic tis is true. It must be te case tat te ratio /p is moderate suc tat bot variables influence te optimal policy. 13 is is a useful goal for te firm. If any tresold cange leaves long run average consumer costs constant but canges te buying pattern, consumers sould continue to purcase at te same rate. At te same time,

18 16 suc a cange be accompanied by iger or lower prices? o answer tis question, consider te impact of an increase in te retail price p on consumers welfare in terms of teir total long run average sopping cost. A price increase as two effects: (1) a direct negative effect, as it increases consumers purcasing costs, and (2) an indirect positive effect, as it increases te likeliood tat consumers reac te free-sipping tresold over teir repeated purcase visits (and ence save on sipping fees over a greater number of purcase visits). Figure 5 sows tat (under te conditions specified in Lemmas 3 and 4) te iso-cost curve is inverted-u saped. Wen te current retail price is low and to te left of te peak, te indirect positive effect dominates te direct negative effect. Consumers are better off wit te price increase. If te goal of te site is to alter beavior but leave consumers equally well off in terms of teir total long run average sopping costs, te firm accompanies te price increase wit a raising of te sipping tresold. is allows te firm to recapture some of te surplus given to consumers wo would oterwise benefit from te price increase by triggering te free sipping tresold more often, were it to remain uncanged. Conversely, wen te current retail price is already ig (to te rigt of te peak in Figure 5), te direct negative effect dominates. Consumers are worse off wit a price increase. If te goal is to again keep consumer costs constant, te firm sould accompany te price increase wit a lowering of te sipping tresold. is compensates consumers for te surplus tat would ave been taken away ad te tresold remained uncanged. e answer to te initial question is now evident. A firm wit already low prices (to te left of te peak in Figure 5) sould drop prices furter wen lowering te tresold. Oterwise total consumer costs are interior to te iso-cost curve and consumers receive a benefit at te firm s expense. For te same reason, a firm wit ig prices sould increase prices furter wen lowering te free sipping tresold. Free Sipping resold and Internet Retail Price Dispersion e price-tresold relationsip just analyzed can be extended to provide insigt into price dispersion. For ease of exposition we compare a ig tresold site wit a low tresold profit implications for te firm could be very different. e firm may, for example, prefer to sip four small orders of value x/4 to one large order of x.

19 17 site. 14 Let LR (H) and LR (L) be te optimal long run average costs per unit time at te ig tresold site and te low tresold site, respectively. Imagine bot wis to be viewed as equally competitive, in te sense tat tey impose te same total long run average cost on te rational sopper: LR (H) = LR (L) = LR. From Proposition 2 we know tat for any given free sipping tresold, tere are two price points a low and a ig price tat impose te same total long run average cost on te rational sopper (see Figure 5). Define p 1 (L ) and p 2 (L ) to be tese prices at te low tresold site, wit p 1 (L ) <p 2 (L ). Similarly, Let p 1 (H) and p 2 (H) be te prices at te ig tresold site, wit p 1 (H) <p 2 (H). e iso-cost curve in Figure 5 implies tat all four price and tresold combinations impose te same long run average cost. at is, LR is identical witin and across sites. It is easy to see tat te price dispersion p 2 (L ) p 1 (L ) te low tresold firm can witstand is larger tan te price dispersion p 2 (H) p 1 (H) tat te ig tresold firm can witstand (see Figure 6). [ Figure 6 About Here ] Corollary 1 Suppose tat bot Internet sites would like to be viewed as equally competitive in te sense tat LR (H) =LR (L). en te Internet store wit te iger free sipping tresold will ave a lower price dispersion. 3 Empirical Analysis e contribution of tis researc is to develop a model of consumers Internet sopping beavior under various sipping fee structures, and derive closed form caracterizations of te optimal sopping policies. We sow tat in te presence of value-contingent sipping, retail price and te free-sipping tresold interact to impact consumers ordering policy in a complex yet predictable way. is researc, terefore, also offers implications tat can be examined empirically. We describe our data and two ypoteses to be tested. 14 e ig tresold site (for example) requires purcases of $49 as qualification for free sipping wile te low tresold site requires only $25.

20 18 Data Description comscore compile data on Internet browsing and purcasing beavior and make it available for academic researc. More tan 100,000 Internet users were tracked for te period July 1 troug December 31, is panel is a random sample drawn from a cross-section of global Internet users wo ave given comscore explicit permission to monitor teir Internet activity. For eac sample member, te data contain information on wen and wat tey purcase, were tey purcase from, and ow muc tey pay. Hypoteses and Findings We test te following ypoteses: H 1 (Purcase Quantity and Sipping resolds): Average purcase quantities increase wit te level of te free sipping tresold. H 2 (Price Dispersion and Sipping resolds): Price dispersion for omogenous goods decreases wit te level of te free sipping tresold. Hypotesis 1 is consisent wit data in Lewis et al (2005) and able 1. o test it furter, we examined comscore data for an Internet site wit repeat purcasing were te tresold canged. e best candidate site was Amazon. 15 Stated limitations notwitstanding, use of a single site allows us to somewat control for oter exogenous canges in te environment or customer mix tat migt ave also led to canges in te average purcase quantities. From July 1, 2002 to August 24, 2002 orders tat exceeded $49 qualified for free sipping. From August 25, 2002 troug October 18, 2002 tey qualified at $ Under te $49 regime, te average purcase quantity of products per order was Under te $25 regime it was ese averages are significantly different (p <0.001). e finding is consistent wit H 1. A small sample of witin-individual data also supports H 1. ere were 45 panelists wo 15 Repeat purcasing takes place at Amazon, owever te core produts of books, music, movies and video games depart somewat from te notion of consumables in our analytical model. ese products are more likely to be accumulated tan used in te traditional sense. is limitation aside, tese are te best data available troug comscore. 16 is was te only cange during te period of te data. Note we are examining two periods of equal lengt (seven weeks) and ave excluded obvious oliday seasons.

21 19 qualified for free sipping under bot regimes. ey spent $17 less per free-sipping order wen buying under te $25 tresold and purcased 1.82 fewer items. e second ypotesis is also tested wit comscore data from Amazon.com. 17 comscore assigns products to te following categories: Books, Movies and Video, Music, and Video Games. Using tese categories, it is relatively straigtforward to obtain exact matces in te log files. Specifically, we must use exactly te same product (book, CD, etc.) and compute two observations on price dispersion: (1) price dispersion under te $49 regime, and (2) price dispersion and under te $25 regime. is resulted in 40 unique qualifying products and a total of 80 observations for te regression analysis (data are available upon request). We considered every book, CD, DVD and video game tat was purcased at least twice during bot periods outlined above as a minimum of two observations per item, per period, are needed to compute our measure of price dispersion. e teory implies tat te lower tresold period sould ave a iger price dispersion for omogenous goods. is follows from Corollary 1 and Figure 6. By considering individual items (books, CDs, DVDs and video games) tat are purcased at least twice in eac period we ave truly omogenous goods in tat we can compare te cange (if any) in price dispersion for a specific item across te ig ($49) and low ($25) tresold regimes. According to Corollary 1 item-specific price dispersion under eac regime is simply te difference between te maximum and minimum price for te item during te regime. is definition of dispersion is also consistent wit recent work in economics by Sorensen (2001) in is examination of dispersion for prescription drugs. e following regression is used to analyze te relationsip between price dispersion PD i for item i and te tresold (14) PD i = α 0 + α 1 MUSIC + α 2 BOOK + α 3 MOVIE + βl were MUSIC, BOOK and MOVIE are category fixed effects. L = 1 wen te free sipping tresold is $25, and L = 0 wen te tresold is $49. e teory predicts greater price dispersion wen te tresold value is lower, so we expect β>0. [ able 2 About Here ] 17 Proposition 2 and Collorary 1 apply equally to two different sites, or to one site wic canges its tresold at different points in time. e only requirement is tat one focus on a omogenous good.

22 20 able 2 sows tat consistent wit H 2, β is significantly greater tan zero (p <0.05); price dispersion for omogeneous goods is iger wen te tresold value is lower. (Average price dispersion is $10.25 under te $25 regime and $2.39 under te $49 regime.) Moreover, if prices of a given item decline over time one would expect less dispersion (variation) for tat item in te second period of te data. Had Amazon set a low tresold ($25) for te first period, and a ig tresold ($49) for te second period, evidence for iger variation in te first period could be tainted. More variation under te $25 regime could simply be due to iger price levels at te beginning of te data (rater tan attributable to te tresold effect). Fortunately, te naturally occurring ordering of a $49 tresold followed by a $25 tresold period works against tis possibility. us, we can rule out one potential confound iger average prices under te low tresold regime. 18 Wile te tests of H 1 and H 2 are intended as illustrative rater tan exaustive, tey do provide evidence tat is directionally consistent wit te predictions of te model. 4 Discussion and Conclusion Free sipping is considered te most effective marketing tactic in e-tailing. Managers affirm tis conjecture and recent academic researc as sows dramatic effects of sipping tresolds on site traffic and purcase quantities (see Lewis 2005, Lewis et al 2005). Our researc complements tese insigts wit an analytical model of ow sipping costs influence rational sopping beavior for goods bougt repeatedly. A base scenario were soppers encounter eiter fixed fees or free sipping sows tat tey will increase purcase quantities per site visit and increase inter-visit times wen faced wit sipping fees. is result is intuitive and borne out by te data. e more complex case of value-contingent sipping offers additional insigts. In particular, we sow tat iger prices are not necessarily bad news for soppers. Wile iger prices do increase purcase costs, tey also increase te probability tat a sopper will it te free sipping tresold. is is one important way tat e-tailing differs from traditional retailing. In offline retailing 18 Average prices under te $49 and $25 regimes for eac category and te p-value for equal means are as follows. Books ($14.69, $16.35, p<0.532), Movies and Video ($21.41, $23.59, p<0.134), Music ($13.24, $12.68, p<0.784) and Video Games ($49.98, $43.74, p<0.208). aking all observations togeter, tere is also no signifcant difference between average prices in te two periods (p <0.411).

23 21 price increases are always negative for soppers, everyting else eld constant. We derive an iso-cost function and sow tat for any tresold level tere are always two prices a ig and a low price tat impose te same long run average cost on a rational sopper. is insigt results from te countervailing effects of iger prices just described. ey increase purcase costs, but also elp te sopper qualify for free sipping. Wen te site wants to old consumer long run average costs constant, weter or not a lowering of te tresold sould be accompanied by a raising or lowering of te current price was sown to depend on te current price level. A site wit an already low price will want to lower prices furter to avoid giving up surplus to consumers. A site wit already ig prices will need to increase tem. e result was extended to sow tat lower tresolds imply greater price dispersion for omogenous goods. us our researc not only offers insigt into ow sipping tresolds work, but also into ow tey interact wit te oter key marketing mix variable, price. Preliminary empirical analysis of comscore data yields results consistent wit key predictions. e empirical results for purcase quantity also concur wit tose reported in Lewis (2005) and Lewis et al (2005). Sipping fees will continue to be an important marketing tool for Internet retailers. On Marc 15, 2005 Amazon CEO Jeff Bezos announced Amazon Prime all-you-can-eat express sipping. A fixed annual fee of $79 gives soppers free two-day sipping and $3.99 overnigt sipping (instead of $16.48). Bezos announced We expect Amazon Prime to be expensive for Amazon.com in te sort term. In te long term we ope to earn even more of your business... Wile we do not consider tis variation explicitly, our researc is a first attempt at an analytical framework for understanding te effect of suc policies. Future work migt also consider different classes of sipping service defined by delivery speed. 19 In addition, future analysis could consider firm profitability of different scemes. Wile we sow ow tresolds and prices affect consumer beavior troug te optimal sopping policy, we do not address te optimal coice of tresold or prices by firms. Weter te firm prefers customers to visit frequently and place small orders or less frequently and place large orders depends upon te cost of sipping and oter factors not considered ere. 19 A colleague and eavy user of Amazon expressed distaste for Bezos Amazon Prime. Se compiles an order over time but does not actually execute it until tere is sufficient value to it te tresold (tereby avoiding any sipping fees). Membersip in Amazon Prime would cause er to pay $79.

24 References [1] Avriel, Mordecai Nonlinear Programming: Analysis and Metods. Prentice-Hall, Inc., Englewood Cliffs, NJ. [2] Cao, Yong and Hao Zao Evaluations of E-tailers Delivery Fulfillment, Journal of Service Researc, 6 (4), [3] Cox, Bet Adventures in te Sipping Wars, Jupitermedia, June 21, [4] DMA Survey Studies Wy Consumers Abandon Online Sopping Carts; Sipping and Handling Costs rigger 52% of Abandonment, e Direct Marketing Association Newsstand, January 14, [5] Golabi, Kamal Optimal Ordering Policies Wen Inventories are Geometric, Operations Researc, 33, (3), [6] Hess, D. J., Cu, W., and Gerstner, E Controlling Product Returns in Direct Marketing, Marketing Letters, 7 (4), [7] Ho, eck-hua, Cristoper S. ang and David R. Bell Rational Sopping Beavior and te Option Value of Variable Pricing, Management Science, 44, (12:2), S [8] Jung, Helen Amazon s Free Sipping Pressures Oter Dot-Coms, Associated Press, January 28, [9] Lewis, Micael e Effect of Sipping Fees on Purcase Quantity, Customer Acquisition and Store raffic, Working Paper, University of Florida. [10], Visal Sing and Scott Fay An Empirical Study of te Effect of Nonlinear Sipping and Handling Fees on Purcase Incidence and Expenditure Decisions, Marketing Science, fortcoming. [11] Miller, Paul and Mark Del Franco e Price of Free S&H, Catalog Age, Oct 1, [12] Morwitz, V. G., Greenleaf, E. A., Jonson, E. J Divide and Prosper: Consumers Reactions to Partitioned Prices, Journal of Marketing Researc, 35 (4), [13] Ross, S Introduction to Probability Models, Second Edition, Academic Press, New York. [14] Sop.org Hig Satisfaction and Improved Fulfillment Drive Successful Online Holiday Season, December 19, [15] Scindler, Robert M., Morrin, Maureen, and Nada Nasr Becwati Sipping Carges and Sipping-Carge Skepticism: Implications for Marketers Pricing Formats, Journal of Interactive Marketing, 19 (1), [16] Sorensen, Alan Equilibrium Price Dispersion in Retail Markets for Prescription Drugs, Journal of Political Economy, 108 (4),

25 23 Appendix Proof of Proposition 1 Recall te cost function (10): ( L F ixed (Q) = 2 ( LR(Q) = L Int (Q) = 2 ( L Free (Q) = 2 ) Q 2 F ixed Q + Q + pr, wen Q p β ) Q 2 Int Q + Q Q 2 F ree Q + Q ) 2β + pr, wen Q ( p β, p + β) + pr, wen Q p + β o determine te optimal sopping policy tat arises from te cost function (10), we proceed in two steps. First, we obtained te optimal sopping policy for eac of te tree brances of te cost function (10). Second, we solve for te global optimum tat emerges from tis cost function, and determine over wic range of p eac of te candidate value is indeed te global optimal policy. Step 1 e cost functions L Free (Q),L F ixed (Q) and L Int (Q) in eac of te tree brances of (10) are pseudoconvex in Q since eac one of tem is te ratio of a quadratic function by a linear one (Avriel 1976). For eac one of tese tree cost functions, te optimal order quantity on an open interval can terefore be obtained by straigtforward differentiation. Free Branc. In tis first extreme situation we ave Q p + β so tat Φ( p Q) = 0 meaning tat te sopper always buys enoug to satisfy te (low) requirement for free sipping. In tis case te optimal sopping policy is caracterized by Q = Q Free if Q Free > p + β and Q = p + β if Q Free p + β Denote X Free = Q Free β and we ave: (15) { Q = Q Free and LR(Q )=L Free = Q Free + pr if p <X Free Q = p + β and LR(Q )=L Free p + β if p X Free Fixed Branc. Similarly, in te oter extreme situation, it is straigtforward to sow tat te free sipping tresold is so ig tat it is never met(q p β, so tat Φ( p Q) = 1), te optimal sopping policy is ten caracterized by Q = Q F ixed if Q F ixed < p β and Q = p β if Q F ixed p β Denote X F ixed = Q F ixed + β and we ave: (16) { Q = Q F ixed and LR(Q )=L F ixed = Q F ixed + pr if Q = p β and LR(Q )=L F ixed p β if p >X F ixed p X F ixed