The Effect of Market Structure and Conduct on the Incentive for a Horizontal Merger

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1 Volue 5, Nuber, June 000 The Effect of Market Structure and Conduct on the Incentve for a Horzontal Merger Hyukseung Shn In ths paper, we exane how arket structure and frs conduct affect the prvate ncentve and welfare effect of a erger. The an result of ths paper s as follows. Frst, as arket becoes ore concentrated, the ncrease n the jont proft of ergng frs becoes lower for the case of the sae cost savngs by a erger. Ths ples that as arket concentraton ncreases, t s necessary for a erger to attan larger cost reducton n order to be proftable. Second, the ncrease n welfare by a erger rses (or, the decrease n welfare by a erger falls) as the arket structure goes toward copetton. Thrd, As the colluson level aong frs becoes hgher, the ncrease n the jont proft of ergng frs goes down. Fourth, As the colluson aong frs decreases, the requred level of cost savngs for a erger to rase welfare also goes down. Ffth, a erger can nduce a stable cartel whch was not fored before erger. I. Introducton There has been a lot of research on the prvate ncentve and welfare effect of a horzontal erger. For the prvate proftablty of a horzontal erger, the copetton type (that s, Cournot vs. Bertrand copetto becoes very portant. Salant et al. (983) showed that a horzontal erger can be unproftable by usng Cournot odel. The an reason for ths result s due to the response of outsders. Mergng frs usually reduce jont output n order to exercse arket power. In reacton to ths event, non-ergng frs rase output accordng to ther reacton functons, whch has a negatve nfluence on ergng frs snce output s a strategc substtute. Contrary to ths result, Deneckere and Davdson (985) showed that a erger of any sze s prvately proftable by usng Bertrand odel. They argued that a erged fr rases ts prce to rase arket power. In response to ths, outsders ncrease ther prce, whch has a postve effect on the proft of a erged fr snce prce s a strategc copleent. Usually a horzontal erger of two frs have xed effects on welfare because t affects arket structure and effcency of frs. The negatve sde of a erger s that t rases arket power due to the concentraton of a arket and postve sde of a erger s that t ay enhance effcency by synergy effect. Wllason (968) developed a ethod by whch we can evaluate the welfare effect of a erger. He argued that a erger can enhance effcency through soe sort of synergy effect. If ths effcency effect s large enough to Departent of Econocs, Sookyung Woen s Unversty.. Bulow et al. (985) ntroduced the concept of strategc substtutes and copleents.

2 outwegh arket power effect, then a erger can rase socal welfare. Farrell and Shapro (990) derved the condton under whch a prvately proftable erger s also socally desrable. In ths paper, we are concerned wth the queston how the prvate ncentve and welfare effect of a erger are affected by the change n arket structure. Suppose all the ergers can attan the sae level of cost reducton, then as arket structure becoes ore concentrated, s t ore lkely (or unlkely) that a erger s prvately proftable (or socally desrable)? If we can answer for ths knd of queston, then we can dentfy the relaton between arket structure and ncentve for a erger. Here, we also exane the relaton between the degree of copettveness (or collusveness) and the erger ncentve. By ths analyss, we can see how frs conduct n ters of colluson can nfluence the erger ncentve. Fnally, we see the case where a erger generates a stable cartel. If a cartel s nduced by a erger, negatve welfare effect of a erger becoes donant and so governent had better adopt a strct erger allowance polcy. The structure of ths paper s as follows. In Secton II, we look at the change n the proftablty and socal desrablty of a erger accordng to the change n arket structure usng Cournot odel. In Secton III, we ntroduce the conjectural varaton ters n the odel n order to exane the effect of colluson level on the erger ncentve. By ths way, we nvestgate how erger ncentve s nfluenced by frs conduct such as degree of colluson. In Secton IV, we show the case where a erger can occur even wthout cost savngs n a Cournot odel. That s, we derve the condton under whch a erger can trgger the foraton of a cartel n a repeated gae context. In Secton V, we suarze an results of the paper and pont out soe ltatons of ths paper. II. Market Structure and Merger Incentve We assue that there are n dentcal frs n the arket. Each fr has a constant returns to scale technology and has a argnal cost (MC) of c at frst. The nverse arket deand s lnear; P a bq, where P s the arket prce and Q s the total arket output. All the frs n arket are nvolved n Cournot copetton. We assue that the MC of a erged fr goes down fro c to c. (where, c < c, d c c ) Here we would lke to look at the change n prvate proftablty and socal desrablty of a erger accordng to the change n arket structure. In order to see ths, we are gong to derve the change n the jont proft of ergng frs and socal welfare by a erger.. Pre-erger case Before a erger, each fr has the sae MC of c. We can easly derve each fr s Cournot equlbru output and proft as follows.. Salant et al. (983) showed that a erger lowers jont proft of ergng frs for the case of lnear deand and constant MC usng Cournot odel. So n order for a proftable erger to happen, t s necessary to assue MC reducton by a erger.

3 SHIN: THE EFFECT OF MARKET STRUCTURE AND CONDUCT ON THE INCENTIVE q α/ b( n + ), Π α / b( n + ) (where, α a c,,,..., n ) (). Post-erger case We consder the case where (n-) th fr and (n-) th fr erge nto (n-) th fr. After a erger, a erged fr s MC becoes c, whle the reanng (n-) frs have MC s of c. Then probles of a non-ergng fr and a erged fr are as follows. ax ( a bq c) q, (where,,..., n ) () q ax ( a bq c) qn. q n Now by solvng (n-) frst order condtons (FOC s) sultaneously, we get the post-erger Cournot equlbru output and proft of each fr as follows. q α d (,,..., n ), qn bn α + ( n ) d bn (3) Π n [ α+ ( n ) d] bn, Π ( α d) bn, (,,..., n ). By usng the pre -erger proft and post-erger proft n () and (3), we can get the change n the jont proft of ergng frs by a erger. Π Π ( Π + Π ) (4) n n n n {[ α+ ( n ) d] ( n + ) α n } bn ( n + ) {( n ) d + ( n + ) ( n ) α d + ( n + n + ) α } bn ( n + ) Now we are n a poston to analyze the effect of change n arket structure on the change n the jont proft of ergng frs by the followng proposton. Proposton : Gven the sae level of cost savngs by a erger, f a erger s prvately proftable when there are n frs n the arket, then t s also prvately proftable when there are n frs n the arket. (where, n < n, n 4) 3

4 Pf) The change n the jont proft of ergng frs when the aount of cost savngs s d s n Equaton (4), whch s Π {( n ) d + ( n + ) ( n ) d + ( n + n + ) } f ( n bn ( n + ) α α b Now we want to show f '( > 0. Let K n ( n + ). Then K ) f '( [4n( n ) d + (3n )( n + ) α d + ( n + ) α ] n ( n + [( n ) d + ( n + ) ( n ) α d + ( n + n + ) α ]n(n + )( n + ) Fro ths equaton, we get f '( as below. f ' ( n( n + ) g( K 3 (where, g( d ( n )( n + ) + α d ( n + ) [ n(7n 3) ] + α [ n( n 3n 3) ] ) So the sgn of f '( s the sae as that of g (. For n 4, g ( > 0 holds. Therefore f '( > 0 holds. Q.E.D. Accordng to the above proposton, wth the sae level of cost savngs, the proft ncrease by a erger becoes lessened as the nuber of frs decreases. That s, as a arket becoes ore concentrated, t s ore dffcult for a erger to be prvately proftable. We can nterpret ths result as follows. As a arket becoes ore concentrated, pre-erger proft of each fr ncreases due to the reducton n copetton. So large cost savngs s necessary n order for a erger to rase jont proft of ergng frs n ths case. In ths respect, t s ore dffcult for a erger to occur as arket concentraton goes up. Ths knd of phenoena has a desrable aspect fro the vew-ponts of socal welfare. In general, the ncrease n arket concentraton gves a negatve pact on welfare. But, n a concentrated arket, a erger can occur only when effcency gan s hgh enough, whch rases the possblty that a erger can have a postve welfare effect. Next, we would lke to see how the arket structure affects the welfare effect of a erger. In order to exane ths, we need to know the change n socal welfare by a erger. We provde the dervaton of ths change n the appendx. Proposton : Gven the sae level of cost savngs by a erger, f a erger s socally desrable when there are n frs n the arket, then t s also socally desrable when there are n frs n the arket. (where, n < n, n 3) 4

5 SHIN: THE EFFECT OF MARKET STRUCTURE AND CONDUCT ON THE INCENTIVE Pf) Fro the appendx, the change n socal welfare by a erger s SW 3 [( n + ) (n n ) d + α d( n + 3n n ) (n + ) α ] bn ( n + ) b f ( Now, we would lke to show f '( > 0. Let K n ( n + ). Then K ) f '( [( n + )(4n n ) d + α d(3n + 6n ) α ] n ( n + 3 [( n + ) (n n ) d + α d( n + 3n n ) (n + ) α ]n(n + )( n + ) n ( n + ) g( 3 (where, g( d ( n + ) (8n 3n 6n ) + α d[ n( n + )(3n + 6n ) + (n + )( n 3 + 3n n )] + α [3n + 3n ] ) Fro the above relaton, we get f '( as below. f ' ( n( n + ) g( K So the sgn of f '( s the sae as that of g (. Now, let 3 h ( 8n 3n 6n. Then h ( s an ncreasng functon of n snce h ' ( 6n(4n ) 6 > 0 (where, n 3). Therefore, h ( h(3) 9 > 0. Next, let 3 k ( n + 3n n. Then, k ( s an ncreasng functon of n snce k '( 3n( n + ) > 0 (where, n 3). Therefore, k ( k(3) 50 > 0. Fro the above result, t s true that g ( > 0 (where, n 3). So f '( > 0 holds. Q.E.D. 5

6 The above proposton explans the relaton between the change n arket structure and the welfare effect of a erger. Suppose that the level of cost reducton by a erger s the sae rrespectve of a arket structure. Then, as the nuber of frs ncreases, the welfare ncrease by a erger becoes larger (or the welfare decrease becoes saller). Therefore, t s possble that a erger lowers welfare for a concentrated arket but t rases welfare for a ore copettve arket. So even f the effcency enhanceent effect by a erger s the sae, t s necessary to adopt dfferent polcy drecton for a erger dependng on the arket structure. Naely, as the arket becoes ore copettve, the governent polcy toward a erger needs to be generous. III. Degree of Copettveness and Merger Incentve Untl now we assued that each fr n an ndustry conjectures that the output of the other frs does not change wth the change of ts own output;.e., σ dq / dq 0 (where, Q n q j j ) was assued. Now we ntroduce the non-zero conjectural varaton ters n the odel to exane how the dfferent degree of copettveness changes the welfare plcaton of a erger. We assue that σ does not change before and after a erger. 3 In ths secton, we are gong to analyze how the change n copettveness n ters of conduct affects the prvate ncentve for a erger. In the appendx, we derve the change n the jont proft of ergng frs wth non-zero conjectural varaton ters. And by usng ths result, we get the followng proposton that represents the relaton between the degree of colluson and the ncentve for a erger. Proposton 3: Gven the sae level of cost savngs by a erger, the ncrease n the jont proft of ergng frs becoes lessened (or the decrease n the jont proft becoes enlarged) as the degree of colluson goes up n the arket. Pf) Fro the appendx, we have the change n the jont proft of ergng frs when the conjectural varaton s σ as follows. ( σ ) [(( n + ) d + ( + ( n + σ + ) ( n + σ ) αd Z n We want to show f '( < 0 + (( n + + ( n + )(+ α ] f ( σ ) 3. Here, the range of σ that we consder s fro 0 to (n-) because we are nterested n the case where the degree of colluson s between Cournot behavor and perfect colluson. Also, the upper bound of σ s (n-) because the nuber of the rval frs for each fr becoes (n-) after a erger. 6

7 SHIN: THE EFFECT OF MARKET STRUCTURE AND CONDUCT ON THE INCENTIVE Now, Z f ' ( σ ) ( n + ( n + + [ Ad + Bαd + Cα ( + ) ] σ (where, A ( + )[4t ( )( + (4t + ) + t)] 3 B ( + ) t ( ), C ( + )(+ )( t) + t( ) and where, n + σ, t + σ, 0 σ n ) Now t s suffcent to show A < 0, B < 0 and C < 0. step ) Fro A, let g ( ) 4t ( )( + (4t + ) + t) 3 By splfcaton, we get g ( ) + (4t + ) + t. Then, g () s a decreasng functon of snce g' ( ) (4t + ) 3( n + σ ) 4n + 5 < 0, (where, n 3, σ 0) Snce 3, g () attans the axu when 3 (whch s the case where n 3 and σ 0). So, g ( ) g(3) 4t 4 4( < 0, snce σ 0 for 3. Therefore, A ( + ) g( ) < 0. step ) Fro B, ( ) s negatve snce 3. Therefore, 3 B ( + ) t ( ) < 0. step 3) Now, fro C ( + )( + )( t) + t( ), ( + ) ( ) + < 0, snce 3. t ( n + (+ n σ 0, snce 0 σ n. Therefore, C < 0 holds. Q.E.D. The above result represents the relaton between the degree of copettveness (or colluso n conduct and prvate proftablty of a erger. Suppose that the aount of cost savngs are the sae rrespectve of the copettveness n a arket, then as the ntensty of cooperaton aong frs becoes stronger, the prvate gan by a erger becoes lower. Usually, the gan by a erger coes fro the ncrease n arket power due to the reducton n copetton. When the cooperaton aong frs becoes prevalent n a arket, each fr already has a sgnfcant arket power. In ths stuaton, the addtonal gan by a erger becoes lower. Ths knd of relaton has a desrable welfare plcaton n the followng respect. That s, fro the socal welfare vew-ponts, t becoes ore dffcult to go to the worse state (the state where arket becoes ore concentrated by a erger) fro the bad state (the state where degree of colluson aong frs s large). Next, we would lke to look at the relaton between the degree of colluson and the 7

8 welfare change of a erger. Snce the dfferentaton of the welfare change on the nuber of frs becoes so coplex, we could not get the defnte sgn. Instead of ths, we are gong to derve the nu level of cost savngs that guarantees the ncrease n welfare by a erger. And by sulaton, we wll get the relaton between the degree of colluson and the requred cost savngs, whch gves us ndrect nforaton about the relaton between the copettveness n conduct and welfare change by a erger. We obtan the followng result by sulaton. (Refer to the Table n appendx.) Sulaton Result : As the degree of colluson goes up, the requred level of cost savngs to rase socal welfare rses. We can explan above result as follows. Usually a erger provdes a negatve effect on consuer surplus and postve effect on producer surplus. The postve effect of a erger on producer surplus s dnshed as σ goes up, because for the hgh value of σ, each fr already got hgh pre-erger proft by cooperaton. Therefore we need ore cost savngs to rase postve effect and to lower negatve effect to get a socally desrable erger as σ goes up. One plcaton of ths result s that even for the case of the sae arket structure, the polcy toward a erger needs to reflect the degree of colluson n the arket. IV. Relaton between a Merger and Cartel Stablty Untl now, we deal wth the case where cost reducton s necessary for a erger to be proftable. But f a erger nduces the ndustry-wde cartel whch was not fored before a erger, then a erger can be proftable even wthout cost savngs. The reason why ths s possble coes fro the fact that a erger changes the arket structure, whch n turn affects the condton for the stable cartel n a repeated gae context. In the appendx, we derve the condton for the stable cartel n an nfntely repeated gae. Proposton 4: As the nuber of frs decreases, the crtcal level of dscount factor above whch cartel s stable also decreases. Pf) Fro the appendx, the crtcal dscount factor above whch cartel s stable when there are n frs s as follows. ( n + ) δ c ( f (. It s suffcent to show f '( > 0. Then ( n + 6n + ) f ' ( [(n + )( n + 6n + ) ( n + n + )(n + 6)] (where, K n + 6n + ) K 4 ( n + )( n ) > 0 K snce n 3. Q.E.D. 8

9 SHIN: THE EFFECT OF MARKET STRUCTURE AND CONDUCT ON THE INCENTIVE Accordng to the above result, as arket becoes ore concentrated, t s ore lkely that a stable cartel s fored. In soe case, t s possble that ndustry-wde cartel s unstable for the copettve arket, but t becoes stable for the concentrated arket. In ths sense, a erger can generate a stable cartel whch was not fored before a erger because arket concentraton ncreases due to a erger. Therefore, we need to consder the possblty of cartel foraton due to a erger as well as arket power and effcency effect. Thus f the dscount factor s n the range where a stable cartel s fored by a erger, t s necessary to adopt a strct erger allowance polcy. V. Concluson Untl now, we have exaned the followng ssues; () the relaton between a arket structure and the erger ncentve, () the relaton between a degree of copettveness (or collusveness) n ters of conduct and the erger ncentve, (3) the relaton between a erger and ndustry-wde cartel foraton. We can have soe plcaton for the governent polcy toward a horzontal erger by ths knd of analyss. The an result of ths paper can be suarzed as follows. Frst, for the case where the cost reducton by any erger s the sae, the ncrease n jont proft of ergng frs becoes lower as arket becoes ore concentrated. Thus, as arket concentraton ncreases, t s necessary for a erger to attan larger cost reducton n order to be prvately proftable. Ths s soewhat good news to the econoy snce t s ore dffcult for a erger to occur as arket structure goes away fro the perfect copetton. Second, for the sae cost savngs by a erger, the ncrease n socal welfare by a erger rses (or the decrease n socal welfare falls) as the arket structure goes toward copetton. That s, as arket becoes copettve, t s ore lkely that a erger has a postve effect on welfare. Thrd, the effect of a erger on the jont proft also depends on the degree of copetton (or colluso aong frs. As the colluson level becoes hgher aong frs, the proftablty of a erger goes down. So t becoes ore dffcult for a erger to coe out n ths case, whch reduces the negatve effect of a erger. Fourth, As the colluson aong frs goes down, the requred level of cost savngs for a erger to rase welfare also goes down. So the polcy toward a erger needs to consder the degree of colluson n ters of frs conduct. Ffth, a erger can nduce a ndustry-wde cartel whch was not fored before a erger. In ths case, a erger s always prvately proftable even f there s no cost savngs by a erger, whch has a negatve effect on welfare. One plcaton of ths paper s that the polcy toward a erger had better take nto account the arket structure, the type of frs conduct and the possblty of cartel foraton. So even f a erger acheves the sae effcency enhanceent, the governent needs to take dfferent polces dependng on the state of arket structure and fr s conduct. Fnally, ltatons of ths paper and further research drectons can be stated as follows. Frst, we use Cournot odel to analyze the erger effect. It would be better to check the robustness (or senstvty) of ths result by usng another odel lke Bertrand copetton. Second, here lnear deand and constant returns to scale technology are assued. So we need to see how the result changes as the deand and cost functons are generalzed. Thrd, here we deal wth the case of syetrc frs. Usually frs n a real 9

10 arket are n asyetrc postons. If we can encopass the case of asyetrc frs, then the applcaton of the result can be enlarged. 0

11 SHIN: THE EFFECT OF MARKET STRUCTURE AND CONDUCT ON THE INCENTIVE Appendx. The dervaton of the change n socal welfare by a erger [] Pre-erger case Before a erger, we can derve the producer surplus by sung up the pre-erger proft of each fr as below. n PS Π nα b( n + ) Also, the consuer surplus s gven below. b n α CS Q b( n + ) [] Post-erger case By usng Equaton (3) n Secton II, we get the post-erger producer surplus as below. PS n Π + Π n ( n n ) d + ad + ( n ) α bn Also, we can get the post-erger total ndustry output as follows. Q n q + q n ( n + ) α + d bn So, we get the post-erger consuer surplus. CS b [( n ) α+ ( Q ) bn d] [3] socal welfare change by a erger Now we get the welfare change by a erger by usng the results of [] and [] as follows. SW ( PS + CS ) ( PS + CS) 3 [( n + ) (n n ) d + α d( n + 3n n ) (n + ) α ] bn ( n + )

12 . The dervaton of the change n the jont proft of ergng frs and socal welfare when there s a conjectural varaton paraeter. [] pre-erger case The frst order condton for each fr s axzaton proble s as follows. dq b( + σ ) q + ( a bq c) 0, (where, σ Q n q ) dq j (,,..., j Fro ths condton, we get equlbru output and proft as follows. q α ( + α, Π b( n + + ( ), b n + + σ nα Q b( n + + So we get pre-erger producer surplus and consuer surplus as below. n PS Π n( + α b( n + + b n α CS Q b( n + + [] post-erger case After (n-) th and n th fr erger nto a (n-) th fr, the proble of a non-ergng fr and a erged fr s the sae as the one gven n Equaton () n Secton II. The frst order condton for ths probles s gven as below. b( + σ ) q + ( a bq c) 0, (,,..., n ) b( + σ ) q + ( a bq c) 0 n Now usng the (n-) equatons, we get the post-erger output and proft as follows. (+ α d b( + ( n + q (,,..., n ), q n ( + α+ ( n + σ ) d b(+ ( n + Q ( n ) α+ d b( n + ) n q + qn σ

13 SHIN: THE EFFECT OF MARKET STRUCTURE AND CONDUCT ON THE INCENTIVE Π [(+ α d] (,,..., n ) b( + ( n + [(+ α+ ( n + σ ) d], Π n b (+ ( n + Now usng the equlbru proft and output, we get the post-erger producer surplus and consuer surplus. n PS Π + Π n [( n )(( + σ ) α d) + ((+ α+ ( n + σ ) d)]. K (where, K b( +σ )( n + ) CS b [( n ) α+ d] ( Q ) b( n + [3] Change n the jont proft of ergng frs and socal welfare Now the change n the jont proft of ergng frs s gven below. Π Π ( Π + Π n n n n ) {(( n + σ ) ) d + ( + ( n + σ + ) ( n + σ ) αd Z + (( n + + σ ) ( n + )(+ α } (where, Z b( + σ )( n + ( n + + ) Also, the change n the producer surplus ( PS PS PS ) s gven below. PS {(( n + σ ) Z + ( n ))( n + σ ) d + (+ ( n + σ + ) αd + (( n )( n + + σ ) n( n + ) α ( + σ ) } Next, the change n consuer surplus ( CS CS {( CS θ n + + d + ( n )( n + + αd CS ) s gven below. 3

14 + (( n + + σ ) ( n ) n ( n + ) α } (where, θ b ( n + ( n + + ) Now we get the change n socal welfare ( SW PS + CS ) as follows. SW {( n Z + (4σ ) n + (σ 3σ ))( n + + d + α( + ( n + σ + ) ( n + σ + ) d + (( n + σ + )( n )( n + + n( n + σ + )( n + )(+ α } Let λ be the nu d that satsfes SW 0. Then, the value of λ s α{ (+ ( n + σ + )( n + σ + ) + (+ ( n + σ + ) ( n + σ + ) E } λ ( n + σ + ){( n + σ ) + ( n ) + (+ } where, E ( + {( n + σ ) + ( n ) + (+ }{( n + σ + )( n )( n + σ + ) n( n + σ + )( n + }. 4

15 SHIN: THE EFFECT OF MARKET STRUCTURE AND CONDUCT ON THE INCENTIVE 3. Sulaton result Now we use the sulaton ethod n order to see the relaton between σ and λ whch s derved n (Secton II) n ths appendx. The sulaton result s suarzed n the followng table. Table N σ λ N σ λ N s the nuber of frs n the ndustry. σ s the conjectural varaton paraeter. λ s the requred cost savngs for a socally benefcal erger. α s set to. 5

16 4. The dervaton of a crtcal dscount factor for the stable cartel n a repeated gae. We consder the followng strategy of each fr n a repeated gae; () At perod t, each fr produces cartel output f no one has devated fro t before perod t. () At perod t, f soe fr has devated fro the cartel output before, then each fr produces Cournot-Nash equlbru output forever. Fro ths strategy, we are gong to derve the condton for the stablty of cartel. Frst, the total cartel output level s equal to onopoly output level. Snce there are n dentcal frs ntally, each fr produces / n of total cartel output and get / n of the total proft; q c c α/ bn, Π α / 4 bn. Now let s look at the gan that a fr can get by devatng fro a cartel output. Gven that other frs stck to the cartel output level, a defectng fr would produce q d d α n / 4b( n ) and get Π α n / 6 b( n ). The one perod d c gan by cheatng s Π Π α ( n ) /6b( n ) (A). The present dscount value of the future loss by defectng, when a dscount factor s δ, s δα ( n ) / 4( δ) b( n ) n (B). A cartel s stable f the loss (B) s greater than the gan (A). Therefore, the range of δ n whch a cartel s stable s δ > ( n + ) /( n + 6n + ) δ ( n ). c 6

17 SHIN: THE EFFECT OF MARKET STRUCTURE AND CONDUCT ON THE INCENTIVE References Bulow, J., J. Geanakoplos, and P. Kleperer (985), Multarket Olgopoly: Strategc Substtutes and Copleents, Journal of Poltcal Econoy, 93, Deneckere, R., and C. Davdson (985), Incentve to For Coaltons wth Bertrand Copetton, Rand Journal of Econocs, Wnter, 6, Farrell, J., and C. Shapro (990), Horzontal Mergers: An Equlbru Analyss, Aercan Econoc Revew, March, 80, Salant, S., S. Swtzer, and R. Reynolds (983), Losses Due to Mergers: The Effects of an Exogenous Change n Industry Structure on Cournot-Nash Equlbru, Quarterly Journal of Econocs, May, 98, Wllason, O.E. (968), Econoes as an Anttrust Defense: The Welfare Tradeoffs, Aercan Econoc Revew, March, 58,