Opportunity Costs and Non-Scale Free Capabilities: Profit Maximization, Corporate Scope, and Profit Margins

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1 Opportunity Cot and on-scale Free Capabilitie: Profit Maximization, Corporate Scope, and Profit Margin Daniel A. Levinthal* Reginald H. Jone Profeor of Corporate Strategy 309 Steinberg-Dietrich Hall Wharton School, Univerity of Pennylvania Philadelphia, PA (phone) (fax) Brian Wu Aitant Profeor of Strategy Stephen M. Ro School of Buine Univerity of Michigan 70 Tappan Street, R4388 Ann Arbor, M (phone) (fax) wux@umich.edu Running Head: Opportunity Cot and on-scale Free Capabilitie Keyword: corporate diverification, firm capabilitie, opportunity cot, diverification dicount, indutry dynamic, reource view of the firm * Correponding author Forthcoming in Strategic Management Journal Augut 009 We wih to thank the Mack Center for Emerging Technologie for generouly upporting thi reearch. We have benefited from comment on prior draft by Ron Adner, David Colli, Glenn MacDonald, Cota Markide, icolaj Siggelkow, Harbir Singh, Sid Winter, the aociate editor Joeph Mahoney, and two anonymou referee, a well a eminar audience at the Tuck School, Dartmouth College, the Atlanta Competitive Advantage Conference, the Academy of Management, and the Harvard Strategy Conference.

2 Opportunity Cot and on-scale Free Capabilitie: Profit Maximization, Corporate Scope, and Profit Margin Abtract The reource-baed view on firm diverification, ubequent to Penroe (959), ha focued primarily on the fungibility of reource acro domain. We make a clear analytical ditinction between cale-free capabilitie and thoe that are ubject to opportunity cot and mut be allocated to one ue or another, thereby hifting the dicoure back to Penroe (959) original argument regarding the tock of organizational capabilitie. The exitence of reource and capabilitie that mut be allocated acro alternative ue implie that profit-maximizing diverification deciion hould be baed upon the opportunity cot of their ue in one domain or another. Thi opportunity cot logic provide a rational explanation for the divergence between total profit and profit margin. Firm make profit-maximizing deciion to increae total profit via diverification when the indutrie in which they are currently competing become relatively mature. Due to the preading of thee capabilitie acro more egment, we may oberve that firm' profit-maximizing diverification action lead to total profit growth but lower average return. The model provide an alternative explanation for empirical obervation regarding the diverification dicount. The elf-election effect noted in recent work in corporate finance may not be indicative of inferior capabilitie of diverifying firm but of the limited opportunity context in which thee firm are operating. Running Head: Opportunity Cot and on-scale Free Capabilitie Keyword: corporate diverification, firm capabilitie, opportunity cot, diverification dicount, indutry dynanmic, reource view of the firm

3 TRODUCTO The reource-baed view of the firm ha long recognized that firm diverify in order to exploit firm-pecific reource for which factor market are imperfect (Penroe, 959; Teece, 98). A Mahoney and Pandian (99) note, thi argument i baed both upon the availability of reource, in particular the degree to which there may be lack reource in the firm current market context, a well a implication of the nature of the firm reource for the direction of poible diverification effort. The diverification literature along the line of the reource-baed view ha largely focued on thi latter point highlighting the fungibility of reource, or the degree to which the value of reource may be diminihed a reource are leveraged in etting more ditant from the original context in which the reource (e.g., brand-name or technical capability) wa developed (cf., Montgomery and Wernerfelt, 988). The fungibility of reource i the bai for the explanation a to why related diverification tend to outperform unrelated diverification and, in turn, why firm tend to purue more related diverification (Betti, 98; Markide and Williamon, 994; Montgomery and Wernerfelt, 988; Robin and Wierema, 995; Rumelt, 974). mplicitly, and at time explicitly, reource are often treated a having a cale-free property in the ene that the value of reource i aumed to be not reduced a a reult of the heer magnitude of firm operation over which they are applied. A Chang (995: 387) note, The dominant view in diverification reearch i that intangible reource, uch a technology and marketing kill, encourage firm to diverify into new buinee in order to exploit the public good nature of information-intenive aet. However, a argued in Penroe (959), Reource and capabilitie are ued interchangeably in thi paper. t i alo important to note that owning a more fungible reource doe not necearily lead to competitive advantage, ince it might be in more abundant upply (Montgomery and Wernerfelt, 988) or attract more competition (Adner and Zemky, 008).

4 the tock of a firm' reource and the degree to which they are fungible acro product market are both critical in determining diverification deciion. Many of the reource that may underpin a firm diverification effort, uch a an effective management team or product development expertie in a particular domain, have the feature that they are ubject to opportunity cot. At any point in time, thee reource mut be allocated among alternative activitie, and the ue of thee reource in one activity preclude their ue in other etting. While ome reource, uch a a brand name or patent, may have a public good-like quality, mot firm reource or capabilitie do not. 3 The mot familiar example in the buine etting i a firm-pecific management team (Slater, 980). While a uperior management team can improve the productivitie acro all egment, the team alo ha to allocate it limited time and attention (Roen, 98). Thi iue of the need to allocate capabilitie acro market and, a a conequence, the linking of diverification effort to demand condition in alternative market i highlighted by Chandler (969), which maintain that it wa the decline in product market activity in the late 90 and the 930 that precipitated the enormou growth in diverification of indutrial firm in the U.S. Chandler (969: 75) ubmit that firm uch a DuPont and General Electric that had accumulated vat reource in killed manpower, facilitie, and equipment were under great preure to find new market a their exiting one ceaed to grow. More generally, a Mahoney and Pandian (99) point out, there i an important line of inquiry running from Uzawa (969), Chandler (969; 977), Rubin (973), Slater (980), and Teece (98) that take onboard Penroe (959) concern for the dynamic of reource accumulation by the firm and the implication of thee dynamic for diverification effort. n a 3 Even a reource uch a a brand name may not be a pure public good a the application of a brand name for one product might impact it value in another. Thu, when Gucci wildly applied it brand name to a number of lowerend product in the 980, the value of the brand wa argued to have been reduced (Aaker, 004).

5 imilar vein, Helfat and Eienhardt (004) ugget that firm may reallocate reource acro domain over time in order to achieve, what they term, inter-temporal cope economie. However, the reearch literature ha not been clear about the ditinction between calefree capabilitie and thoe capabilitie that mut be allocated among alternative ue. Thi ditinction i critical becaue we believe that it i thi latter cla of capabilitie that capture the eence of Penroe (959) argument regarding diverification. f capabilitie are all cale-free, a i often implicitly aumed in the literature, iue of opportunity cot and reource allocation are inconequential, ince cale-free capabilitie can alway be leveraged in other area and hence will alway have exce capacity. Thu, it i only reource ubject to an opportunity cot that affect how reource hould optimally be allocated. n thi ene, we are making an analytical return to the original enibility of Penroe (959) capability-baed perpective on diverification. However, it i important to note that Penroe (959) focued on the limit cae in which firm had exce capabilitie. Thi exce derive from two poible ource. One tem from the fact that ome reource contitute dicrete invetment, uch a a phyical plant. f a manufacturing facility i not being fully utilized in the production of the firm current product, then uch a facility can be a free reource that can be applied, in part, to other mean. The other ource reult from managerial learning, which enable a given managerial team to handle a greater range of reponibilitie over time. Yet, reource, particularly human capital-baed reource, tend to be fully allocated to particular tak and initiative at any point in time. n that ene, uch reource are not in exce. However, there till remain the quetion of what i the bet allocation of the time of a ale force, product development team, or top management group baed on their opportunity cot. 3

6 n addition to extending Penroe (959) notion of exce reource to the more general notion of opportunity cot, we incorporate a greater conideration of the role of the demand environment in influencing the opportunity cot aociated with a firm reource. The emphai in Penroe (959) work wa on the internal growth of reource a the ource of exce capacity in the context of demand environment that i implicitly aumed to be tatic. We examine how the dynamic of the demand environment influence the allocation of a firm reource, it diverification effort, and meaure of performance. Specifically, ince the criteria of carrying out an activity are baed upon the opportunity cot of applying capabilitie in one domain or another (Rubin, 973; Slater, 980), a complete account of exce capacity of capabilitie hould take into account not only internal growth in firm-pecific capabilitie but alo the change in external opportunitie acro different market. Underutilized capacity become available when the growth opportunitie in the current market cannot keep pace with the internal growth of capabilitie. The maturity of the current market relative to other potential market could either reduce the value of applying non-cale free capabilitie in the current market or raie the opportunity cot of not applying ome of thee capabilitie in related product market. 4 t i in thi ene that reource become underutilized or exce. Alternatively, if the current market continue to offer ufficiently favorable opportunitie, it will not be economically rational to divert non-cale free reource into other indutrie a long a there i any imperfect fungibility in the value of capabilitie when applied to other domain. Building on thee iue concerning firm internal reource bae and their external product market environment, we develop a baic economic model that provide a rational 4 The relative maturity of the current market could arie either from the decline of the current market or from the fat growth of other market. An example of the former cae i the defene indutry after the mid-980 (Anand and Singh, 997), while an example of the latter cae i the mature dektop PC market in comparion with the rapidly growing hand-held device market. 4

7 explanation of firm diverification behavior in trading off profit margin for corporate growth. Largely ignored by the reearch literature i the fact that profit-maximizing diverification deciion imply that firm eek to increae total profit but not necearily their profit margin or market-to-book value, with the latter two meaure being among the more common performance meaure ued in the diverification literature (Palich, Cardinal, and Miller, 000). Firm make rational deciion to increae total profit via diverification when the indutrie in which they are currently competing become relatively mature. n thi proce, however, firm need to allocate their non-cale free reource away from the current buine to the new one. Due to the preading of thee capabilitie acro more egment, we may oberve that firm' profitmaximizing diverification action lead to total profit growth but lower average return. n a imilar vein, Montgomery and Wernerfelt (988) how that a wider level of diverification can lead to lower average rent (Tobin q) due to the imperfect fungibility of firm-pecific factor. We find that the decline in average return may arie from the reallocation of capabilitie to new product market, even in the abence of any imperfect fungibility of firm-pecific capabilitie. We firt examine thi model in a imple Bertrand et-up in which we demontrate the baic reult regarding the implication of profit maximizing diverification on profit margin. We then expand thi to a Cournot model that allow for a more explicit treatment of competition. n the Cournot etting, we can generate cro-ectional reult in which a firm with inferior capabilitie remain focued on a ingle product market and earn higher profit margin, but le profit, than it more capable competitor. We alo find that a firm become more aymmetric in their capabilitie, the neceary ize of the new product market to elicit diverification on the part of the more capable firm rie. With greater aymmetry in capabilitie, the original market in which both firm compete become more attractive, thereby diminihing the incentive to 5

8 diverify. Thu, the Cournot reult allow u to expand the conideration of competitive effect and alo demontrate the robutne of our original reult to thoe effect. The remainder of the paper i organized a follow. The next ection further develop the notion of non-cale free capabilitie that mut be allocated among alternative ue and it contrat with cale-free capabilitie. We then et up and analyze the formal model by linking capability-baed argument regarding diverification and the demand condition in the market in which the firm doe and may participate. After developing ome general reult under Bertrand and Cournot competition for the relationhip among diverification deciion, firm capabilitie, and profit margin, we engage in a numeric analyi of the Cournot model to further develop the implication of competitive force on both diverification deciion and profit margin. Finally, we dicu the broader implication of thee reult. OPPORTUTY COST AD DVERSFCATO nert Table about here Table illutrate the contrat between what we term cale-free capabilitie and thoe reource that are congetible and require allocation to ditinct purpoe. n addition to thi dimenion by which capabilitie may differ, there i the more traditional iue of fungibility, or the range of activitie over which a reource or capability may be applied. The mot retricted ort of reource reide in the lower left cell. Highly pecific human or phyical capital not only ha the property that it pecificity narrow the domain of activitie over which the reource can be applied, but alo that it ue in one activity contrain it poible ue in other activitie. The cell in the upper left again offer human and phyical capital example, but in thi cae the capital i applicable over a wider domain of activitie. While an auditor may not be uefully 6

9 applied in a marketing function, he or he can apply their auditing expertie to a wide variety of enterprie. Similarly, power generation equipment i a general purpoe capital infratructure that could be applied to an enormou range of ue. However, per the iue of opportunity cot, it i important to note that the ue of an auditor in one engagement retrict their poible ue in another; and the application of a certain magnitude of kilowatt to one purpoe reduce the kilowatt available for another. n the right-hand ide, the reource are not ubject to opportunity cot. There are no inherent contraint on how many good or ervice can bear a common brand name. or doe the ue of a computer program on one machine preclude it ue on another. 5 While the fungibility of a brand name or computer operating ytem i not limitle, the range of application i generally greater than either a pecific piece of intellectual property or the range of ue of a particular cutomer relationhip. The extant reearch literature on diverification ha tended to focu on cale-free capabilitie, uch a technical know-how and reputation, which lead to economie of cope or ynergie in the diverification proce becaue they diplay ome of the characteritic of a public good in that it may be ued in many different non-competing application without it value in any one application being ubtantially impaired (Teece, 980: 6). The recognition of cale-free capabilitie ha had a profound influence on both academic reearch and indutry practice, ince it highlight the role of knowledge and competence a trategic aet (Winter, 987). Winter and Szulanki (00) tudy of replication procee provide a paradigmatic example of a cale-free capability, defining the Arrow core a the informational endowment a firm extract from an original etting which can be replicated to other etting. The ditinctive property of uch information-like reource i that unlike any reource that i rivalrou in ue, an 5 The producer may retrict the replication of the program through ite licene or copy retriction but clearly uch contraint are to addre iue of value appropriation and are not related to technological contraint to the application of a given program to multiple application. 7

10 information-like reource i infinitely leverageable it doe not have to be withdrawn from one ue to be applied to another (Winter and Szulanki, 00: 74). The critical contraint in the application of cale-free reource i not by definition the cale of the operation over which they are applied, but rather the cope or range of their applicability. ndeed, the iue of reource relatedne and fungibility i arguably the mot tudied quetion in corporate trategy. Rumelt (974), in a pioneering examination of thi iue, howed that firm puruing related diverification outperform thoe puruing a trategy of unrelated diverification. Thi baic finding ha been reconidered with a variety of different meaure of relatedne, but the general reult ha tood up (Betti, 98; Markide and Williamon, 994; Montgomery and Wernerfelt, 988; Robin and Wierema, 995). While Penroe (959) emphai on a firm tock of capabilitie a a bai for diverification ha played a econdary role to the conideration of the fungibility of reource, there ha been ome awarene in the literature that there may be opportunity cot aociated with the ue of reource. n hi brief dicuion on the limit to diverification economie, Teece (98: 53) ugget that, Know-how i generally not embodied in blueprint alone; the human factor i critically important in technology tranfer. Accordingly, a the demand for haring know-how increae, bottleneck in the form of over-extended cientit, engineer, and manager can be anticipated. Recent empirical work in both finance and management ha provided uggetive evidence of the opportunity cot of allocating reource from one product domain to another. Schoar (00) find that after a firm diverifie into a new indutry by acquiring a plant, the incumbent plant will incur a decreae in productivity, while the acquired plant increae productivity. Similarly, Robert and McEvily (005) find that entering a new pharmaceutical product market reduce a firm performance in it current market. Finally, Hitt et al. (99: 8

11 695) oberve that acquiition tend to reduce both the extent and productivity of firm R&D invetment, uggeting that the reource remaining for managerial allocation may become contrained, cauing manager to forgo other invetment opportunitie. Conider the following example of thee argument. A the tronget player in the microproceor indutry, ntel ha been experiencing luggih growth in the PC microproceor market due to aturated demand and increaing competition from Advanced Micro Device. n order to pur growth, ntel ha ought to extend it reach beyond the PC microproceor indutry into mobile phone and conumer electronic. The maturity of the PC microproceor market ha made the opportunitie of uing it capabilitie in other indutrie more attractive, and, correpondingly, the opportunity cot of taying focued ha rien. At the ame time, diverification require ntel to allocate it carce reource into thee new egment. Conequently, our theory would predict that, on the whole, ntel diverification effort will increae ale and total profit. However, it average return will decline, reflecting both the hifting away of firm-pecific reource from the development and manufacturing of microproceor for PC and the poible reduced efficacy of thee ame reource in the related product market into which the firm i diverifying. 6 Baed upon the above reaoning, we develop the following argument regarding diverification effort. Firt, it i important to ditinguih between diverification effort baed on cale-free and non-cale free capabilitie. A cale-free reource, uch a brand name, face limit on the breadth of it fungibility (i.e., how broadly fungible i a given brand name) but not on it extent of application (i.e., the number of market in which a given brand can be applied for a given level of fungibility). n contrat, the application of thoe non-cale free capabilitie i 6 Of coure, another bai for the decline in average return i the hift from a market in which ntel ha a dominant poition to market that may be more competitive; however, the fact that ntel i entering thee more competitive, but more rapidly growing, market i further tetimony to the need to reallocate non-cale free capabilitie. 9

12 driven by the logic of opportunity cot. On the margin, i the greatet value of thee firmpecific capabilitie realized within the current product market context or in diverifying to a new context? Thi opportunity cot i, in turn, importantly affected by the ize, growth, and competitive condition in alternative product market. Thu, when there are multiple egment, the range of diverification activity i contrained by the total tock of capabilitie. Thi analyi upplement the inight in the trategy literature that the imperfect fungibility of cale-free capabilitie retrict corporate cope (e.g., Montgomery and Wernerfelt, 988). Thi analyi alo provide new inight into the diverification dicount, the obervation that diverified firm tend to have a lower valuation, typically meaured a the relationhip between market value to book value or Tobin q, than an amalgamation of an equivalent et of focued firm (Berger and Ofek, 995; Lang and Stulz, 994). Agency theorit ugget that diverification detroy value for reaon uch a manager empire building behavior that aim to increae their own tatu, power, and pecuniary compenation (e.g., Jenen, 986). Recently, however, there ha been a growing literature in the corporate finance field uggeting that a diverification dicount arie even when firm are value maximizer. Econometrically ophiticated analye of the profitability of diverified firm (e.g., Campa and Kedia, 00; Villalonga, 004) indicate that there i omething ytematically different about firm that diverify. t i thi endogenou election into the act of diverification, rather than diverification per e, that lead to diverification dicount: the failure to control for firm characteritic that lead firm to diverify and be dicounted may wrongly attribute the dicount to diverification intead of the underlying characteritic. For example, conider a firm facing technological change, which adverely affect it competitive advantage in it indutry. Thi poorly performing firm will trade at a dicount relative to other firm in the indutry. Such a firm will alo have lower opportunity cot of aigning it carce reource in other indutrie, and thi might lead it to diverify. f poorly performing firm tend to diverify, then not taking into account pat performance and it effect on the deciion to diverify will reult in 0

13 attributing the dicount to diverification activity, rather than to the poor performance of the firm. (Campa and Kedia, 00: 73) n exiting analytical explanation of thi empirical finding that, controlling for endogeniety in diverification behavior, there i no diverification dicount (e.g., Gome and Livdan, 004), the act of diverification i interpreted a a ignal that the firm ha relatively few ex-ante capabilitie and i diverifying due to the correpondingly low rate of return in it initial market. n the preence of diminihing return to production, firm with lower productivity will reach their optimal ize in the incumbent egment at a lower ize level than thoe firm with higher productivity and, a a reult, firm with lower productivity are more likely to diverify. We agree with thee recent empirical finding that there i omething ytematic about thoe firm that ort themelve into a poitive diverification deciion. However, the above analytical explanation i not fully conitent with the well-evidenced propoition in the trategy field that firm with more relevant capabilitie (R&D or marketing capabilitie) tend to enter a new field earlier and perform better (e.g., Helfat, 003; Klepper and Simon, 000; Mitchell, 989). n contrat, in the pirit of the long-tanding treatment of diverification in the trategy literature, we ugget that the omething different i not that thee firm are a bad type and are lacking in capabilitie. Rather, thee are firm with relatively uperior capabilitie; and the bad ignal may be a tatement about the market context in which thee firm are operating, uch a demand maturity, rather than a tatement about the firm relative lack of capabilitie. 7 n the puruit of the bet ue of the firm non-cale free reource, there i ome allocation of 7 The recent treatment of the diverification dicount uch a Campa and Kedia (00) and Villalonga (004) do control for indutry demand condition when examining the elf-election effect of the act of diverification on the o-called diverification dicount. However, due to data limitation, uch work mut rely on meaure of indutry at the four-digit level of the SC code. Thi level of aggregation mak coniderable diverity of demand environment at the product level. We elaborate on thi iue in the dicuion ection.

14 reource away from etablihed market and, at the acrifice of profit margin but not total profit, a hift of thee reource to new market. Thu, both our model and thoe developed in the corporate finance literature are conitent with the empirical finding regarding the diverification dicount ; however, the two explanation differ in their prediction a to which firm (more or le capable) are likely to be more or le diverified. MODEL STRUCTURE We model a firm diverification deciion with regard to two market egment indexed by m (The initial egment m and the new egment m ). Production in each egment i decribed aq m t m m Tk m, where m i the firm cale-free capabilitie, t m i the hare of the firm total non-cale free capabilitie, T, that mut be divided among activitie, and capital k m whoe replacement cot per unit i r which reflect the current market value of capital. For the ake of implicity, we aume that firm are endowed with a particular capability tock T and do not conider the cot of developing thi, but only the opportunity cot of how it i applied acro different market egment within the firm. The amount of k m needed to produceq m, given t m, i therefore Q t m m m T rqm, with total cot tt m m c Q, where m m c m r () tt m m ote that (i) cale-free capabilitie,, and non-cale free capabilitie, T, are firm m pecific and ubject to imperfect input market (Teece, 98); (ii) providing more of capabilitie reduce both total and marginal cot ince it ubtitute for the purchaed capital; (iii) c m i decreaing in t m and increae to infinity a t m approache zero; (iv) we pecify the following

15 relationhip between cale-free capabilitie in the two market: ( ). Thi relationhip implie that cale-free capabilitie,, are not perfectly fungible, and that the effectivene of cale-free capabilitie,, diminihe by a factor ( 0 ) when i applied to the new egment. 8 t i important to relate thi production function and aociated cot function to our underlying argument regarding cale-free and non-cale free capabilitie. Our focu i on the allocation of non-cale-free capabilitie acro market context. Thi capability could be a product development team that might be pread acro multiple initiative, a highlighted in Chritenen and Bower (996) work on the dik drive indutry, the allocation of carce production capacity a in Burgleman (994) work on ntel, or the attention of the top management team (Roen, 98). For the ake of implicity, we are not addreing thi allocation with repect to the cale of activity within a given buine unit. Thu, a buine unit i aumed to be able to cale up it activity at a contant marginal cot. Thi implification follow on the work of Klepper (996) and Lippman and Rumelt (98) on indutry evolution, which, in order to highlight the effect of acro-firm heterogeneity, potulate a production technology with a contant marginal cot of production. Thi aumption of contant return to production cale alo allow u to demontrate that diverification can arie from the change in demand condition in the abence of diminihing return to production cale, in contrat to recent work in corporate finance (cf., Gome and Livdan, 004; Makimovic and Phillip, 00) in which diminihing return to production cale act a an underlying driver for diverification. 8 A we point out in Table, non-cale free capabilitie are alo ubject to the iue of imperfect fungibility, but the ditinctive feature of non-cale free capabilitie i that they mut be allocated acro alternative ue baed on opportunity cot. n order to highlight the iue of allocation, we aume that non-cale free capabilitie are perfectly fungible; however, o that the model more cloely correpond to Montgomery and Wernerfelt (988), we allow for the cale-free capability to have imperfect fungibility acro alternative ue. 3

16 We denote the demand and price for a given firm product in egment m a q m and repectively. Should the firm engage in both activitie, it profit i q ( p c ) q ( p c ) or r r q( p ) q( p ) tt t T. Auming the optimal t and t are both trictly poitive, the firm problem i: q q r r max{( pq pq) r( ) t t, p,and p} tt t T t T tt () ote that it may not be optimal for the firm to engage in both activitie imultaneouly. Furthermore, if it i optimal for the firm to be diverified into both activitie, then the optimal allocation of non-cale-free capabilitie t * and t * are bounded away from zero. That i, to get p m into the new activity require a dicrete reduction in the capabilitie employed in the initial activity. ndeed, depending on the magnitude of the firm capabilitie and the market price, a firm may not be competitively viable in a given market. Thi above etting offer a general framework for analyzing firm diverification deciion and the aociated performance effect baed on (non-cale-free) capability allocation. n the following ection, we examine the diverification problem characterized in thi general framework uing the two mot widely ued market model: the Bertrand model and the Cournot model, which uefully complement each other. The Bertrand analyi allow u to develop the baic inight regarding the allocation of carce capabilitie acro line of buine and it implication for firm profitability. ntroducing Cournot competition allow u to examine more directly the impact of competitive interaction among firm. However, the Cournot analyi in thi context doe not lend itelf to a full cloed form analytical olution a the reaction function are neither continuou nor monotonic. Thu, we analytically derive the general reult regarding firm diverification deciion, and then perform a numerical analyi to characterize more 4

17 pecific propertie regarding profit margin and the pattern of diverification. Further, we analyze a wide array of parameter value to both explore further inight of the model and the robutne of our reult. AALYSS: Bertrand Model Each market i pecified to be a Bertrand duopoly, where whenever the firm allocate non-cale-free capabilitie uch that it marginal cot i lower than that of the competitor, the firm erve the whole market with demand. The demand ide of egment m conit of m conumer. Thu, the firm that capture the market produce quantity qm m, charge a price of r pm equal to the competitor marginal cot, and ha profit m( pm cm), where c m mtt i m defined a in equation (). n thi Bertrand etting, a given firm diverifie into the new egment when demand condition are uch that the maximization problem () ha an interior olution * * (, ) t t. The total r r profit aociated with the diverification trategy i ( p ) ( ) * p * tt t T, andthe total ale aociated with the diverification trategy i p p. Therefore, the profit margin aociated with the diverification trategy, which we denote a *, i * r r ( p ) ( p ) p p Tt p p Tt * * ( ) (3) 5

18 n contrat, when firm focu on the initial egment, the profit margin i r ( p ) T, p while when firm focu on the new egment the profit margin i r ( p ) ( ) T p. Therefore, the weighted average of the profit margin of the two focu trategie, which we denote a w, with relative ale p p p and p p p a the repective weight, i w r r ( p ) ( p ) p p T p p ( ) T (4) w i a tandard benchmark ued to compare the performance of diverified and focued firm (Berger and Ofek, 995; Lang and Stulz, 994). The relation between the profit margin of the diverification trategy (equation (3)) and that of focued trategie (equation (4)) i characterized by equation (5). * w r p p ( ) T (5) A a reult, we have the following propoition. Propoition : The profit margin of the profit-maximizing diverification trategy for a firm with capability tock T i lower than the weighted average of the profit margin of focuing thi capability tock T in each of the two market. The difference i characterized by equation (5). (See Appendix for a proof.) Propoition allow u to identify the ource of the declining profit margin aociated with diverification by decompoing the profit margin of the diverification trategy into two part: the weighted average of the two focu trategie and the dicount due to the preading of non-cale-free capabilitie. The econd term of w in equation (4) indicate how the profit 6

19 margin of the diverification trategy decline with the degree to which the effectivene of cale-free capabilitie diminihe in the new egment. Thi i the cae tudied in Montgomery and Wernerfelt (988) who account for a decline in profit margin or Tobin q a firm apply, what we term, cale-free capabilitie in increaingly ditant market. Adding to thi conideration of imperfect fungibility, the econd term of equation (5) capture the dicount due to the preading of non-cale-free capabilitie. Therefore, equation (5) provide a more complete picture of the diverification dicount from the reource-baed view by incorporating the effect of non-cale-free reource that need to be allocated acro application. Propoition ugget that the exitence of a diverification dicount doe not necearily reult from agency behavior that deviate from profit maximization. The preading of non-cale-free capabilitie acro more application baed on opportunity cot implie that the profit margin will be acrificed to ome extent in the puruit of total profit maximization. n parallel to thi dicuion of the impact of diverification on the firm profit margin, we can alo how that rational diverification effort lead to lower Tobin q, a widely ued meaure in the empirical analyi of diverification performance. Given that there i no hort-run variable production cot (e.g., depreciation and labor) in the model, the market value of the firm in thi tylized one-period model can be repreented by operating profit p mm, which i the earning tream that i generated from the firm capital tock of m r T m. Therefore, Tobin q, defined a the market value of the firm divided by the replacement cot of capital (Lindenberg pmm and Ro, 98; Winter, 995), can be repreented a q. m r T m 7

20 We denote the Tobin q aociated with the diverification trategy a q DV and the Tobin q aociated with the weighted average of two focued trategie a q FOC the relationhip in equation (5), the ratio of qfoc and qdv i. Analogou to q q FOC DV (6) A a reult, we have the following corollary. Corollary : The Tobin q of the profit-maximizing diverification trategy for a firm with capability tock T i lower than the weighted average of the Tobin q of focuing thi capability tock T in each of the two market. The difference, in ratio term, i characterized by equation (6). (See Appendix for a proof.) Therefore, whether the average return to capital i meaured a economic profit margin (equation (5)) or a Tobin q (equation (6)), we ee that profit-maximizing diverification lead to a reduction in thee common meaure of firm performance due to the preading of firm reource over multiple product market. AALYSS: Cournot Model The prior analyi examined the profit maximizing tradeoff between total profit and profit margin baed on a Bertrand model. Thi analyi model the diverification of a focal firm that face competitive contraint, but doe not explicitly model an endogenou competitive proce. n thi ection, we addre thi gap by introducing a model of Cournot competition. We develop thi analyi uing the ame analytical tructure for firm capabilitie and their aociated cot function, but the Cournot tructure require u to more fully pecify a demand function. 8

21 Demand in the initial market i pecified a: p a b ( q q ), where q and q are the output of firm and in the initial market. Similarly, in the new market, demand i: p a b( q q), where q and q are the output of firm and in the new market. A before (equation ()), firm are characterized by their non-cale-free capabilityt and T, repectively. However, we et the value of cale-free capabilitie for the two competitor to be the ame a we are focuing on the role of non-cale-free capabilitie. The marginal production cot for firm and in market and are given by c, tt c, c t T ( ) ( t ) T, and c ( ) ( t ) T, where t and t are the fraction of non-cale-free capability of firm and inveted on the initial market, repectively, and ( ) i the effectivene of cale-free capabilitie,, when i applied to the new egment ( 0 ). Thu, firm profit in each market are given by ( p c ) q, for i, ; m,. im m im im The equencing of the firm choice problem i that firm firt chooe their non-cale-free capability allocation, characterized by t and t. Second, given the choen t and t, firm chooe their production quantitie q and q in the initial market and q and q in the new market. The aociated optimization problem can be well pecified via backward induction. However, in thi context, the problem doe not lend itelf to a general analytical olution. ndeed, we will how in the ubequent analyi that the bet-repone function that underpin the equilibrium analyi may, in ome cae, be non-continuou and non-monotonic. 9 9 n thi repect, it i worth noting that our model i related to but ditinct from a claic O model developed by Krep and Scheinkman (983), which howed that a two-tage model of production capacity invetment followed by Bertrand price competition can be treated in a relatively traightforward manner a being equivalent to a one-tage 9

22 The bet repone curve are not continuou for two reaon. Firt, the optimal allocation of non-cale-free capabilitie are bounded away from zero, i.e., to get into the new activity require a dicrete reduction in the capabilitie employed in the initial activity. t would never be optimal for a firm to allocate le than ome epilon to the new market. The firm mut allocate ufficient capabilitie into the new market uch that it can etablih competitive viability in thi market. Furthermore, the firm mut make ure the gain in the new market to which thee capabilitie are being applied i larger than the loe incurred by allocating thee capabilitie away from the old market. A a reult, the bet repone curve alway ha a jump from zero at the point of diverification to ome dicrete magnitude. The econd reaon that the bet repone curve may not be continuou i that the bet repone curve have mall jump at the point where the competitor either make a dicrete move into or out of a product market in repone to it competitor change in allocation of capabilitie acro market. ote that thi econd reaon for the bet repone curve not being continuou i alo the reaon why the bet repone curve are not monotonic (ee Appendix 3 for an illutration of the above argument and ome more detailed explanation). Even in the preence of the analytical challenge identified above, we are till able to derive the following propoition. To capture the change in relative demand, without lo of model of Cournot competition. The firt-tage deciion variable i production capacity in Krep and Scheinkman model, but in the context of our model it i the allocation of capabilitie. The allocated capabilitie determine the level of average cot in a given market (ee equation () on p. 3). Alo, in contrat to Krep and Scheinkman (983), we aume there i no contraint to production capacity and thu production capacity can cale up imultaneouly with the output deciion. Under thi pecification, the equencing of the firm choice problem i that firm firt chooe their non-cale free capability allocation, which in turn determine firm cot level in each market. Second, given the choen capability allocation and the aociated cot level, firm either chooe their price, if under the Bertrand competition, or chooe production quantitie, if under Cournot competition. The firm optimization problem can then be analyzed via backward induction. n um, our model differ from Krep and Scheinkman model in two important way. Firt, Krep and Scheinkman (983) model examine only one market, while we model the allocation of capabilitie acro multiple market along with diverification deciion. Second, Krep and Scheinkman (983) model examine Cournot competition auming homogeneou firm capabilitie, while our model examine how capabilitie in each market are endogenouly determined prior to Cournot competition. 0

23 generality, we hold contant the ize of the initial market a and only vary the ize of the new market a. Let P Pa (, T, T, t, t ) be firm profit function given the new market ize a, firm capability T, the competitor firm capability T, firm allocation t, and the competitor firm allocation t. Similarly, P Pa (, T, T, t, t ) repreent firm profit function given the new market ize a, firm capability T, the competitor firm capability T, firm allocation t, and the competitor firm allocation t. We ue t * and * t to denote firm allocation in equilibrium. Given an initial etting ( a 0 ) in which both firm compete in the initial market, we are able to tate the following propoition: Propoition a: For i,, there exit an aˆ 0, 0,and 0, uch that, when the ize of the new market a get ufficiently large but not too large ( aˆ ˆ a a ) and the two firm capability aymmetry i mall enough ( Ti T(3 i) ), there exit a pure trategy ah equilibrium in which either firm may firt diverify ( t * (3 i) ) while the other firm tay focued at the initial market ( t * i ). Propoition b: For i,, fixing T i a the le capable firm capability level, there exit a T 0, a 0, and 0 uch that, when the ize of the new market a get ufficiently large ( a a a ) and when the two firm capability aymmetry i ufficiently large ( T (3 i) T ), there exit a unique pure trategy ah equilibrium in which only the more capable * firm will firt diverify ( 0t(3 i ) ) while the le capable firm tay focued at the initial market ( t * i ). Propoition c: For i,, given a a the ize of the initial market and T3 i a the more capable firm capability level, there exit T 0 uch that the firm without ufficient capabilitie ( 0 Ti T ) will either focu on the initial market ( t * i ) or witch all reource from one market to the other ( t * i 0 ) in any pure trategy ah equilibrium. (See Appendix 4 for proof.) Thee three propoition highlight how firm diverification deciion differ when the ize of the new market increae, depending on their capability aymmetry. Propoition a

24 highlight the role of competitive condition being endogenou on the reallocation of reource acro product market. n thi cae, when one firm diverifie to take advantage of the new market opportunity, the current market become more attractive a the diverifying firm withdraw capabilitie from thi market. Therefore, there exit an equilibrium in which either the more capable firm or the le capable diverifie firt while the other firm tay focued on the initial market. 0 n addition, it i not an equilibrium for both firm to tart diverifying imultaneouly a the relative demand change, even when thee two firm have equal capabilitie. However, while Propoition a provide a baeline reult when firm are relatively ymmetric, the core iue that i of primary interet to the trategy field i when firm are, to a ignificant degree, aymmetric in their capabilitie. Propoition b demontrate that with ufficient aymmetry in capabilitie, there exit a unique pure trategy equilibrium in which the more capable firm diverifie firt. n thi cae, for the more capable firm, the need to reallocate capabilitie to the new market due to opportunity cot dominate the trategic conideration of waiting for the le capable firm to diverify firt and thu alleviate competition in the initial egment. Propoition (c) indicate that a minimum amount of capabilitie are neceary for the diverification trategy ever to be the optimal trategy, irrepective of relative demand condition acro alternative market. When relative demand change, the more capable firm goe through a diverification proce; however, without ufficient capabilitie, the le capable firm may never become diverified. t will focu on the initial market when the relative market ize of the new 0 * * * * There could be two pure trategy ah equilibria in Propoition a ( ( t,0 ) or ( t, 0) ). However, in either cae, Propoition a hold. Either firm can diverify firt (diverify partly into the new market * (0 t(3 i) ) or completely witch to the new market ( t * (3 i) 0) ), while the other firm tay focued in the initial * market ( t ). i i t(3 i) i t(3 i)

25 market i mall. When the relative market ize of the new market get larger, the le capable firm may completely witch to the new market but will never imultaneouly engage both market. Thi propoition further highlight the critical role of non-cale-free reource in determining the cope of the firm. n the following numerical analyi, we examine more fully the impact of aymmetry of capabilitie on the diverification deciion and, in particular, the threhold of relative ize of the new and the initial market that trigger diverification. n addition, we examine the impact on profit margin of diverification. Thi analyi not only generalize Propoition to the Cournot cae, but it allow u to examine the cro-ectional implication of diverification behavior on the profit margin for firm with varying capability level. UMERCAL AALYSS OF COMPETTVE TERACTO For our numerical analyi, we et the baeline parameter value a follow: a 0, b b, cale-free capabilitie, and the fungibility of cale-free capabilitie ( ) 0.8. n the ubequent analyi, we highlight the impact of varying level of firm capabilitie and market ize ( a, the ize of the new market). Thi later variable allow u to capture relative demand maturity baed on the increae in the ize of the new market a. Holding contant the new market and varying the initial market would lead to the ame reult. mplication of numerical invetigation for diverification deciion n the Cournot analyi, we are able to analytically how that when two firm capability aymmetry i ufficiently large and the new market ize i of ufficient ize, the more capable ote that while we keep cale-free capabilitie and their fungibility ( ) in the model to tay connected with the exiting literature, we do not explore thee two parameter in the analyi ince the focu of thi paper i noncale free capabilitie. See MacDonald and Ryall (004: ) and Adner and Zemky (008) for analytical examination of cale-free capabilitie and the effect of their fungibility on profitability. 3

26 firm will diverify firt while the le capable firm tay focued on the initial market. Building on thi property, we conduct the following numerical analyi to examine how the demand threhold to diverify change with the degree of capability aymmetry. n o doing, we identify ome intereting competitive effect of aymmetry in firm capabilitie nert Figure about here n Figure, a i the demand threhold where the more capable firm (with capabilitiet ) firt chooe to diverify, while the le capable firm (with capabilitiet ) i till focued. The downward movement along a given curve capture the capacity effect, meaning that a the focal firm' own capabilitie ( T ) increae, it threhold to diverify become maller, or firm reache the threhold to diverify earlier. The hift in curve from quare ( T.5) to diamond ( T 0.5 ) capture the competition effect, meaning that a the competitor' capabilitie ( T ) decreae, the threhold for the more capable firm (with capabilitiet ) to tart diverifying become greater. Thi mean that the more capable firm diverifie later (for a larger ize of the new market), ince the current market become more attractive. mplication of numerical invetigation for profit margin and diverification Having characterized diverification behavior under Cournot competition, we now addre the central reult regarding the impact of diverification on profit margin. n particular, the numerical analyi examine whether Propoition regarding the tradeoff between total profit and profit margin hold under Cournot competition. n Propoition, under the Bertrand etting, we compare the profit margin of a diverified firm with a hypothetical benchmark of the weighted average of the firm focuing 4

27 eparately on the two market. However, in the Bertrand etting, ince there i eentially a ingle firm, we cannot make cro-ectional comparion of firm with heterogeneou capabilitie. The following analyi in the Cournot etting addree thi iue. With the ame baeline parameter value of a 0, b b, 0.8, we let the more capable firm have capabilitie T and the le capable one have capabilitie T nert Figure about here Examining profit margin a the ize of the new market varie we ee a number of intereting propertie (Figure ). Firt, conitent with Propoition, for both the more and le capable firm, there i a ubtantial drop in profit margin when the relative demand level in the new market pae the threhold ufficient to elicit diverification and market entry. Second, conitent with Propoition, given the ignificant heterogeneity in capabilitie the firt firm to diverify i the more capable firm. n the interim range of market demand for which it i optimal for the high-capability firm to diverify but for the low-capability firm to remain focued on the initial market, we ee that the more capable firm may end up with a lower profit margin than the le capable firm. A firm rational diverification deciion i driven by it puruit of profit maximization rather than profit margin maximization. Thu, profit margin may not be a good proxy indicator for difference in capabilitie among firm that vary in their degree of diverification. Another finding i that while both firm profit margin drop ubtantially when the relative demand level in the new market pae the threhold ufficient to elicit diverification, their profit margin will gradually increae a the relative demand grow further. Moreover, Two working paper how a imilar reult by auming multiple equal-ized market that are perfectly competitive (Santalo, 00) or monopolitically competitive (ocke and Yeaple, 008). 5