Loyalty Program: the Dilemma of Shipping Fee Xue Tan

Yi-Chun Ho

Yong Tan

June 22, 2015

(The bulk of work was done by student.) Abstract Loyalty programs that offers free shipping after consumers subscribe the membership has become prevalent in recent years. This paper studies the mechanism of the novel membership free shipping and compares it with contingent free shipping, a traditional shipping schedule in which consumers are eligible for free shipping when the order size reaches a threshold. We find that the intrinsic difference membership free shipping brings is product differentiation by changing the speed consumers receive their products. By providing a higher value to consumers, retailers gain more profit, but society loses efficiency because of higher incidence of more expensive shipping. We also find that membership free shipping is a new invention that makes better use of consumer heterogeneity in terms of profitability. In contingent free shipping, retailers suffer from accommodating consumers with different demand. However, in membership free shipping, retailers benefit from heterogeneity of consumers when the value provided by the expedited shipping is high. This feature of membership free shipping is never discovered before. We also find that if one retailer enters the market earlier than the opponent, he enjoys first-mover advantage.

1

1

Introduction

Shipping fee is an important element of e-business ([7]). In early days, companies are in favor of contingent free shipping (CFS). Under this schedule, consumers enjoy free shipping after the cart size or transactional amount reaches a pre-determined threshold. CFS is widely used because it serves as quantity discount which can entice consumers to order more at a time[6]. From retailers’ perspective, this increases truckload utilization, and results in cost saving ([1]). In recent years, membership free shipping (MFS) has gained lots of popularity as a new form of free shipping. MFS is advertised as a premium service included in a merchant’s loyalty program. Consumers prepay an annual membership fee, and enjoy free shipping along with other benefits. The free shipping attached to loyalty program is usually expedited shipping, and other benefits include free return ship, and cash back. One example is Amazons Prime, a membership program offering a variety of services provided by Amazon. Since its launch in 2005, Amazon Prime has had more than 20 million members by January 2014. By paying an annual membership fee of $79, consumers enjoy free two-day shipping over selected Prime items. It’s regarded the best loyalty program in e-commerce in a sense that the Prime members consider Amazon their default online store mainly due to the free, expedited shipping ([9]). Despite its effectiveness in customer retention, the free shipping policy is a double-edged sword as the burden of shipping cost would completely lay on the retailers ([7], [6]). It has been estimated that Amazon lost at least $11 for each member to supply all the services it provides ([11]). It was also reported that Drugstore.com loses between $10 and $15 per order, and the loss is largely due to the shipping and handling fees ([2]). While investors regard membership free shipping as a disruptive model ([10]), to the best of our knowledge, no systematic research has been conducted over the economic impact of this new shipping schedule. In this paper, we are motivated to explore the intrinsic difference of two free shipping schedules: CFS and MFS. We study how customer demand heterogeneity 2

and value difference between loyalty and regular program affect online retailers’ profitability in a duopoly setting. Our rich set of results stem from a stylized analytical model that captures the intrinsic difference between MFS and CFS. Here we define the two effects that drive the decision of shipping strategy. The first effect is shipping effect. Small-basket and large-basket buyers both face the same product price, but large basket-buyer don’t pay the shipping fee because of the screening. Therefore small-basket consumers share part of the shipping cost from large-basket buyer. The second effect is membership effect. Large-basket consumers contribute to small-basket buyers by paying membership fee that drives the price low. By capturing the trade-off between shipping effect and membership effect, we are able to model the essential complication of accommodating heterogeneous consumers. Our results offer substantial insights into the decision making of price and shipping policy, and provide a well explanation to the phenomenons in online retailing industry.To the best of our knowledge, this is the first time membership free shipping is studied in a systematic manner. Methodologically, we provide a new way to revise linear city Hotelling model so that consumer heterogeneity does not only lay on preference, but also on demand. Traditionally, the Hotelling model assumes all consumers to have one unit demand. By allowing a portion of consumers to have two-unit demand, we introduce demand heterogeneity, enabling the analysis of the loyalty program. The revision of Hotelling model can be applied in many other circumstances. This paper is organized as follows. In section 2 we discuss related literature, and in section 3 we introduce notations and our model setup. In section 4 we do the equilibrium analysis, and compare different settings. In section 5 we draw conclusions.

3

2

Literature Review

Product differentiation and price competition was studied extensively in marketing literature([5],[3],[8]). Moorthy used a stylized model to represent firms’ choice of product quality, and allowed consumers to be heterogeneous in their willingness to pay. He examined price equilibrium, and product equilibrium both under simultaneous move and sequential move setting. We follow the spirit of Moorthy’s work to conduct our analysis. In Moorthy’s work, both product quality and consumers’ type are continuous. In our work, product quality is discretized at high quality and low quality, and consumers are homogeneous in valuing the differentiated product. The consumer heterogeneity is brought up only by different demands. This is crucial because it allows us to focus on the role of demand heterogeneity with a more complicated pricing schedule. Quantity discount as a nonlinear price schedule has been widely studied in economics literature. [4] reviewed the different non-linear price schedules, and stated that two-block tariffs generate profits that are greater than or equal to two-part tariffs. In our study, the membership free shipping is a form of two-part tariff, and the contingent free shipping has a flavor of two-block tariff. We have similar conclusion that MFS brings higher profit to retailers than CFS if both retailers are using the same shipping strategy. Loyalty program or promotions that are associated with reduced shipping fee has been studied in marketing literature. [6] and [7] empirically examined the impact of different shipping schedule over consumers’ purchase incidence and order quantity, and find the positive effect of contingent free shipping. In sum, it’s unclear from previous literature how membership free shipping and contingent free shipping impact profitability and social efficiency differently. Academia lacks theories to answer to the questions raised by retailers of how to choose shipping policy.

4

3

Models

The following assumptions rationalize our analytical model.

3.1

Setup and Notations

Throughout this paper, we use MFS to denote membership free shipping, CFS to denote contingent free shipping, and NFS to denote no free shipping. Namely, membership free shipping is the loyalty program that charges a membership fee over a certain period, and offers free shipping regardless of cart size during that period. Contingent free shipping is a policy that offers free shipping when cart size reaches a threshold. The key difference between contingent free shipping and membership free shipping is that membership free shipping provides a differentiated product by offering expedited shipping. This comes from the fact that membership free shipping is usually in the form of expedited shipping, and consumers treat shipping speed as part of the value attached to this product. This is saying, although retailers are basically reselling products, they can differentiate the product by using different shipping policies. Notation Description MFS membership free shipping CFS contingent free shipping NFS no free shipping (consumers pay shipping fee) δ proportion of two-unit demand consumers 1−δ proportion of one-unit demand consumers h holding cost d membership fee t mismatch cost vl value of product with regular shipping vh value of product with expedited shipping sl regular shipping fee sh expedited shipping fee vd value difference x consumer location at the horizontal line p unit price c unit cost Table 1: Notations 5

1. We use a revised Hotelling model to conduct our analysis in a duopoly setting. In the online appendix1 , we also study the case of monopoly’s decision as extension. In our model, we allow two competing online retailers to choose different unit prices and shipping policies. The two retailers have different user interface and ordering process. The differentiated service posits horizontally different transactional costs to consumers. We index the first retailer 1, and the second online retailer 2. We assume that retailer 1 locates and 0, and retailer 2 locates at 1 in a horizontal line of length 1. Consumers lay uniformly in this horizontal line. Their position indicates their transaction cost to purchase from either retailer. A consumer locating at x incurs a transaction cost of xt if she buys from retailer 1, and (1−x)t if she buys from retailer 2. t is the unit measurement of the transaction cost, and can be interpreted as the competitiveness or extent of similarity of the two retailers. 2. There are two types of consumers. The first type have two units demand in their life of two periods. They consume one unit in each period. We call them large-basket buyer. The second type have one unit demand. We call them small-basket buyer. The portion of two-unit demand consumers is δ , and the portion of one-unit demand consumers is 1 − δ. Both type of consumers are distributed uniformly along the line. 3. When a two-unit demand consumer purchases two units of product at the beginning of the first period, she suffers from a holding cost of h. This is because she only consumes one unit in the first period, and the other unit has to be held until the second period. We can think of the holding cost being the extra space needed to stock it, the effort of planing ahead, or the discount factor of cash flow. This setting accommodates consumer heterogeneity in demand level.The holding cost is assumed to satisfy h < sl so that when a two-unit demand consumer chooses to pay the shipping fee by herself, she will buy two units and store them instead of purchasing one unit in every period. 4. We assume that retailers successfully screen consumers. A two-unit demand consumer will always opt to CFS/MFS rather than NFS, and a one-unit demand consumer will always 1 Online Appendix: https://www.researchgate.net/publication/278968301_Loyalty_Program_ the_Dilemma_of_Shipping_Fee_(Online_Appendix)

6

choose NFS. Note that NFS is always available to consumers as an option regardless of the availability of CFS or MFS. It is necessary for our setup because without this assumption, two-unit demand customers is equivalent to one unit demand customers purchasing twice. Mathematically, this assumption is equivalent to sl + vh − vl ≤ d ≤ h + sl + 2vh − 2vl where d is the membership fee. 5. When a consumer purchases one unit of product, she receives value of vl if the retailer uses regular shipping method (NFS or CFS), and vh if the retailer uses expedited shipping (MFS). Regular shipping is associated with shipping fee sl , and expedited shipping is associated with shipping fee sh . We assume that a higher value difference is correlated to a higher shipping fee difference. This relationship is internalized by setting vd = vh −vl = sh −sl . The setup allows value difference not only to be caused by different shipping strategy, but also other benefits of the loyalty program. By providing additional benefits other than expedited free shipping, the retailer can increase vh , correspondingly, this will lead to an increased cost sh . 6. We assume that the transaction cost decreases when consumers place a repeated order. When consumers order for the second time from the same retailer, they are more familiar with the ordering process and page layout than when they do it for the first time. The system may have their address and card information stored, and they check out faster. To operationalize this assumption, we normalize the transaction cost t to zero if a consumer purchase for the second time from the same retailer. The reason for imposing this assumption is two folds. First, it’s in accordance with common practice. In reality, Amazon has a special button for 1-click free shipping, and Shop Runner saves payment information and address for customers to fast check out. Second, this assumption directly relates to an important feature of MFS, the ability to make use of consumer heterogeneity. 7. In this paper, we assume that competition in both two-unit market and one-unit market exists. If we denote the location of indifferent customer at two-unit demand market by xb , and the location of indifferent customer at one-unit demand market by xs , competition

7

exists when 0 ≤ xb ≤ 1 and 0 ≤ xs ≤ 1. This is guaranteed when t > sl . Consumer utility is denoted by u, and is constituted with the value consumers receive, subtracted by the cost they pay. The cost consists of price, mismatch, holding cost, membership fee, and shipping fee. Depending on specific shipping method and consumer demand, some of the cost may not apply. I use three-letter subscription for shipping method, one digit subscription (“1” or “2”) for the choice of retailer, and one digit subscription (“b” or “s”) for demand. For example, uCFS1s is the utility derived by one-unit demand consumer if she goes to retailer 1 who provides contingent free shipping.

3.2

Timeline of the Game

We first look into the the price equilibrium when the shipping policy taken by retailer 1 and retailer 2 are known, and then study the what shipping strategy they will adopt given a simultaneous move game setting and a sequential move game setting. The timeline for simultaneous move game is as follows: • In stage 1, retailers choose shipping strategy simultaneously. • In stage 2, retailers who use membership free shipping announce the membership fee. • In stage 3, retailer 1 and retailer 2 both chooses unit prices at the same time. • In stage 4, consumers choose retailer to fulfill their demand. The timeline for sequential move game is as follows: • In stage 1, pioneer retailer chooses shipping strategy and announce it (but not the price). • In stage 2, competing retailer chooses shipping strategy. • In stage 3, retailers who use membership free shipping announce the membership fee. • In stage 4, both retailers choose price simultaneously. 8

• In stage 5, consumers choose retailer to fulfill their demand.

4

Equilibrium Analysis

In section 4.1 we present the price equilibrium, the payoffs given all possible combinations of retailers’ choices. There are three possible combinations: CFS vs. CFS, MFS vs. MFS, and MFS vs. CFS. Next, in section 4.2 and 4.3, we investigate the shipping strategy equilibrium by using these payoffs as input of two games. First, we solve a simultaneous move game. In the simultaneous move game, retailers choose shipping schedule at the same time. Their actions are based on their belief about the opponent retailer’s strategy.This setting illustrates the circumstance where retailers enter a new market at the same time. Second, we solve a sequential move game where one retailer is pioneer. This leading retailer decides his strategy based on the anticipated reaction of other retailers. The sequential game setting illustrates the case where one retailer enters early.

4.1

Price Equilibrium

In this section, we compare the price, profit, social welfare given the shipping policies of both retailers. We also analyze the membership fee in case MFS vs. MFS and MFS vs. CFS. We conduct a comparative analysis to examine the role of δ, and conclude on how consumer heterogeneity affects profitability.

4.1.1

CFS vs. CFS

In our context, contingent free shipping retailer offers free shipping when a consumer purchases two units at a time. We set the incentive compatibility constraint such that a two-unit demand consumer never pays the shipping by herself to purchase unit by unit. She always buy two units at the beginning of the first period to enjoy the free shipping benefit. The

9

demand is solved by finding the indifferent consumer in both markets. We then maximize the profit, and derive the response functions. Solving this system of equations, we get the price equilibrium. The consumer utilities are:

uCFS1b = 2(vl − p) − xb t − h uCFS2b = 2(vl − p) − (1 − xb )t − h uCFS1s = vl − p − xs t − sl uCFS2s = vl − p − (1 − xs )t − sl

The optimal price is pCFS = c + 4.1.2

1+δ 2δ sl + t 1 + 3δ 1 + 3δ

(1)

MFS vs. CFS

In this section we present the case when retailer 1 uses membership free shipping, and retailer 2 uses contingent free shipping. The retailer specific utilities are:

uMFS1b = 2(vh − p) − xb t − d uCFS2b = 2(vl − p) − (1 − xb )t − h uMFS1s = vl − p − xs t − sl uCFS2s = vl − p − (1 − xs )t − sl

The optimal membership fee is

d=

h t + 2sh − sl − 2 2

(2)

We check our compatibility constraint, and the membership fee is optimal if t < h + 2sh − 2sl holds. In such conditions,

10

2δ 4δ 2δ 1+δ 2δ d+ h+ sh − sl + t 1 + 3δ 3(1 + 3δ) 1 + 3δ 3(1 + 3δ) 1 + 3δ 2δ 8δ 1+δ = c− h+ sl + t 3(1 + 3δ) 3(1 + 3δ) 1 + 3δ

pMFS.CFS = c −

(3)

pCFS.MFS

(4)

pMFS.CFS is the unit price for the retailer who adopts MFS when the other retailer uses CFS, and vise versa.

4.1.3

MFS vs. MFS

In this section we introduce the setting when both retailers use membership free shipping. Apparently a two-unit demand consumer will choose to place one order with one unit at the beginning of each period to avoid holding cost. Consumer utilities are defied as follows.

uMFS1b = 2(vh − p) − xb t − d uMFS2b = 2(vh − p) − (1 − xb )t − d uMFS1s = vl − p − xs t − sl uMFS2s = vl − p − (1 − xs )t − sl

The optimal price is pMFS = c − 4.1.4

2δ 4δ 1+δ d+ sh + t 1 + 3δ 1 + 3δ 1 + 3δ

(5)

Price Discrimination

At price equilibrium, we have the average cost of one unit of product for one-unit demand consumer, and the difference of average cost between one-unit demand and two-unit demand consumer as follows: The key insight from the first column of the table is that both one-unit demand consumer

11

Shipping Strategy Avg. Cost for One-unit Demand 1+δ 2δ sl + 1+3δ t + sl CFS c + 1+3δ 2δ 1+δ MFS c + 1+3δ sh + 1+3δ t + sl 2δ 8δ 1+δ CFS.MFS c − 3(1+3δ) h + 3(1+3δ) sl + 1+3δ t + sl δ 4δ 1+2δ MFS.CFS c − 3(1+3δ) h + 3(1+3δ) sl + 1+3δ t + sl

Cost Difference sl − 12 h sl − 12 sh sl − 12 h 1 (t + 6sl − h − 4sh ) 4

Table 2: Average Cost at Price Equilibrium and two-unit demand consumer share the same unit price. One-unit demand consumers have to share part of the shipping fee of two-unit demand consumers, we call this shipping effects. The membership fee paid by two-unit demand consumers subsidize one-unit demand consumers by lowing the price, and we call this membership effect. For example, in the case when both retailers use CFS, the shipping effect is

2δ s. 1+3δ l

The important findings from the second column of the table is that the unit price when both retailers use MFS is higher than that when both use CFS, but the cost difference between two-unit demand consumers and one-unit demand consumers is less when both retailers use MFS. That is to say, MFS price discriminate less.

4.1.5

Profit Comparison

In this section, we compare the profit between a world where all retailers use MFS and the world where all retailers use CFS to understand the difference between them. The case with one using MFS and the other using CFS is more complicated, and will be discussed in later sections. Proposition 1. When both retailers choose membership free shipping, retailers gain higher profit than when they both choose contingent free shipping. The higher the value difference vd is, the higher the profit difference will be. (1 + δ)2 δ(1 − δ) sl + t 2 + 6δ 2 + 6δ δ(1 − δ) (1 + δ)2 = sh + t 2 + 6δ 2 + 6δ

πCFS = πMFS

12

This proposition reveals the intrinsic difference between contingent free shipping and membership free shipping. By providing a higher product value, retailers obtain higher profit.

4.1.6

Monopoly’s Choice

We study an interesting case when the two retailers are owned by the same company. The problem becomes a monopoly’s decision of retailer differentiation. By comparing the total profits which consists of the profit from retailer 1 and retailer 2, the following conclusions can be drawn. Proposition 2. If a firm owns both retailers, he should never let both retailers use CFS. He would let one retailer use MFS, and the other use CFS if the following conditions meet, otherwise he should let both retailers use MFS. −9h2 + 18hsl + 18ht + 72sh t − 90sl t − 9t2 13 . Retailers gain minimum profit when δ = 31 . • When both retailers use MFS, consumer heterogeneity harms profitability if t > sh > sl , and boosts profitability if sh > t > sl .

Figure 3: Profits When Both Retailers Choose MFS

15

Unlike common wisdom suggests, a larger consumer base does not necessarily lead to higher profit. In terms of CFS, retailers always suffer from accommodating heterogeneous consumers. In the case when both retailers use MFS, retailers will benefit from consumer heterogeneity if the competition isn’t very intense. This reveals one intrinsic advantage of membership free shipping.

4.2

Shipping Strategy Equilibrium with Simultaneous Choice

In this section, we use the payoffs from the price equilibrium to conduct a simultaneous move game. This setting illustrates the condition when retailers enter a new market at the same time.

Figure 4: Simultaneous Matrix Game Proposition 5. In the simultaneous move game, • CFS vs. CFS is pure strategy Nash equilibrium if B < δ < 1 and sh < A. • MFS vs. MFS is pure strategy Nash equilibrium if 0 < δ < B and sh > A where

A=

−8δh2 + 25ahsl + 24aht − 26δs2l + 3δsl t − 9hsl + 24ht + 18s2l − 51sl t 18δt − 18t

and B=

−9h2 + 36sl h − 30th − 36s2l − 9t2 + 48sl t 7h2 + 4sl h + 66th − 20s2l − 9t2 − 48sl t 16

As can be seen from the graph below, MFS vs. MFS will be pure strategy Nash equilibrium if the fraction of two-unit demand consumer is low, competition is intense, and expedited shipping fee is relatively high.

Figure 5: Pure Strategy Nash Equilibrium in Simultaneous Move Game

4.3

Shipping Strategy Equilibrium with Sequential Move

Now we let retailer 1 to choose shipping strategy before retailer 2 based on his anticipation of retailer 2’s behavior. Note that they still choose price simultaneously. This setting is more common in real life. We compare the equilibrium with that of simultaneous move game, and examine whether there’s first-mover advantage. The game tree is illustrated as follows.

Figure 6: Game Tree of Sequential Choice

17

Proposition 6. When retailer 1 chooses shipping strategy before retailer 2, the equilibrium is as follows. 1. When sh > A, then retailer 1 choose MFS, and retailer 2 follows up by choosing MFS. 2. When sh < A, there are three conditions based on the range of δ (a) if 0 ≤ δ < B 0 , then retailer 1 chooses MFS, and retailer 2 chooses CFS . Retailer 1 gains more profit than retailer 2, enjoying first-mover advantage. (b) if B 0 < δ < B, then retailer 1 chooses CFS, and retailer 2 chooses MFS . Retailer 1 gains more profit than retailer 2, enjoying first-mover advantage. (c) if B < δ < 1, then both retailers choose CFS. where

A=

−8δh2 + 25δhsl + 24δht − 26δs2l + 3δsl t − 9hsl + 24ht + 18s2l − 51sl t 18δt − 18t −9h2 + 36hsl − 30ht − 36s2l + 48sl t − 9t2 B= 7h2 + 4hsl + 66ht − 20s2l − 48sl t − 9t2 B0 =

3h2 − 18hsl + 26ht + 24s2l − 38sl t + 3t2 3h2 − 18hsl − 38ht + 24s2l + 26sl t + 3t2

Figure 7: Equilibrium of Sequential Move Game 18

In the sequential move game, retailer 1 always enjoy weak first-mover advantage.

5

Conclusions

By allowing a portion of consumers to have two-unit demand, we capture consumers’ tradeoff between buying as needed and buying and stock. This modeling technique enables us to compare contingent free shipping and membership free shipping. We find that the intrinsic difference of membership free shipping is product differentiation. By using expedited shipping, retailer change the product value. When providing a higher value to customers, retailers gain more profit, but society loses efficiency because higher incidence of more expensive shipping. We also find that membership free shipping is a new invention that makes best use of consumer demand heterogeneity. This feature of membership free shipping is never discovered before.

References [1] Nihat Altintas, Feryal Erhun, and Sridhar Tayur. Quantity Discounts Under Demand Uncertainty. Management Science, 54:777–792, 2008. [2] Joanna Barsh, Blair Crawford, and Chris Grosso. How e-tailing can rise from the ashes. McKinsey Quarterly, pages 98–109, 2000. [3] C. d’Aspremont, J. Jaskold Gabszewicz, and J.-F. Thisse. On hotelling’s ”stability in competition”. Econometrica, 47(5):1145–1150, 1979. [4] Robert J. Dolan. Quantity discounts: Managerial issues and research opportunities. Marketing Science, 6(1):1–22, 1987. [5] Harold Hotelling. Stability in competition. The Economic Journal, 39(153):41–57, 1929.

19

[6] Michael Lewis. The effect of shipping fees on customer acquisition, customer retention, and purchase quantities. Journal of Retailing, 82:13–23, 2006. [7] Michael Lewis, Vishal Singh, and Scott Fay. An empirical study of the impact of nonlinear shipping and handling fees on purchase incidence and expenditure decisions. Marketing Science, 25(1):51–64, 2006. [8] K Sridhar Moorthy. Product and price competition in a duopoly. Marketing Science, 7(2):141–168, 1988. [9] Mark Rogowsky. Prime factors: Should Amazon really mess with the best loyalty program in retail?, Feb 2014. [Online; posted 01-Feb-2014]. [10] Thad Rueter. E-commerce shipping service shoprunner raises more than $200 million, October 2013. [11] Brad Tuttle. Amazon prime loses $11 annually per member. and it’s a huge success, November 2011.

20