Is Social Welfare Increased By Private Firm Entry. Introduction

Transcription

1 Is Socal elfare Increased By Prvate Frm Entry From a coopetton vewpont Unversty of Hyogo graduate school doctoral course n economcs Takesh Yoshkawa Introducton Many studes on a mxed olgopoly manly deal wth competton between publc and prvate frms, the effects of prvatzaton on market performance, and endogenous tmng. In realty, however, many frms choose to partake not only n compettve but also n cooperatve behavors. For example, when new communcaton goods are developed, ble phone companes frst nvest n advertsng to form a market for the new products, and then they compete wth each other n the market. Ths stuaton s called coopetton 2. The objectve of ths paper s to look nto the effects on socal welfare of the emergence of prvate frms n a market nopolzed by sem-publc frms by usng a coopetton del. The followng three cases are consdered: ) See De Fraja, G., and Delbono, F. (989), Pal, D. (998), hte (996), Fjell, K., Pal, D. (996), Anderson, S. P., de Palma, A. and Thsse J. -F. (997), Matsumura (998), Nshr and Ogawa (2002), Haruna (2005). 2 See Brandenburger and Nalebuff (997), Krshnamurthy (2000), Dearden and Llen (200), Ngo and Okura (2008). a sem-publc nopoly where the market s nopolzed by a sem-publc frm, 2) a mxed duopoly wth one sem-publc frm and one prvate frm n the market, and 3) a mxed olgopoly wth one sem-publc frm and two prvate frms n the market. Two effects appear from the emergence of prvate frms; ) the market sze s larger n a sem-publc nopoly than n a mxed duopoly f there exsts a hghly prvatzed sem-publc frm n the market, and 2) the socal welfare s greater n a mxed duopoly than n a mxed olgopoly f there exsts a hghly prvatzed sem-publc frm n the market because the change n the sum of the equlbrum cooperatve behavor levels trggered by prvate frms enterng the market has a postve effect (an ncrease n the sum of the equlbrum output level) rather than a negatve effect (an ncrease n the total cost).

2 Model e assume hogeneous goods markets and compare the followng three cases: ) a sem-publc nopoly where the market s nopolzed by a sem-publc frm, 2) a mxed duopoly wth one sem-publc frm and one prvate frm n the market, and 3) a mxed olgopoly wth one sem-publc frm and two prvate frms n the market. Frms exstng n the market play a two-stage game. In the frst stage, the frms choose ther own cooperatve behavor levels. The cooperatve behavor level s denoted by k for,2,3, whch ncreases the market sze. The overall market nverse demand functon s gven by P A Q, () where Q s the total supply and A represents the market sze and s the sum of a (a postve constant number) and K (the total cooperatve behavor level). Hence, A s formulated by A a K. In the second stage, the frms choose ther output levels for,2,3 q, representng ther compettve behavor. The cost of expendng cooperatve behavor s denoted by k 2. The margnal cost of producton denoted by c s assumed to be a c and s also assumed to be the same for all the frms. Hence, the total cost functon s gven by C cq k for,2,3 (2) 2 Frm 2 and frm 3 denote prvate frms, whch maxmze ther profts. Usng () and (2), the proft functon s gven by Pq C for 2,3, (3) and a sem-publc frm s denoted by frm. Usng (2) and (3), the objectve functon s U (, (4) ) where, whch s the sum of the consumer surpluscs and the producer surplus PS, represents the socal welfare. The socal welfare s thus gven by CS PS. (5) The parameter [0,] can be nterpreted n two ways; t represents the weght of the government s partcpaton n frm. It can be regarded as the mport level attrbuted to the government s objectve, and the government can control t by regulatng the shareholdng rato. Therefore, we can vew as the degree of prvatzaton;.e. 0 sgnfes that frm s solely concerned about ts proft whle means that frm ams to maxmze socal welfare regardless of ts proft. Table expresses A,CS, PS, and n the three cases. 2

3 Comparsons Ths secton scrutnzes the nequalty relatonshps of the three cases to elaborate the effects of the emergence of prvate frms on socal welfare. Comparson of K Ths subsecton deals wth the nequalty relatonshps of K (the total sum of the equlbrum cooperatve behavor levels) n the three cases 3. Fndng. The nequalty relatonshps of K n the three cases. K K k (0 0.84), (54) K k K ( ), (55) k K K ( ), (56) k K K (0.489 ). (57) The ntercepts of reacton functons s greater n a mxed duopoly than n a mxed olgopoly and the slop of reacton functons of sem-publc frm s aller n a mxed duopoly than n a mxed olgopoly, when there exsts a hghly prvatzed sem-publc frm n the market, as shown n (54). On the other hand, the slop of reacton functons of prvate frm s aller n a mxed duopoly than n a mxed olgopoly. That s, partcpaton prvate frm n a mxed duopoly market, 3 Rounded to three decmal places. reducng the elastcty of the reacton functon. Hence, k s the greatest of the three cases and K s greater than K when a hghly prvatzed sem-publc frm exsts n the market. Comparson of consumer surplus Ths subsecton consders the nequalty relatonshps of the consumer surpluses. Fndng 2. The nequalty relatonshps of the consumer surpluses. CS CS CS. (58) The emergence of prvate frms ncreases the total supply, thus boostng the consumer surplus. Comparson of producer surplus Ths subsecton concerns the nequalty relatonshps of the producer surpluses 4 Fndng 3. The nequalty relatonshps of the producer surpluses. PS PS PS ( 0 0.4), (59) PS PS PS ( ), (60) PS PS PS ( 0.30 ). (6) 4 Rounded to three decmal places. 3

4 The nequalty relatonshp of the total sum of the equlbrum cooperatve behavor level s K K when there exsts a hghly prvatzed sem-publc frm n the market, as shown by (59). In a mxed duopoly the postve effects, such as the ncrease n the market sze are aller than the negatve effects, such as the ncrease n the sum of the frm s total costs. On the other hand, n a mxed olgopoly the postve effects are aller than the negatve effects. Hence, we conclude that the emergence of prvate frms has two effects on the producer surplus. ) The entrance of two prvate frms always decreases the producer surplus, and 2) f there exsts a hghly prvatzed sem-publc frm n the market, the producer surplus s aller n a sem-publc nopoly than n a mxed duopoly. Comparson of socal welfare Ths subsecton consders the nequalty relatonshps of the socal welfare. Fgure 4, whch shows the rela- tonshps of,, yelds Fndng 4 5. and Fndng 4. The nequalty relatonshps of the socal welfare. ( ), (62) ( 0.04 ). (63) [Fgure 4 nsertons] to hen there exsts a hghly prvatzed sem-publc frm n the market, as shown n (62), the nequalty relatonshp of the consumer surplus s CS CS CS and the nequalty relatonshp of the producer surplus s PS PS PS, and the nequalty relatonshp of the total sum of the equlbrum cooperatve behavor levels s K K k. e can thus say that the change n the sum of the equlbrum cooperatve behavor levels caused by the entrance of prvate frms has a postve effect (an ncrease n the equlbrum output level) rather than a negatve effect (an ncrease n the total cost) f there exsts a hghly prvatzed sem-publc frm n the market. Therefore, the socal welfare s aller n a mxed olgopoly market made up of two prvate frms and a hghly prvatzed sem-publc frm than n a mxed duopoly market composed of a prvate frm and a hghly prvatzed sem-publc frm. If a less prvatzed rather than hghly prvatzed sem-publc frm exsts n the market, the socal welfare wll ncrease n ether case. e conclude that deregulaton results n dmnshng the socal welfare when a hghly prvatzed sem-publc frm exsts n the market, as n the case of a prvate frm enterng a mxed duopoly market. However, t should be noted that deregulaton ncreases the socal welfare when a less prvatzed sem-publc frm exsts n the market. 5 Rounded to three decmal places. 4

5 Conclusons Usng a coopetton del, we have shown two effects of the emergence of prvate frms: ) the market sze s larger n a sem-publc nopoly than n a mxed duopoly f a hghly prvatzed sem-publc frm s n the market, and 2) the socal welfare s greater n a mxed duopoly than n a mxed olgopoly f a hghly prvatzed sem-publc frm s n the market, because the change n the sum of the equlbrum cooperatve behavor levels trggered by prvate frms enterng the market has a postve effect (an ncrease n the sum of the equlbrum output level) rather than a negatve effect (an ncrease n the total cost). e conclude that deregulaton results n dmnshng the socal welfare when a hghly prvatzed sem-publc frm exsts n the market, as n the case of two prvate frms enterng a sem-publc nopoly market. e don t refer the relatonshp of the optmal value of to the number of prvate frms exstng n the market. Extendng our del to ths drecton remans for future research. 5

6 Fgure 4 The relaton of to n the three cases