UNIVERSITY OF NOTTINGHAM. Discussion Papers in Economics WHERE TO ENCOURAGE ENTRY: UPSTREAM OR DOWNSTREAM

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1 UNVERSTY OF NOTTNGHAM Discussion Ppers in Economics Discussion Pper No. 0/1 WHERE TO ENCOURAGE ENTRY: UPSTREAM OR DOWNSTREAM by Arijit Mukherjee nd Som Mukherjee August 00 DP 0/1 SSN

2 UNVERSTY OF NOTTNGHAM Discussion Ppers in Economics Discussion Pper No. 0/1 WHERE TO ENCOURAGE ENTRY: UPSTREAM OR DOWNSTREAM by Arijit Mukherjee nd Som Mukherjee Arijit Mukherjee is Lecturer, School of Economics, University of Nottinghm nd Som Mukherjee is Reserch Plnning Officer, Keele University

3 August 00

4 Where to encourge entry: upstrem or downstrem * Arijit Mukherjee University of Nottinghm nd The Leverhulme Centre for Reserch in Globlistion nd Economic Policy, U.K. nd Som Mukherjee Keele University, U.K. July 00 Abstrct: n verticlly seprted industry, where the input suppliers hve significnt mrket power, not only entry but lso the mrkets (upstrem or downstrem) with entry possibilities might be concern to the policy mkers. While entry in the downstrem mrket only lwys increses welfre, entry in the upstrem mrket only increses welfre provided the technology of the upstrem entrnt is not sufficiently inferior to tht of the incumbent. However, entry in the upstrem mrket ccompnied by entry in the downstrem mrket my lwys increse welfre. Our results re importnt for the competition policy. Key Words: Downstrem mrket, Entry, Upstrem mrket, Welfre JEL Clssifiction: D4, L1, 04 Correspondence to: Arijit Mukherjee, School of Economics, University of Nottinghm, University Prk, Nottinghm, NG7 RD, U.K. E-mil: rijit.mukherjee@nottinghm.c.uk Fx: * The uthors re solely responsible for the views presented here but not the Universities.

5 Where to encourge entry: upstrem or downstrem 1 ntroduction Common wisdom suggests tht competition increses welfre of n economy. One mjor chllenge of the competition policy is to design government policies to increse competition through new entry. Reserchers hve lredy discussed the implictions of entry on socil welfre to lrge extent nd found tht entry does not increse welfre lwys. For exmple, while nlyzing the innovtive ctivity of firms in oligopolistic mrkets, Stiglitz (1981), Spence (1984) nd Tndon (1984) hve shown the possibility of lower welfre cused by either potentil entrnts or free entry nd exit of firms. Schmlensee (1976), von Weizsäcker (1980, b), Mnkiw nd Whinston (1986) nd Suzumur nd Kiyono (1987) hve shown tht the equilibrium number of firms in model of free entry nd exit is greter thn the welfre mximizing number of firms nd hence, welfre increses in less competitive mrket. gnoring the existence of fixed cost, Klemperer (1988) nd Lhiri nd Ono (1988) hve rgued tht entry in quntity setting oligopolistic mrket increses welfre provided the mrginl cost of production of the entrnt is not sufficiently high compred to tht of the incumbent. Asymmetric mrginl cost of production (or, uneven technologies) becomes the importnt ingredient in Klemperer (1988) nd Lhiri nd Ono (1988). While debting on the impct of entry, previous works hve ignored the possibility of verticlly seprted industry where the input producers hve significnt mrket power, which my rise importnt questions relted to this debte. So, while the previous works re useful when either the input mrkets re perfectly competitive or the input suppliers nd finl good producers re verticlly integrted, those nlyses my not be suitble in verticlly seprted industries where the input mrket is imperfectly competitive. Empiricl evidence shows tht, like finl goods mrket, the input mrkets re often chrcterized by imperfect competition. As demonstrted by Tygi (1999), the mrket for microprocessors, ircrft-engines, pckged products nd mny others re chrcterized by oligopolistic competition. The energy or powergenerting sector in the U.K. lso shows tht few firms re operting in tht sector. 1

6 f the industry is verticlly seprted nd the input suppliers hve significnt mrket power, it is importnt not only to nlyze the impct of entry but lso to consider whether entry occurs in the upstrem mrket (producing inputs) nd/or in the downstrem mrket (producing finl goods). t is esy to understnd tht entry in upstrem or downstrem mrket hs different effects on demnd for inputs. Entry in the upstrem mrket does not ffect the demnd for input for given price of the input, but increses competition nd shifts production from the incumbent to the entrnt. But, in cse of entry in the downstrem mrket, entry chnges the demnd function for input nd cretes further effect by chnging the demnd function for input. Hence, the considertion whether the new firms enter the upstrem or downstrem mrket my hve importnt consequences on the equilibrium outcomes nd is lso importnt to the policy mkers. n simple model of verticlly seprted industry where the input supplier is restricted to liner pricing (reson for which is given lter), we exmine the effects of entry in the upstrem nd/or downstrem mrket. We find tht entry in the downstrem mrket only lwys increses welfre but entry in the upstrem mrket only increses welfre when the technology of the upstrem entrnt is not sufficiently inferior compred to tht of the incumbent. Wheres, if there is entry in both upstrem nd downstrem mrkets, welfre my lwys be higher under entry compred to noentry. Thus, we show tht the industry, where entry occurs, nd the technologicl differences between the incumbent nd the entrnt, re crucil for nlyzing the effects of entry. Our results imply tht if the industries re verticlly seprted, where the upstrem firms hve mrket power, the policy mkers do not need to be worried when entry occurs in the finl goods mrket s it is more likely to increse the welfre of the economy. f entry occurs in the input mrket only, the technologicl inefficiency of the entrnt needs to be questioned. Thus, we suggest tht while government policy will be designed to encourge entry in the finl goods mrket, entry in the input mrket might require creful considertion nd restriction. The reminder of the pper is orgnized s follows. Section nd Section consider the problem of entry in the downstrem mrket only nd in the upstrem mrket only respectively. Section 4 discusses the possibility of entry in both mrkets. Section 5 concludes.

7 Possibility of entry in the downstrem mrket only Let us consider n economy with upstrem nd downstrem mrkets. Assume tht there is monopolist upstrem firm who produces input for the downstrem firm. The upstrem monopolist fces constnt mrginl cost of production, which is ssumed to be zero, for simplicity. The upstrem monopolist chooses the mount of input production. The price of the input, w, is determined from the demnd function for input. There is no further cost ssocited with input production. Our ssumption of liner pricing for input is similr to Choi (1991), Gerstner nd Hess (1995), Economides (1998), Vills-Bos (1998), Tygi (1999), Ro nd Srinivsn (001) nd others. Following the pproch tken in the chnnel coordintion literture (e.g., Gerstner nd Hess, 1995), we ssume wy the possibility of upstrem firm either chrging fixed fee or enforcing contrct requiring the downstrem firm to buy fixed proportion from the upstrem firm for resons outside of the model. The ssumption of liner pricing my be justified by the rguments given by Ro nd Srinivsn (001) in the context of frnchising. f the upstrem nd the downstrem firms re in ongoing reltionship where the demnd nd cost conditions vry over time, the uniform pricing of the upstrem output is optiml if significnt costs re involved in re-writing the contrcts between the upstrem nd downstrem firms. Our experience bout the U.K. energy sector lso shows tht the firms do not chrge fixed-fee to its customers. We lso rule out the possibility of verticl integrtion in our nlysis. As evident from Hrt nd Tirole (1990), significnt mount of costs involved in verticl integrtion cn mke it n unprofitble strtegy. The firms in the downstrem mrket tke the price of inputs s given while mking their production decisions. For simplicity, we ssume tht the downstrem firms need only this input for their production. Hence, input price cts s the mrginl cost of production for the downstrem firms. Agin, for simplicity, we ssume tht there re no other costs ssocited with finl goods production.

8 To find out the effect of entry in the downstrem industry only on socil welfre 1, we consider two situtions for the downstrem industry. First, when the downstrem industry is monopoly of finl good producer. Second, when the downstrem industry is duopoly. We ssume tht the incumbent nd the entrnt in the downstrem mrket hve different production technologies. The incumbent firm needs one unit of input to produce one unit of output nd the entrnt needs λ units of input to produce one unit of output, where λ > 1. So, the incumbent firm hs better production technology compred to the entrnt. We further ssume tht, in cse of entry, firms compete like Cournot duopolists with homogeneous products. Assume tht the inverse mrket demnd for the finl product is P = q, (1) where the nottions hve usul menings..1 Monopoly in the downstrem mrket Let us strt the nlysis with sitution where the incumbent firm is monopolist in the downstrem mrket. So, given the input price q w, the optiml input demnd is ( w) =. () The upstrem monopolist chooses the optiml mount of input supply to mximize the following objective function: Mx( q ) q. () q Mximizing (), we find tht the optiml input supply nd the corresponding input prices re 4 nd respectively. Totl input demnd (which is lso equl to the totl output of the downstrem incumbent) nd optiml profit of the downstrem incumbent firm re nd 4 16 respectively. economy is Therefore, if there is monopolist in the downstrem mrket, welfre of the 1 Socil welfre is defined s the summtion of consumer surplus nd totl profits generted in the upstrem nd downstrem mrkets. 4

9 7 W ne =. (4). Duopoly in the downstrem mrket Let us now consider sitution where new firm (the entrnt) enters the downstrem mrket so tht the mrket becomes duopoly. Given the input price, the optiml outputs of the downstrem incumbent nd entrnt re respectively ( w + λ ) = nd * w q i ( λw + q e = * w ). (5) t is importnt to note tht the output of the entrnt is zero provided Therefore, totl demnd for input is given by nd q q * * ( (1 + λ) w(1 + λ ) + λw) = qi + λqe =, for * ( w) = qi =, for n our study there is no input demnd for w >. w. ( λ w (6) ( λ w. (7) ( λ Given this structure of the input demnd, it is esy to understnd tht, in cse of entry, whether the upstrem monopolist supplies for both downstrem firms (i.e., the corresponding input price is less thn ) or only for the technologiclly ( λ efficient downstrem firm (i.e., the corresponding input price is higher thn ) ( λ is lso decision of the upstrem monopolist. As we will show in the following nlysis, if the vlue of λ is less thn, it is better for the upstrem monopolist to produce for both downstrem firms. We ssume tht λ [1, ), since, otherwise, entry does not hve ny rel impct in our nlysis. f the upstrem monopolist supplies to both downstrem firms, i.e., fces the demnd for input s in (6), the upstrem monopolist mximizes the following expression: ( (1 + λ) q ) q Mx. (8) q ( + λ λ) 5

10 Mximizing (8), we find tht the optiml input supply nd the corresponding input ( 1+ λ) (1 + λ) prices re nd respectively. t is esy to verify tht 6 (4 + 4λ 4λ) (1 + λ) (4 + 4λ 4λ) is less thn ( λ for λ [1, ). The totl output of the downstrem incumbent nd entrnt together is (7 + 7λ 10λ). The profits of the upstrem monopolist, downstrem incumbent 1(1 + λ λ) nd downstrem entrnt re respectively (1 + λ) 4(1 + λ λ) ( + 5λ 5λ) 9(4 + 4λ 4λ), nd (5 + λ 5λ) 9(4 + 4λ 4λ). Therefore, in cse of entry in the downstrem mrket only, welfre of the economy is W e = (5 + λ 5λ) + ( + 5λ 5λ) 9(4 + 4λ 4λ) (1 + λ) (7 + 7λ 10λ) + + 4(1 + λ λ) 88(1 + λ λ). Hence, we hve the following proposition. (9) Proposition 1: Welfre is higher under entry compred to no-entry for ny λ [1, ). Proof: We subtrct (4) from (9) nd plot this difference in Figure 1. Figure 1 The inspection of Figure 1 proves the result. Q.E.D. f there is entry in the downstrem mrket, it hs three effects on socil welfre. Firstly, entry increses competition. Given the price of the input, higher competition in the downstrem mrket tends to increse socil welfre. Secondly, entry shifts production from the incumbent to the entrnt. Given the price of the input, entry of firm in the downstrem mrket reduces the mrket shre of the incumbent nd reduces its profit. f the entrnt is inferior compred to the incumbent, entry cretes production inefficiency by shifting production from the technologiclly efficient incumbent to the technologiclly inefficient entrnt. Hence, this hs We used The Mthemtic 4. for Figure 1. 6

11 negtive impct on socil welfre. These two effects re similr to the effects demonstrted by the previous works of the literture. However, entry in the verticlly seprted mrket cretes nother effect on socil welfre by ffecting the demnd function for the input. Entry in the downstrem industry chnges the demnd for input nd reduces the price of the input. n cse of no entry, price of the input is, while under entry it is (1 + λ). This lower input price reduces the mrginl cost of (4 + 4λ 4λ) the downstrem mrket nd cretes positive impct on socil welfre. The effect of chnging demnd function for input long with higher competition outweighs the negtive effect of production inefficiency creted by entry. As result, entry lwys increses socil welfre. n our nlysis we restrict λ to be greter thn or equl to 1. f λ < 1, it implies tht the entrnt is technologiclly superior compred to the incumbent. n this sitution, entry cretes production efficiency by shifting output from the incumbent to the entrnt. So, when λ < 1, ll the bove-mentioned effects of entry hve positive impct on socil welfre nd therefore, entry lwys increses welfre. So fr we hve ssumed tht, in cse of entry, the upstrem monopolist produces for both downstrem firms when λ [1, ). Now, we exmine the vlidity of this ssumption. n cse of entry, if the upstrem monopolist produced for the technologiclly efficient downstrem firm only (i.e., effectively the downstrem mrket becomes monopoly) then the upstrem firm fces the input demnd function given in (7). n this sitution, the optiml input supply is 4 nd the corresponding price of the input is. However, stisfies the restriction given in (7), i.e., greter thn or equl to, provided ( λ λ. So, while producing for the technologiclly efficient downstrem firm only, optiml input supply is for λ [,). But, is less thn 4 ( λ for λ [1, ]. Hence, if the upstrem firm produces mount of inputs 4 7

12 when λ [1, ], it encourges both downstrem firms to buy the inputs. So, to prevent the technologiclly inefficient downstrem firm from buying the inputs, totl input ( λ supply cnnot exceed when λ [1, ], nd, lso, it will not be less thn (λ ( λ ( λ since, is less thn for λ [1, ]. Therefore, the optiml input (λ (λ 4 ( λ supply of the upstrem firm is for λ [1, ], nd for λ [,). (λ 4 So, if producing for the technologiclly efficient downstrem firm only, the ( λ optiml profits of the upstrem monopolist re (λ for λ [1, ], nd 8 for λ [,). But, s mentioned in the bove nlysis, if, in cse of entry, the upstrem firm produces for both downstrem firms, the optiml input price is (1 + λ) (4 + 4λ 4λ) nd the optiml profit of the upstrem monopolist is (1 + λ). Compring the 6(4 + 4λ 4λ) profit levels we find tht (1 + λ) 6(4 + 4λ 4λ) ( λ is greter thn (λ nd (1 + λ) 6(4 + 4λ 4λ) is greter thn 8 for λ <. Hence, it is optiml for the upstrem monopolist to produce for both downstrem firms when λ [1, ). Possibility of entry in the upstrem mrket only n this section, we will consider entry in the upstrem mrket only. Agin we will consider two situtions. One, when there is n upstrem monopolist nd downstrem monopolist, nd the other, when there is downstrem monopolist with the upstrem mrket s duopoly. We ssume tht the upstrem incumbent hs constnt mrginl cost of production, which is for simplicity, ssumed to be zero, nd the upstrem entrnt hs constnt mrginl cost of production c. n cse of entry in the upstrem mrket, the upstrem firms compete like Cournot duopolists with homogeneous input. 8

13 .1 No-entry in the upstrem mrket n presence of n upstrem monopolist nd downstrem monopolist with no-entry in the upstrem mrket, our nlysis becomes similr to tht nlyzed in subsection.1. Hence, the welfre of the economy is given by the expression (4).. Entry in the upstrem mrket Now, consider sitution where the downstrem mrket is monopoly with two upstrem firms. The input demnd function is given by the expression or, w = ( q q ( w) =, ). So, the upstrem incumbent nd the entrnt mximize the following expressions respectively Mx q ( q q i i i q e ) (10) nd where e i e Mx q ( q q c), (11) i q q e e nd q re the outputs of the incumbent nd the entrnt respectively. We find tht the optiml input supply of the upstrem incumbent nd the entrnt re ( + c) ( c) nd 6 6 produces positive output provided consider the vlue of c [0, ). ( + c) respectively. t is importnt to note tht the upstrem entrnt c <. To mke entry meningful, we will Totl input supply nd the corresponding price of the input re ( c) 6 respectively. The profit of the downstrem monopolist, the upstrem nd incumbent nd the entrnt re respectively ( c) 6, ( + c) 18 nd ( c) 18 Therefore, in cse of entry in the upstrem mrket only, welfre is. W e ( c) ( + c) + ( c) ( c) = + +. (1)

14 Proposition : Welfre under entry is higher compred to no-entry provided c is less * thn c, where c (0, ). * Proof: The relevnt expressions for welfre re (4) nd (1). The expression (1) is convex with respect to c over [ 0, ] nd reches minimum vlue t Expression (1) is greter thn nd equl to (4) t c = 0 nd Further, (1) is less thn (4) t 10 c =. c = respectively. 10 c =. This implies tht (1) is greter thn (4) * * provided c is less thn the criticl vlue, sy c, where c (0, ). Hence, it proves the result. Q.E.D. n cse of entry in the upstrem mrket only, the demnd function for input remins sme under entry nd no-entry in the upstrem mrket. While entry increses competition in the upstrem mrket, it lso cretes production inefficiency becuse of shift in production from the technologiclly efficient incumbent to the technologiclly inefficient entrnt. f the technologicl difference between the incumbent nd the entrnt is not very much, production inefficiency due to entry of technologiclly inferior firm is sufficiently smll. So, in this sitution, the former effect domintes the ltter nd for sufficiently low technologicl differences between these firms, entry increses welfre. On the other hnd, if the technologicl difference between the incumbent nd the entrnt is sufficiently lrge, the benefit from competition is sufficiently smll. But, sufficiently high cost of production of the entrnt cretes significnt mount of production inefficiency. Hence, for lrge technologicl differences between these firms, the ltter effect domintes the former nd entry reduces welfre. So, entry in the upstrem mrket only cretes similr effects of Klemperer (1988) nd Lhiri nd Ono (1988) even under verticlly seprted industry. 10

15 4 Possibility of entry in both upstrem nd downstrem mrkets The purpose of this section is to show tht the Proposition my be different when there is entry in both mrkets. n prticulr, we show tht entry my increse welfre for ll possible technologicl differences between the incumbent nd the entrnt in the upstrem mrket. 4.1 No-entry scenrio Like the previous sections ssume tht, in cse of no-entry, both upstrem nd downstrem mrkets re monopoly. So, in cse of no-entry, welfre is given by the expression (4). 4. Entry in both upstrem nd downstrem mrkets Now let us consider entry of new firm in both mrkets. For simplicity, we will ssume tht the downstrem incumbent nd entrnt hve similr technology, i.e., λ = 1. However, we ssume tht the mrginl cost of production of the upstrem incumbent nd the entrnt is 0 nd competition previls in both mrkets. c respectively. n cse of entry, Cournot Since, the downstrem firms re symmetric, the upstrem firms will produce for both the downstrem firms. The upstrem firms fce the following input demnd function: q * * ( w) = qi + qe =. (1) ( + c) The optiml input supply by the upstrem incumbent nd the entrnt re nd 9 ( c) 9 prices re respectively. Therefore, totl input supply nd the corresponding input ( 4 c) 9 nd ( + c) upstrem firms produce positive output for respectively. t is importnt to note tht both c <, which is ssumed to hold. 11

16 The optiml profit of the upstrem incumbent, upstrem entrnt, downstrem incumbent nd downstrem entrnt re respectively ( + c) 7, ( c) 7, ( c) 81 nd ( c) 81. So, welfre of the economy is given by W e e 4( c) + 6( + c) + 6( c) =. (14) 81 Proposition : Consider entry in both upstrem nd downstrem mrkets, where the upstrem entrnt s technology is inferior to the upstrem incumbent s technology but the technology of the downstrem incumbent nd the entrnt is similr. Here, entry lwys increses welfre. Proof: Compring (4) with (14) nd fter rerrnging, we find tht (14) is greter thn (4) provided 9 896c c > 0. (15) Left hnd side (LHS) of (15) is continuous nd convex in minimum vlue t 7 c =. Further, LHS of (15) is positive t 17 c over [ 0, ] nd ttins 7 c =. This implies 17 tht LHS of (15) is positive for ll c [0, ]. This proves the result. Q.E.D. Entry in the downstrem mrket chnges the demnd function for input. So, in cse of entry in both mrkets, the effects due to chnge in the demnd function for input is in force long with higher competition nd production inefficiency. We find tht the positive effects due to chnge in the demnd function for input long with higher competition outweighs the negtive impct of production inefficiency nd entry cretes higher welfre. n Proposition, we hve considered no technologicl difference between the downstrem firms. t is esy to check tht welfre is continuous with respect to the technologicl differences between the downstrem incumbent nd the entrnt. This immeditely implies tht, like Proposition, entry lwys increses welfre even for some degree of technologicl differences between the downstrem firms. 1

17 The bove results suggests tht, from the point of view of the policy mkers, it is importnt to consider the industril structure long with the technologicl differences of the firms while encourging entry in n industry. n presence of mrket power of the input suppliers, while government policies might be designed to encourge entry in the finl goods mrket, policies might need to restrict entry in the input mrket. Hence, our findings re importnt for the competition policies. 5 Conclusion Contrry to the common wisdom, previous reserch hve shown tht entry my reduce welfre of n economy. While, some reserchers hve rgued tht the existence of fixed cost cn reduce welfre due to entry, others hve showed tht difference in mrginl cost (or, technologies) is the reson for lower welfre under entry. However, the previous literture hve ignored the role of industril structure nd re relevnt for the industries where either the input mrkets re perfectly competitive or the firms re verticlly integrted. Like the finl goods mrket, often the input mrkets re imperfectly competitive where the input suppliers hve significnt power. So, in cse of verticlly seprted industry, entry s well s the mrket where entry occurs is n importnt concern. We find tht entry in the downstrem mrket only lwys increses welfre. n cse of entry in the upstrem mrket only, welfre increses provided the technology of the upstrem entrnt is not sufficiently inferior compred to the technology of the upstrem incumbent. However, welfre my lwys be higher for entry in both mrkets. 1

18 References Choi, S. C., 1991, Price competition in chnnel structure with common retiler, Mrketing Science, 10: Economides, N., 1998, The incentive for non-price discrimintion by n input monopolist, nterntionl Journl of ndustril Orgniztion, 16: Gerstner, E. nd H. Hess, 1995, Pull promotions nd chnnel coordintion, Mrketing Science, 14: Hrt, O. nd J. Tirole, 1990, Verticl integrtion nd mrket foreclosure, Brookings Ppers on Economic Activity, nd Klemperer, P., 1988, Welfre effects of entry into mrkets with switching costs, The Journl of ndustril Economics, XXXV: Lhiri, S. nd Y. Ono, 1988, Helping minor firms reduces welfre, Economic Journl, 98: Mnkiw, A. G. nd M. D. Wihinston, 1986, Free entry nd socil inefficiency, Rnd Journl of Economics, 17: Ro, R. nd S. Srinivsn, 001, An nlysis of dvertising roylty in frnchise contrcts, Journl of Mrketing Chnnels, 8: Schmlensee, R., 1976, s more competition necessrily good, ndustril Orgnistion Review, 4: Spence, M., 1984, Cost reduction, competition, nd industry performnce, Econometric, 5: Stiglitz, J. E., 1981, Potentil competition my reduce welfre, The Americn Review, 71: Suzumur, K. nd K. Kiyono, 1987, Entry brriers nd economic welfre, The Review of Economic Studies, 54: Tndon, P., 1984, nnovtion, mrket structure, nd welfre, The Americn Economic Review, 74: Tygi, R. K., 1999, On the effects of downstrem entry, Mngement Science, 45: Vills-Bos, J. M., 1998, Product line design for distribution chnnel, Mrketing Science, 17:

19 von Weizsäcker, C. C., 1980, A welfre nlysis of brriers to entry, Bell Journl of Economics, 11: von Weizsäcker, C. C., 1980b, Brriers to entry: theoreticl tretment, Berlin, Springer Verlg. 15

20 λ Figure 1: Subtrcting (4) from (9). 16