Supply Chains and Segment Profitability: How Input Pricing Creates a Latent Cross-Segment Subsidy. Anil Arya. Ohio State University.

Transcription

1 Supply Chains and Segment Profitability: How Input Priing Creates a Latent Cross-Segment Subsidy Anil Arya Ohio State University Brian Mittendorf Yale Shool of Management April 2009

2 Supply Chains and Segment Profitability: How Input Priing Creates a Latent Cross-Segment Subsidy Abstrat Reent years have seen an inreasing emphasis on developing more preise aounting measures of market- and ustomer-level profitability. These efforts are aimed at helping prune unprofitable onstituenies and targeting resoures to more profitable segments. This paper demonstrates that even if perfeted, suh refined segment profitability measures may unwittingly neglet a latent ross-subsidization effet linked with firm partiipation in multiple markets. In partiular, when a firm relies on a privately informed supplier for inputs used aross markets, the wholesale prie it pays depends on the average profitability of its markets. Thus, if a firm were not to serve its less profitable markets, it may fae a steeper wholesale prie. Taking suh interation between upstream priing and the firm's downstream reah into aount, the paper shows that: (i) segment profit alulations an understate or overstate the value added by the segment depending on the segment's relative ontribution margin, and (ii) the firm sometimes benefits from devoting resoures to less profitable segments and perhaps even from serving unprofitable markets and/or ustomers.

3 I. Introdution Aountants have been persistent in attempts to generate disaggregate data that provides meaningful measures of segment profitability, both at the market and ustomer levels. While joint osts and resoure utilization have long been a stiking point in suh endeavors, reent developments stemming from ativity-based osting (ABC) and ustomer lifetime value (CLV) analysis have been highly touted as means of better divining whih markets and ustomers to servie and how muh resoures to devote to them. As a result, reliane on suh measures has grown substantially in reent years. While the desire to finely parse performane is ertainly ommendable, history is rife with examples in whih seemingly perfet performane measures failed to fully reflet opportunity osts of deisions. 1 In the ontext of market- and ustomer-level profitability, the benefits of having a loss leader produt for omplementary demand-side effets on other produts or inurring sustained losses for ompetitive posturing (e.g., dumping or predatory priing) have been well reognized, and pratitioners frequently aount for suh spillover effets in making resoure alloation deisions. The notion of freebie marketing, pioneered by Gillette, is a prominent example. Despite routine losses on heap or even free razors, firms keep suh lines in operation beause they reate aptive onsumers for their (more profitable) razor blade lines. In this paper, we demonstrate that in addition to the well-known demand-side spillovers, supply-side spillovers too may be present neessitating adjustments to segment profits in order to evaluate the value added by a segment. In partiular, we show that even if market and ustomer profitability measures perfetly reveal individual segment profitability, they do not fully reflet the latent ross-subsidization that an arise when a multi-segment firm relies on a supplier for key inputs. The ross-subsidization stems from the fat that 1 Commonly disussed examples inlude the fat that aounting aruals our in undisounted terms and thus fail to reflet the ost of apital, produt line osts do not reflet onstrained apaity, and fixed ost alloations potentially indue a "death spiral" (see, for example, Zimmerman 2003).

4 2 supplier priing is influened by the extent and profitability of the firm's downstream reah. Thus, resoure alloation that is based solely on segment profits fails to fully inorporate the positive supply hain ramifiations obtained from serving less profitable markets. The notion that less profitable segments may help plae downward pressure on wholesale pries for more profitable segments an intuitively be seen through an intertemporal analog. When downstream market onditions deteriorate over time, firms often obtain more favorable upstream priing terms. Examples inlude supplier prie breaks for automobile firms in the wake of falling domesti sales; lower wholesale pries for CDs and DVDs due to ompetition from digital media; and labor onessions in response to unfavorable earnings news (e.g., Bova 2008; Menn 2006). In other words, as retail profitability goes up and down over time, so too do input pries. The premise in this paper is that suh time-series phenomena an also arise in the ross-setion of a multi-segment firm. That is, less profitable segments an often keep input pries low for other, more profitable, segments. As an example, when Target omplained of low margins on DVD sales due to ompetition from digital downloads, Disney responded by utting a deal for redued-fee liensing of lothing lines (Menn 2006). Similarly, easyjet, a prominent no-frills air arrier, was able to obtain favorable pries in a ontrat with Airbus in part by stressing the low margins it obtains in several of its routes (Prada 2002). In these ases, the value added by an underperforming segment (be it DVDs or low-profit routes) went beyond the profit of the segment due to its benefiial effet on supplier priing for other segments (be they lothing lines or high-profit routes). More broadly, the point stressed herein is that the input pries seured by a onglomerate depend on the onditions faed by the portfolio of markets in whih it operates. As a result, altering the portfolio of markets a firm serves will alter the supply environment as well. It may be tempting to onlude that a large retail onglomerate that has expanded beyond the "low hanging fruit" of its prime markets to markets with more modest profitability is able to seure lower input pries due to the buyer power its size affords. The

5 3 results here suggest that there may be more to buyer power than mere size: pries are affeted by average market onditions and expansion to less profitable markets has the onomitant silver lining of lower overall input priing. 2 Besides demonstrating suh a ross-subsidization due to supplier priing, the results herein may provide some justifiation for a variety of puzzling phenomenon, from pereptions of orporate soialism to the staying power of full-servie retailers. Formally, we onsider a basi model of a supplier and buyer under whih the buyer operates in multiple segments. The supplier, who is privy to its own osts, produes and transfers inputs (e.g., labor, materials) to the buyer, who uses the inputs in its various segments (e.g., markets, geographial areas, or ustomer groups). The parties agree to a supply ontrat that stipulates the prie and usage of inputs onditioned on the supplier's reported ost. Supply hain fritions arise beause private information provides the supplier an opportunity to overstate its osts so as to extrat greater profit from the buyer. Aware of this possibility, the buyer ommits to reduing volume for high ost reports. As is typial in suh settings, the buyer weighs information rents (manifest in wholesale prie markups) with restrited purhase quantities when designing the preferred supply ontrat. The question we ask is how this familiar prodution-rents tradeoff an indue a divergene between segment value added and segment profit measurement. Intuitively, the supplier profits from a markup above ost. The size of the markup is tied to the supplier's information advantage as well as to the buyer's potential (downstream) profitability from utilizing the inputs. As might be expeted, the higher is the average profitability of the buyer's segments, the more it is willing to pay for the input, and the greater is the wholesale prie. This implies that eah segment's impat on the markup is tied to its relative profitability. In partiular, serving a segment with less-than-average 2 As an example, the major Amerian auto makers have argued that their large dealer networks to rural and less-profitable metropolitan areas (as ompared to the small, targeted dealership network of their foreign ounterparts) make them deserving of lower pries from parts suppliers, more favorable labor ontrats, and even heaper apital (from government loans).

6 4 profitability lowers the markup, a benefit obtained by inputs proured in all segments. Segment profit alulations, of ourse, fous on the realized input prie, missing out on suh ross-segment effets. Put slightly differently, if the firm eased operation in one of its less profitable segments, firmwide profit would derease by more than indiated by segment profit figures due to the fat that the low-profit segment plays a larger role in utting the required supplier wholesale prie markup. Sine suh wholesale prie adjustments are off-equilibrium, they are not refleted in (on-equilibrium) profit alulations and, as suh, represent a latent subsidy provided by less-profitable markets to more-profitable markets. This fore, in turn, means that retaining an unprofitable market may even be the right ourse of ation for a profit-maximizing firm. Pratitioners routinely ritiize firms for maintaining unprofitable segments, while aademis frown upon apparent orporate soialism in that a small set of highly profitable divisions are often seen to support the many far less profitable divisions. While suh ritiisms may often be well deserved, the analysis herein demonstrates a aveat: divisions with low (or even negative) profitability are not neessarily a drag on overall profits as they an help support lower input pries. In fat, when a firm relies on an external supplier for key inputs, the positive input priing benefits an underperforming division heaps on overperforming divisions may negate the notion of orporate soialism. Further, due to the upstream priing effet, a firm that blindly eliminates segments on the basis of them being unprofitable does so at its own peril. What may seem like benign trimming of unseemly dimensions of a firm's operations may turn out to indue a death spiral. The typial death spiral is driven by a tendeny to assign osts whih are fixed with respet to the keep-ordrop deision in a way that they appear variable. In our supply hain setting, a death spiral arises where a ost whih is variable with respet to the keep-or-drop deision (wholesale prie) is treated as fixed. Another irumstane in whih segment profit alulations are relied upon is when a

7 5 retailer an serve a variety of ustomer groups, some of whih are more profitable than others. 3 A reent inarnation of this issue is the retailer onundrum of reahing ustomers via an online arm, briks-and-mortar store, or both. The expansion of online sales has typially been viewed as a hallenge to traditional retailers and even as a preursor to their elimination. Yet, while online retailers have thrived, traditional retailers have maintained a strong presene, suggesting rumors of their death have been exaggerated. In fat, many of the most svelte online operations (e.g., Dell, Gateway, Apple) have opted to open traditional outlets as a means of serving less teh-savvy ustomers. Viewed in the ontext of this paper's results, the mutual suess of online and traditional retail hannels eah operated under the auspies of one firm may not be as surprising even if traditional hannels perpetually run at a loss. The results herein suggest that having "loss leader ustomers" an put downward pressure on wholesale pries whih, in turn, an boost margins obtained on the more profitable onsumers. Broadly speaking, the theme of this paper lies at the intersetion of disussions about measuring segment profitability and oordinating self-interested supply hain partners. In the realm of profitability measurement, ativity-based osting (ABC) has reated a substantial shift in the ability to trak profits at the market or ustomer level (e.g., Cooper and Kaplan 1988). Through improved ost alloations, these proesses are viewed both by aademis and pratitioners as ritial to properly evaluating produt line hoies, resoure alloation aross segments, and keep-or-drop deisions (e.g., Goebel et al. 1998; Seary 2004; Sopariwala 2005). At the ustomer level, ABC and ustomer lifetime value (CLV) alulations are used jointly to evaluate whih ustomers to serve and target (e.g., Hogan et al. 2002; Kuhta and Troska 2007; Seary 2004; Venkatesan and Kumar 2004). While signifiant efforts have been made to inorporate effets of downstream ompetition 3 Tehnially speaking, different ustomer groups an present a irumstane distint from different produt lines in that retail prie disrimination among different onsumers for the same produt is often prohibited and, even when permitted, may be impratial. Our analysis of this ase inludes suh retail priing onstraints.

8 6 and demand-side omplementarities in suh alulations, this paper points to strategi upstream supplier priing as another onsideration. Supply hain fritions have been srutinized by researhers in many areas of management. A fundamental onern at the forefront of suh studies is the inherent onflit of interest in priing. While supply hain partners have many ommon goals, individual interests an lead to ineffiienies that harm all. Sine Spengler's (1950) analysis of double-marginalization, many studies have onsidered the extent of priing-indued distortions in supply hains and the myriad of means to alleviate suh distortions (for summaries, see Katz 1989 and Lariviere 2008). This stream of work has also onsidered a variety of other onflits of interest, inluding moral hazard among supply hain partiipants (Baiman et al. 2000; Saouma 2008), the role of private information and innovation (Baiman and Rajan 2002), and performane measurement (Baiman et al. 2001). In this paper, we examine whether (and how) suh supply hain oordination onerns interat with deisions an input buyer makes with regard to the markets it serves. In doing so, we demonstrate a supply hain indued interdependeny among produt lines (and ustomers) in a onglomerate that is not refleted in standard segment profit alulations. The remainder of this paper proeeds as follows. Setion 2 presents the basi model. Setion 3 presents the results: 3.1 identifies the equilibrium supply ontrats; 3.2 ompares segment profit and segment value added; and 3.3 onsiders an appliation to ustomer-level profitability analyses and examines the onsequenes of uniform priing. Setion 4 revisits the analysis under more simple (and ommon) supply hain ontrats. Setion 5 onludes. 2. Model A downstream (retail) buyer relies on an upstream (wholesale) supplier for a key input. The supplier produes the input at a onstant unit ost,, [ L, H ]. Beause of its expertise and proximity to operations, the supplier is privately informed of the preise

9 7 value of. The buyer is only aware of g(), the (ommon knowledge) probability density funtion of ; the assoiated umulative distribution funtion is G(). As is standard, we presume the hazard rate of the distribution is monotoni, i.e., H () 0, where H() = G() g(). 4 The retailer serves n segments, n 2, and requires one unit of input per unit of output in eah segment. In segment i, i = 1,K,n, the retailer is a monopolist and faes an inverse onsumer demand urve p i = a i q i, where a i is the demand interept, p i is the retail prie for eah unit and q i is the number of units sold in segment i. The selling and operating ost for segment i is v i q i + F i where v i is the (per unit) variable ost and F i is the fixed ost of downstream operations. For ease of notation, define α i = a i v i and α n n = i=1 α i. That is, α i is the demand interept net of variable ost for segment i and n α n is the ross-segment average α -value. To ensure nontrivial partiipation in eah segment (i.e., interior solutions), we assume α i > H + H( H ). Given these supply and demand onditions, the buyer and supplier agree to a supply ontrat that speifies quantities used in eah segment, q, q = {q i } n i=1, and the (per unit) wholesale prie, w. Under suh a ontrat, segment i profit, i = 1,K,n, is π i (q i,w), π i (q i,w) = [a i q i ]q i wq i v i q i F i, and the firm's profit from the first s segments, s s i=1 n, is Π s (q,w), Π s (q,w) = π i (q i,w). To determine the buyer's optimal supply ontrat, from the Revelation Priniple (Myerson 1979), it is without loss of generality to restrit attention to diret revelation mehanisms that indue truthful supplier reporting. That is, upon deiding to operate in n segments, the buyer ommits to a menu of ontrats speifying {q(ĉ),w(ĉ)}, where n q(ĉ) = {q i (ĉ)} i=1 represents the (vetor of) inputs purhased and w(ĉ) denotes the wholesale prie given a supplier ost report of ĉ, ĉ [ L, H ]. The buyer's hosen menu 4 The monotone hazard rate assumption ensures the "loal" inentive onstraints are binding in traditional adverse seletion models. The assumption is satisfied by several ommon distributions, inluding uniform, normal, logisti, hi-squared, exponential, and Laplae. For more on this and the related issue of log-onavity, see Bagnoli and Bergstrom (2005).

10 8 solves program (P). In the program, the (IR) onstraints require that the supplier reeive a minimum level of profit, normalized to zero, while the (IC) onstraints require that the supplier's profit when providing a truthful ost report is at least as high as under any other ost report. (P) Max {q(),w()} H L [Π n (q(),w())] g()d s.t. [1 q()][w() ] 0 (IR) [1 q()][w() ] [1 q(ĉ)][w(ĉ) ],ĉ (IC) Denote the solution to (P) by {q n (),w n ()}, where q n () = {q n i ()} n i=1. Given this setup, our interest is in determining the value added by a segment. Without loss of generality, onsider the value of segment n. Using the above notation, in equilibrium, segment n's realized aounting profit, denoted by π n (), is π n () = π n (q n n (),w n ()), while firm-wide profit is Π n (q n (),w n ()). The value added by segment n is firm profit with segment n less firm profit that would be realized in the absene of segment n. That is, the value added by segment n, denoted V n (), is V n () = Π n (q n (),w n ()) Π n 1 (q n 1 (),w n 1 ()). The question we address in subsequent analyses is if and how aounting segment profit, π n (), differs from segment value added, V n (). 3. Results 3.1. Equilibrium Supply Contrats Before omparing the aounting measure of segment value with the underlying value added by a segment, we first derive the equilibrium outome for operations in a given set of segments. Then, omparing outomes under n vs. n-1 segments an provide a full haraterization of the effets of segment n on firm profit. With n segments, n 2, the

11 9 solution to (P) an be determined as follows. First, as one may expet, ontratual ineffiieny arises beause the supplier is tempted to overstate its ost so as to seure a higher wholesale prie. And, sine there is no possibility of suh overreporting for = H, the (IR) onstraint binds (only) in that ase, i.e., w( H ) = H. Turning to the (IC) onstraints, the solution is eased by replaing these onstraints by their "loal" ounterparts. In partiular, the "loal" (IC) onstraint speifies: H [1 q()][w() ] = [1 q( )] d. (1) Intuitively, the "loal" (IC) ondition in (1) demonstrates that if the buyer orders greater quantities (greater 1 q( )) for a ost realization, it requires providing a more attrative ombination of pries (higher w()) and/or purhase quantities (higher 1 q()) for all lower -values so as to indue truthful revelation. So, in hoosing purhase quantities, the buyer equates its marginal revenues with marginal osts where the osts inlude not just the traditional prodution and sales ost but also the ost of information rents paid to the privately informed supplier. Given suh prourement volume, then, the wholesale prie is set so as to satisfy (1). In partiular, Lemma 1 presents the solution to (P). (Formal proofs are provided in the appendix.) Lemma 1. If the firm operates in n segments, the equilibrium outome entails: (i) q i n () = [1 2][α i H()]; and (ii) w n () = + H [α n H( )]d α n. H() The lemma provides a risp presentation of the above intuition. In Lemma 1(i), the quantity proured for use in segment i, i = 1,K,n, depends on the benefit of purhases net of downstream ost in that segment (α i ), less the supplier's diret ost (), less the supplier's information rents ( H()). The information rents term, H(), reflets that an inrease in purhases for a given affets revenues (via a g() onsequene) but requires

12 10 additional payments for all lower osts (via a G() onsequene). The quantities in Lemma 1(i), oupled with the loal (IC) onstraint in (1), yield the agreed-upon wholesale prie in Lemma 1(ii). The wholesale prie reflets a ostreimbursement () plus a markup for information rent. Importantly, the markup depends on average segment profitability ( α n ), and is inreasing in this measure: d[w n () ] dα n = H [ + H( ) H()]d [α n H()] 2 0. Intuitively, the more attrative prourement is to the buyer, the less willing the buyer is to ut prodution and, thus, the more willing it is to grant the supplier rents via a higher wholesale prie. This supply hain inter linkage the upstream prie markup depends on the average profitability of downstream segments proves ritial in our analysis. The linkage implies that eah segment's impat on the wholesale prie depends on how it hanges average segment profitability. Using the supply ontrat in Lemma 1, the expeted buyer profit (the objetive funtion value in (P)) is E{Π n (q n (),w n ())} = [1 / 4] E{[α i H()] 2 } F i. Given the equilibrium ontrat, we next onsider if and how segment profit differs from segment value added. n i=1 n i= Segment Value Added vs. Segment Profit Segment profit is the primary means through whih a firm (and outsiders) view the ontribution eah segment makes to the firm's overall profit. When evaluating a segment's worth, it is often disussed that aounting profit measures may leave out positive (or negative) demand-side spillovers aross segments. In partiular, one produt line may be a "loss leader" in that its segment profit is negative yet it is worth maintaining due to its positive effet on the demand for other, more profitable, produt lines. Inkjet printers represent a prominent example printers are often sold near or below ost, but reate a

13 11 aptive ustomer for artridges whih are sold at a substantial profit. In that ase, looking at poor margins on printers refleted in segment profit learly does not represent the whole story. In a similar manner to suh demand-side effets, this paper seeks to identify the role of supply-side effets on segment value added. In both ases, aounting segment profit figures fairly reflet "what is" but may fail to answer "what if." Segment value added, on the other hand, is a measure of the inremental value of a segment in that it ompares urrent firm value with the value that would have been attained in the absene of that segment. As the following lemma demonstrates, the differene between segment profit and segment value added an risply be aptured by supply-side and demand-side spillovers. Lemma 2. Segment n's value added, V n (), an be expressed as V n () = π n () + S() + D(), where S() = Π n 1 (q n (),w n ()) Π n 1 (q n (),w n 1 ()), and D() = Π n 1 (q n (),w n 1 ()) Π n 1 (q n 1 (),w n 1 ()). As Lemma 2 demonstrates, for a given realization, segment profit ( π n ()) differs from segment value added due to supply-side spillovers ( S()) and demand-side spillovers ( D()). In partiular, S() reflets the hange in profit of the n-1 remaining segments that would be indued by the onomitant hange in supplier priing, holding onstant quantities demanded. Similarly, D() reflets the hange in profit of the n-1 remaining segments that would be indued by the onomitant hange in demand, holding onstant the wholesale prie. Most pertinent to the present analysis is S(), whih an be written more simply as S() = [w n 1 () w n ()][q n n 1 ()+L+q n 1 ()]. Thus, the sign of S () amounts to determining whether segment n's presene serves to inrease or derease the prevailing wholesale prie. If S() > 0, the wholesale prie is redued by operation in segment n; in suh a ase, segment n provides a latent supply-side subsidy to the other segments.

14 12 Determination of the extent of both the supply-side and demand-side effets requires simply substituting the values for q n (), q n 1 (), w n (), and w n 1 () from Lemma 1 into Π n 1 (q(),w()). This exerise reveals that the value added by segment n is V n () = 1 4 ( [α n ]2 [H()] 2 2 H [α n H( )]d ) F n. Further, denoting the segment i (per unit ontribution) margin by m i () = [α i q n i ()] w n (), and the rosssegment average margin by m() = n i=1 m i () n, the following proposition follows. Proposition 1. (i) S() = [1 / 2][α n α n ]k(), and D() = 0, where k() = H [ + H( ) H()]d α n H() 0 ; and (ii) Segments with lower (higher) margins have profit that understates (overstates) the value they provide for all < H. That is, if m n () < m(), then π n () < V n (), and if m n () > m(), then π n () > V n (). Two impliations follow immediately from Proposition 1(i). First, sine D() = 0, this setting is one in whih there are no demand-side spillovers from one segment to another. Beause the upfront ontrat entails ommitment to prodution levels for eah segment and eah segment's demand is presumed to be independent of the operations in other segments, the removal of one segment only affets wholesale priing and not prourement quantities in the other segments. Seond, provided α n α n, there are supplyside spillovers aross segments not refleted in the segment profit alulations. Proposition 1(ii) demonstrates that the nature of supply-side spillovers an be aptured suintly by looking at segment margins. If segment n's margin is below average, its presene helps keep wholesale prie low. As suh, the segment's value added is greater than what segment profit indiates, refleting a latent ross-subsidization of the other, more profitable, segments. Reall, the extent to whih the buyer is willing to hand over rents (in the form of a greater wholesale prie) depends on the average profitability of the segments

15 13 in whih it operates (refleted in α n ). If the buyer operates without a less profitable segment, it impliitly inreases the (per unit) rents it is willing to hand over. This, in turn, leads to an inrease in the wholesale prie. Besides demonstrating an inherent inter linkage in segments when a firm relies on external input supply, the proposition may shed some light on the widely held view that in multi-segment firms, underperforming segments are propped up by overperforming segments (e.g., Gertner et al. 2002; Rajan et al. 2000; Shin and Stulz 1998). Sine suh findings are derived in part from aounting segment profit measures, they may not reflet the latent input prie subsidy provided in the reverse diretion, i.e., a subsidy to overperforming segments provided by an underperforming segment. Even more broadly, the proposition suggests that a firm with multiple segments whih utilize ommon inputs would exhibit seemingly exessive (onstrained) investment in underperforming (overperforming) segments, despite suh behavior being valuemaximizing. Viewed in this light, apparent ineffiienies in resoure alloation may not be evidene of value destrution from diversifiation but rather reflet a form of seletion bias in that multi-segment firms are inherently different from their single-segment ounterparts (e.g., Chevalier 2004). Roughly stated, ontrasting a multi-segment firm with a linear disaggregation of its segments misses out on the fat that third-party relationships of presumptive stand alone segments may be strikingly different than those nurtured by the aggregate firm. Clearly, suh shifts have to be aounted for in order to alulate a meaningful segment diversifiation disount/premium. If this view were borne out empirially, then one would expet the most (least) profitable divisions of a multi-segment firm to perform better (worse) than their single segment ounterparts. Further, this feature would be expeted to be more pronouned the more ritial input supply is to the multisegment firm. The input priing effet of an underperforming segment an also translate into the firm benefiting from retaining a segment that is, at least in aounting terms, unprofitable.

16 14 Sine segment profit fails to reflet the wholesale prie effet of maintaining a low-margin segment, its value is understated. And, if the segment also faes substantial fixed operating osts, the understatement may even lead to the segment being lassified as not viable. In partiular, omparing segment value added and segment profit, and taking expetations yields the following proposition. Proposition 2. If m n () < m(), and F n (F, F), expeted profit of segment n is negative while expeted value added by segment n is positive, where F = [1 / 4]E{[α n H()] 2 } [1 / 2][α n α n ]E{k()}, and F = [1 / 4]E{[α n H()] 2 }. The proposition provides a ontrast to the view that by preisely traing osts and revenues to produt lines (segments), Ativity-Based Costing (ABC) provides an ideal metri for keep-or-drop deisions (e.g., Devine et al. 2005; Sopariwala 2005). While the typial onern in traking produt line profitability is that alloated fixed osts may inorretly be viewed as variable, a wholly different problem arises here. With input priing effets of market reah in play, it turns out that a variable ost with respet to the keep-ordrop deision (wholesale prie) is treated as fixed in any aounting treatment (sine aounting naturally only traks equilibrium outomes) even though wholesale prie is the same for all segments of the firm that utilize the same input, that does not mean the input prie will not hange one a segment is dropped. The following two-segment numerial example demonstrates the first two propositions, exhibiting a stark ontrast to onventional wisdom: α 1 = 30, α 2 = 20, F 1 = 110, F 2 = 30, and is uniformly distributed over [0,10]. For the example, Table 1 desribes the equilibrium quantities, wholesale prie, expeted segment profits, and expeted firm profits under all possible keep-or-drop senarios. In the table, given the buyer's market reah, its optimal prodution level and wholesale prie are determined using Lemma 1;

17 15 segment i's expeted profit is E{[α i q i ]q i wq i } F i if the firm operates in segment i and 0, otherwise; and the firm's expeted profit is the sum of the segment profits. Firm's market reah q 1 () q 2 () w() Segment 1's expeted profit Segment 2's expeted profit Firm's expeted profit Segments 1 & Segment Segment / Table 1: Firm's optimal horizontal reah. In the absene of information asymmetry (first-best), with wholesale prie equal to, it is optimal for the firm to operate in both segments, and produe 15 / 2 and 10 /2 in segments 1 and 2, respetively. From Table 1, the optimal wholesale prie, prodution, and reah are all impated by information asymmetry. In this seond-best setting, where supply hain fritions are nontrivial, the firm pays more than (i.e., the supplier earns information rents) and prodution is ut for all other than at the "top" (i.e., = 0) in response. If the firm opts to operate in both markets, as would be suggested by the first-best setting, the resulting segment profit alulations seemingly imply that the firm is better off operating only in segment 1 sine it is the only segment with positive profit. However, this argument misses the fat that when the firm's horizontal reah hanges, so does its wholesale prie. In partiular, note the expeted margins of segment 1 and segment 2 are and 6.75, respetively. From Proposition 1, it then follows that operating in only the high-margin segment (segment 1) results in an inrease in w(): > As an be gleaned from the table, not only is expeted segment profit a poor measure of the value added by segment 2 due to the latent input priing subsidy it provides

18 16 to segment 1, but that differene may inorretly imply that the firm would be better off without segment 2. In fat, if one were to utilize the segment profit measure as the determinant of the keep-or-drop deision, the deision to drop the losing segment 2 and keep segment 1 would lead to a irumstane in whih the remaining segment is then unprofitable. In other words, wholesale priing effets an introdue a death spiral of sorts, despite the fat that the fixed osts of operating in eah segment are presumed to disappear along with the segment. That is, while the usual death spiral arises due to treating a fixed (ommon) ost as variable with respet to the keep-or-drop deision, in this ase the problem is that a ost whih is variable with respet to the keep-or-drop deision (wholesale prie) is treated as fixed. Importantly, as a result of the latent subsidy segment 2 provides to segment 1, not only is segment 2's ontribution to firm profit understated, but segment 1's ontribution to firm profit is overstated. This effet yields a stark reversal in the example: while the segment profit alulations in the first row of the table might lead one to onlude the firm should operate only in segment 1, the firm's preferred reah is to operate only in segment Customer Profitability Analysis The emphasis in the analysis thus far has deidedly been on analyzing value added by partiular segments, produt lines, or stores that rely on related inputs. Though these represent more traditional units of aounting analysis, reent developments in more mirolevel profitability alulations suggest further appliation at the individual ustomer level. In partiular, reent years have seen expanded use of Ativity-Based Costing (ABC) to determine the osts of serving different ustomers and, thereby, to determine whih ustomers to target and how muh resoures to devote to eah. As an example, retail firms routinely serve ustomers that require little or no ustomer servie (e.g., on-line buyers) as well as those requiring substantial servie (e.g., briks-and-mortar shoppers seeking purhase advie). Similarly, some retailers offer no-questions-asked returns to

19 17 heterogeneous onsumers, some of whom never return produts whereas others are deemed serial returners. These irumstanes often prompt onsideration of whether firms should offer these additional servies so as to "be all things to all ustomers" or whether they should develop a "no-frills" nihe. In making suh deisions, ustomer-level profitability analysis plays an integral role. Provided the firm an harge different pries to different onsumer-types (i.e., offer only on-line disounts, harge restoking fees for returns, et.), ustomer-level analysis is readily seen to be a speial ase of the preeding analysis. Roughly speaking, say ustomers fall into one of two groups, the no-frills ustomers (segment 1) and the fullservie ustomers (segment 2). Though the two types have equal willingness to pay, a 1 = a 2 = a, the ost of selling and serviing the ustomer groups is different, v 2 > v 1. Given this lassifiation, the following orollary presents an appliation of Proposition 1 to the ase of ustomer profitability alulations. Corollary 1. Customer profitability alulations understate the benefits of full servie sales, i.e., π 2 () < V 2 () for all < H. In other words, despite being less profitable, full servie ustomers have an upside not refleted in ustomer profitability alulations in that they help put downward pressure on wholesale pries. If the buyer (retailer) were instead to fous on higher margin ustomers, they would be faed with a higher wholesale prie. Again, despite the fat that the inputs are idential aross onsumer-types, the fat that they entail differential profitability means that the input prie depends on the portfolio of ultimate onsumers. And, as the portfolio hanges, so does input priing. A natural follow-up question may be how the results hange if the retailer is unable to harge different pries to different onsumers. Suh prohibitions on prie disrimination at the retail level may arise due either to regulatory restritions or pratial onsiderations (e.g., it is hard to trak how muh time a partiular sales agent spends with a ustomer and

20 18 thus impratial to harge ustomers for suh time). In suh irumstanes, the ontrat has an additional restrition that the prevailing retail prie aross groups is the same, i.e., a q 1 () = a q 2 (). In this ase, if the firm operates only in the no-frills market, the solution is as presribed by Lemma 1 for n = 1. That is, the firm proures q 1 1 () units at a per-unit prie of w 1 (). When the firm serves both onsumer groups, the solution to the revised ontrating program ((P) with the added uniform priing onstraint) entails a simple adjustment to the previous ontrat: the buyer proures [1 / 2][q 2 1 () + q 2 2 ()] units for eah of its two segments. And, sine total prourement is the same as without the equal priing onstraint, the agreed-upon wholesale prie is w 2 (), also as before. In this ase, the expeted firm profit is [1 / 2]E{[a [1 / 2][v 1 + v 2 ] H()] 2 } F 1 F 2. Another way of viewing the outome is that it is the same as under unrestrited retail prie disrimination, with the v i in eah market being of "average" value. Relative to when the firm only operates in the no-frills market, by serving both types of ustomers, the effetive variable ost in market 1 inreases from v 1 to [1 / 2][v 1 + v 2 ] whih translates into a lowering of wholesale prie, a subsidy not aounted for in segment profit alulations for market 2. That is, the same supply-side onsideration highlighted in Proposition 1 and Corollary 1 persists even in the ase of uniform retail priing restritions. In the ase of uniform retail priing, however, there is also a demand-side onsideration. Not only does the segment profitability figure fail to reflet the wholesale priing spillover that operation in the full servie market entails, but it also fails to reflet the retail priing spillover. Intuitively, if the firm operates only in the heaper no-frills market, it is able to set lower retail pries (proure higher quantities). With operation in both no-frills and full servie markets, the firm onsiders average profitability and, thus, sets a higher retail prie. Proposition 3 provides a suint haraterization of both the supply-side and demand-side effets.

21 19 Proposition 3. In the ase of ustomer profitability analysis and uniform retail priing, S() = [1 / 4][v 2 v 1 ]t() 0, and D() = [1 / 4][v 2 v 1 ][ H (1 / 4)(v 2 v 1 ) H() t()], where t() = H [ + H( ) H()]d a v 1 H() 0. Note that S() in Proposition 3 is similar to that in Proposition 1, with n = 2, and a 1 = a 2 = a (the differene being k() vs. t()). In other words, restritions on retail-level prie disrimination have no substantive effet on the paper's main onsideration of wholesale prie onsequenes of extended market reah. The differene now is that there is also a demand-side effet, D(). While the supply-side effet represents a latent subsidy from serving full-servie ustomers, the demand-side effet is sure to be a tax at large. Sine the demand side ondition too depends ritially on the relative margins of the two ustomer lines, so does the net effet of S() + D(). In partiular, for m() m 2 () < 2[ H H()], π 2 () < V 2 (), and for m() m 2 () > 2[ H H()], π 2 () > V 2 (). Note m() m 2 () > 0 in line with segment 2 having a lower margin ( v 2 > v 1 ). Hene, for suffiiently large (and surely for suh that H H() < 0), π 2 () > V 2 () the negative demand-side externality of serving full-servie ustomers outweighs the positive supply-side externality, so the requirement of uniform retail priing reverses the ordering in Corollary 1. Even in this ase, the demand-side tax is moderated by the wholesale prie subsidy provided by operations in the full-servie market. Thus, the broader point to take from the analysis is not that demand-side effets of partiipation in multiple markets are insignifiant, just that the supply-side wholesale priing effet may provide an additional onsideration. 4. Limited Commitment and Requirements Contrating In analyzing the role of extended downstream market reah on upstream priing in

22 20 the presene of adverse seletion, we have thus far presumed report-ontingent (menubased) supply ontrats. While the revelation priniple ensures that suh ontrats surely apture the buyer's preferred equilibrium under any more detailed arrangement, one may also argue that ontrating on all possible ontingenies is often unrealisti. After all, in pratie many firms sign more simple requirements ontrats, in whih the supplier maintains disretion over wholesale prie but agrees to provide as muh inputs as the buyer desires at the stated prie. In this setion, we revisit the results under the presumption of simple requirements ontrats. That is, instead of the buyer ommitting to a menu of ontrats, the buyer only makes a ommitment to what segments it will operate. Then, the supplier speifies w, after whih the buyer retains disretion over q. 5 In this ase, the equilibrium outome an be derived by working bakward in the game. Given partiipation in n segments and a wholesale prie of w, the buyer's hosen quantities solve: Max q Π n (q,w). (2) The first-order ondition of (2) yields quantities q i (w) = [α i w] 2. Given these quantities, the supplier sets the wholesale prie, w, to solve: Max w n i=1 q i (w)[w ]. (3) The first-order ondition of (3) then yields the supplier's preferred wholesale prie, w n () (the ~ reflets the requirements ontrating ase). Using w n () in q i (w) then yields the quantities proured in equilibrium, denoted q n i (), i.e., q n i () = q i ( w n ()). The outome is summarized in Lemma 3. 5 In this ase, the assumption needed to ensure nontrivial partiipation in eah segment is α i > [α n + ]/2.

23 21 Lemma 3. Under requirements ontrating, the equilibrium outome entails: (i) (ii) q i n () = [1 / 4][2α i α n ]; and w n () = + [1 / 2][α n ]. Notie, under requirements ontrating, the wholesale prie markup again depends on average segment profitability, and is inreasing in the measure: d[ w n () ] dα n = 1 2 > 0. Given the above impliations for the markup, it follows that the relative profitability of segments ontinues to play a ritial role. Using the equilibrium outome outlined in Lemma 3, the results in the ase of requirements ontrating as preisely as before. That is, Lemma 2 ontinues to apply, with q i n () replaed by q i n () and w n () replaed by w n (). Simplifying these expressions yields the following analog to Proposition 1. Proposition 4. Under requirements ontrating, [ α n α n ][ i=1 q i n ()] n 1 α n α n (i) S() =, and D() = 2 n 1 16 n 1 [ ] [ ] 2 [ ] ; and (ii) Segments with lower (higher) margins have profit that understates (overstates) the value they provide for all. That is, if m n () < m(), then π n () < Ṽn (), and if m n () > m(), then π n () > Ṽn (). Inspetion of Proposition 4 onfirms that the sign of S() is again dependent only on α n α n. That is, relative to the ase of omplete report-ontingent ontrating, the supply-side effets of eliminating segment n in the ase of requirements ontrating differ only in terms of magnitude (not the sign). In this ase, sine there is a wholesale prie effet and quantities are diretly tied to wholesale pries, there is also an indued demandside effet, as refleted in D(). Consistent with this intuition, when wholesale pries are

24 22 altered due to segment n, quantities set without regard to suh alterations are ineffiient for the buyer (refleted in D() < 0). As onfirmed in Proposition 4(ii), despite requirements ontrating introduing a demand-side onsideration, the supply-side onsideration is more pressing leading to the same haraterization of the sign of V n () π n () as in the ase of omplete reportontingent ontrating: V n () π n () = S() + D() = [α n α n ]l(), where l() = [2n + 1]α n 3α n 2[n 1] 16[n 1] In short, though requirements ontrating alters the magnitude of segment profit and segment value added alulations it does not alter the essene of the point herein: when a segment has low margins, it has the latent upside of supporting lower wholesale pries. > Conlusion Determining the ontribution of various segments to the overall profit of a diversified entity is a deliate exerise. Refined osting measures have substantially improved this proess and, hene, led to additional reliane on segment profit measures for resoure alloation hoies. Yet, sine aounting profit metris neglet opportunity osts, segment profit figures an deviate from the value added by a segment. The ommon onern in this vein is of downstream omplementarities brought by loss leader produts or loations as means of furthering brand reognition and/or produt loyalty. This paper examines a divergene between segment profit and segment value added due instead to upstream onsiderations. We demonstrate that even if produt demand and long-term ompetitive posturing are not pressing onsiderations, a firm may nonetheless benefit from its less stellar retail performers so as to support more favorable supplier priing terms. Sine less profitable

25 23 markets (be they produt lines or ustomer groups) solidify a relutane to aept markups in supplier priing, a firm's ative partiipation in less profitable markets an help support lower input pries. This effet, in turn, points to an additional onsideration in keep-or-drop deisions. While this fundamental phenomenon is demonstrated in a model wherein industrial struture is taken as given, further researh ould seek to endogenize the struture of industries and, in partiular, the varied produt offerings that a onglomerate would optimally seek in light of input priing onsiderations. Future study may also shed light on other forms of pereived "weakness" that ould prove useful in supply hain relationships, suh as publi dislosure of proprietary information or even limited aquisition of relevant information.

26 24 Appendix Proof of Lemma 1. Denote the supplier's profit when its true ost is and its reported ost is ĉ by ψ(ĉ ). That is, ψ(ĉ ) = [w(ĉ) ]Q(ĉ), where Q(ĉ) = 1 q(ĉ) = n i=1 qi (ĉ). Step 1. In this step, we show global inentive ompatibility onstraints, labeled (IC) in (P), imply the loal inentive ompatibility onstraints and the monotoniity of Q(). Without loss of generality onsider two types and, >. Global inentive ompatibility ditates, ψ( ) ψ( ) = ψ( ) + [ ]Q( ), ψ( ) ψ( ) [ ]Q( ). Reversing and and ombining with the above inequality implies: Q( ) [ ψ( ) ψ( ) ] Q(). (A1) From (A1), Q( ) Q(), so Q( ) is (at least weakly) dereasing. Further, taking the limit of (A1) as yields dψ( ) = Q(). Integrating both sides, with d ψ( H H ) as the onstant of integration, yields the loal (IC) below: H ψ( ) = ψ( H H ) + Q( )d. (A2) Step 2. In this step, we show loal inentive ompatibility onstraint in (A2) and Q() dereasing in imply the global inentive ompatibility onstraints. Again, onsider two types and, >. From (A2): ψ( ) = ψ( ) Q( )d. Given Q( ) is monotonially dereasing, the above equality implies: ψ( ) ψ( ) [ ]Q(), ψ( ) [w() ]Q() = ψ( ). A similar argument shows that ψ( ) ψ( ). Thus, the global inentive ompatibility onstraints for all -types are satisfied.

27 25 Step 3. From (A2), it follows that if (IR) for = H is satisfied, (IR) onstraints for all other -values are also satisfied. Further, (A2) yields w()q() = Q() + ψ( H H ) + H program an be written as: Max q i (),i=1,l,n Q( )d. Substituting this into the objetive funtion in (P), the n H [α i q i ()]q i () q i () H i=1 [ q i ( )d F L i ] g()d ψ( H H ) s.t. ψ( H H ) 0 n dq i () i=1 0 d Clearly, from above, ψ( H H ) = 0. Also, integrating by parts, H H [ q i ( )d L ] g()d = H H()q i () g()d. Thus the first-order ondition of the L relaxed program, one without the onstraint on the monotoniity of Q(), is: α i 2q i () H() = 0, q i () = [1 2][α i H()]. (A3) n dq Using q i () from (A3), i () i=1 = n d dh() d. Given the hazard rate assumption dh() n dq 0, i () i=1 0. Hene, the solution to the relaxed program is also d d the solution to (P), i.e., the hoie of q i () in (A3) is q n i () in Lemma 1(i). H Q( )d From (A2), and ψ( H H ) = 0, w() = +. Using q n i () from part (i), Q() Q() = n[α n H()]. Using this in w() yields w n () in part (ii). This ompletes the proof of Lemma 1. Proof of Lemma 2. The value added by segment n is V n (), V n () = Π n (q n (),w n ()) Π n 1 (q n 1 (),w n 1 ()). Segment n's realized (aounting) profit is π n (), π n () = π n (q n n (),w n ()). Hene, V n () π n () = Π n (q n (),w n ()) Π n 1 (q n 1 (),w n 1 ()) π n (q n n (),w n ()). Sine Π n (q n (),w n ()) = Π n 1 (q n (),w n ()) + π n (q n n (),w n ()), the above an

28 26 be written as: V n () π n () = Π n 1 (q n (),w n ()) Π n 1 (q n 1 (),w n 1 ()). Finally, adding and subtrating Π n 1 (q n (),w n 1 ()), the differene an be written as: [ ] + (A4) [ Π n 1 (q n (),w n 1 ()) Π n 1 (q n 1 (),w n 1 ())]. V n () π n () = Π n 1 (q n (),w n ()) Π n 1 (q n (),w n 1 ()) The first term on the right-hand-side of (A4) is S() and the seond term is D(). This ompletes the proof of Lemma 2. Proof of Proposition 1. Sine Π n 1 (q,w) = π i (q i,w) and π i (q i,w) = [α i q i ]q i wq i F i, the S() and D() expressions in Lemma 2 an be equivalently written as: S() = w n 1 () w n () n 1 i=1 [ ][ i=1 n 1q i n ()], and [ α i w n 1 () q n i () q n 1 i ()][ q i n () q n 1 i ()] n 1 D() = i=1. (A5) From Lemma 1, q n i () = q n 1 i () = [1 2][α i H()] for i = 1,L,n 1; H w n [α n H( )]d () = + α n ; and w n 1 H [α n 1 H( )]d () = + H() α n 1. H() Substituting these in (A5), and replaing α n 1 by using the identity α n = n 1 n α n n α n, yields the expressions for S() and D()in part (i). Sine + H() is inreasing in and α i > H + H( H ), k() 0 with equality only at = H. From Lemma 2 and Proposition 1(i), V n () π n () = S() + D() = [1 / 2][α n α n ]k(). (A6) From Lemma 1(i), q n n () = [1 2][α n H()], so m n () = [α n q n n ()] w n () = [1 2][α n + + H()] w n () and m() = [1 2][α n + + H()] w n (). This implies m() m n () = [1 2][α n α n ]. Thus, (A6) an be written as: V n () π n () = [m() m n ()]k().