SØK/ECON 535 Imperfect Competition and Strategic Interaction. In the absence of entry barriers firms cannot make supernormal profits.

Transcription

1 SØK/ECON 535 Imprfct Comptton and Stratgc Intracton ENTRY AND EXIT Lctur nots Introducton In th absnc of ntry barrrs frms cannot mak suprnormal profts. Barrrs to ntry govrnmnt rgulatons tchnologcal barrrs conoms of scal accss to (ffcnt) producton tchnologs, nputs tc. product dffrntaton, consumr swtchng costs, patnts stratgc barrrs Ban (1956) blockadd ntry dtrrd ntry accommodatd ntry Contstabl markts Potntal (as opposd to ral) comptton (Baumol t al, 1986) sunk costs ht and run stratgs Markt charactrsaton Consdr an xampl n whch frms produc on homognous products may b gnralsd to mult-product frms and dffrntatd products All frms hav accss to th sam tchnology 0 whn q = 0 C( q ) = > 0othrws

2 E Dmand functon: = ( p) Q Q. Markt confguraton: { q, q,..., q, p } 1 A markt confguraton s fasbl f Q p = q 1 ( ) = ( ) n pq C q 0, = 1,,..., n A markt confguraton s sustanabl f thr dos not xst whr p and q n p p and ( ) ( ) q Q p such that pq C q 0, ar th ntrants prc and quantty. A prfctly contstabl markt s markt for whch all markt confguratons ar fasbl and sustanabl. Exampl: natural monopoly C( q) = f + cq, q > 0 fgur (sustanabl markt confguraton whr th dmand curv cuts th avrag-cost curv) Th sustanabl markt confguraton s cost ffcnt and scond-bst (n th Ramsy sns). Gnralsaton to mult-product markts total costs ar mnmsd no frm arns postv proft no cross-subsdsaton Ramsy condtons ar fulflld f th numbr of frms xcds on Not: prc quals margnal cost Parto optmalty dstngush btwn fxd and sunk costs barrrs to ntry ar assocatd wth sunk costs Ht and run Consdr an xampl wth a sngl frm n th markt (natural monopoly).

3 A potntal ntrant can offr th markt a contract at tm 0 that spcfs quantty q prc p, and duraton τ. Th duraton of contract should b thought of as th tm t taks th stablshd frm to ract (.. chang ts prc offr). Lt β b th unt prc of captal at tm 0 α b th unt prc of captal at tm τ Th usr cost of captal µ may b dfnd mplctly by [ β α ] τ r rτ rt rτ 1 0 β α = µ dt µ = βr + Th stablshd frm may consquntly hold a prc that xcds ts own usr cost of captal ( β r ). L C q q and C( q, βr) q. p mplctly dfnd by L L L pq p C( Q p, µ ) = 0; that s, whr th dmand curv cuts th Fgur ( (,µ ) ( ) ( ) avrag-cost curv of th potntal frm). Concluson: th markt s prfctly contstabl f ntry s fr frms fac th sam prc of captal ( β ) frms hav accss to th sam tchnology (C, Q ) xt s costlss β α 1 = 0 rτ [ ] Stratgc ntry barrrs Crdbl ntry dtrrnc An ntry gam btwn a (potntal) ntrant () and an ncumbnt frm (): Stag 1: ntrant dcds whthr or not to ntr th markt; Stag : ncumbnt (havng obsrvd th ntrant s choc) dcds whthr or not to fght th ntrant; 3

4 ) ( Π 0, Π 0 ) payoffs: (Π, Π f ntry s mt by fght ; fght ; and (Π,0 Rsults m ) f thr s no ntry. th stratgy fght s crdbl only f Π Π 0 ; fght lads to dtrrnc only f Π 0 ; f ntry s not mt by f Π 0 and Π <, thn th stratgy combnaton {fght, stay out} s a Π 0 Nash qulbrum but not a Subgam Prfct Equlbrum. Not: t s th x post markt stuaton that s rlvant. Lmt-prcng classc thory : Ban, Sylos-Labn, Modglan gam-thortc crtqu: Spnc, Dxt asymmtrc nformaton and sgnallng: Mlgrom and Robrts A stratgc ntry gam W consdr a nw gam n whch th ncumbnt may tak actons x ant n ordr to dtr ntry; subsquntly a gam smlar to th on abov s playd (ths s summarsd n th rducd-form proft functons): Stag 1: ncumbnt dcds on lvl of ntry barrr b ( b = 0 corrsponds to no barrr); Stag : ntrant dcds whthr or not to ntr; payoffs: ( Π ( b), Π( b ) f ntry taks plac and Π m ( b ),0 othrws. Dfntons ) ( ) ntry s blockadd f Π ( 0) < 0; dtrrnc possbl f thr xsts b such that Π ( b ) < 0 dtrrnc proftabl f Πm( b ) Π ( 0), whr ( ) accommodaton f Π ( b ) < Π ( 0). Issus m Π b = 0 ; b must b rrvrsbl (cannot b changd upon ntry) what forms can b tak?; how dos dffrnt forms of b affct potntal ntrants compttv poston; asymmtrc nformaton; olgopoly. 4

5 Th Spnc-Dxt modl b = k s capacty. Homognous product, lnar dmand: p = 1 Q. Costs x ant (bfor nvstmnt): C( q, ) = +, k ck f q k x post (aftr nvstmnt): (, ) = 0, C q k q k. Aftr ntry has takn plac, frm choos quantty smultanously wth frm choosng both quantty and capacty. Th x post duopoly gam (gvn ntry and k ): clarly not proftabl for frm to hold xcss capacty, hnc q = k ; racton functons: = { mn, 1 } frm s proft: 1 q c 4 f. Not that dtrrnc rqurs q 1 c crdbl f 1 q k k and k = 1 q c f k c f and [ ] Th x post subgam f frm rmans a monopolst: [ ] { } max 1 q q q k ; q 1+ c 3 1 c f,.. c f. at qulbrum w must hav q = k snc margnal rvnu s gratr for a monopolst than for a duopolst and xcss capacty cannot b optmal. Consdr thn th frst-stag choc of frm and suppos frst that th choc nvolvs dtrrnc: { } max [ 1 k c] k f k 1 c f [ ] blockadd ntry f [ ] dtrrnc f [ ] 1 c 1 c f,or c 1 4 f ; { } k = max 1 c,1 c f ; 1 c < 1 c f, yldng profts f 1 c f f. Consdr nxt th frst-stag choc n th cas of accommodaton: xcss capacty clarly unproftabl; { } max 1 k ( ) k3 k c k f whr k( k) = [ k c ] 1 5

6 rsult s k = [ 1 c] and profts [ c] 1 8 f It follows that frm chooss dtrrnc rathr than accommodaton f f 1 c f > [ 1 c] 8, or c 1 4 f, and vc vrsa. Numrcal xampl: f = 0.01: ntry blockadd f c 0.6 ; dtrrnc crdbl f c 0.35 ; dtrrnc blockadd f c Concluson ntry dtrrnc by ovr-nvstmnt n capacty; no xcss capacty; stratgc ncntv for ovr-nvstmnt also n th cas of accommodaton (cf Stacklbrg); prc s low du to larg capacty, but no lmt prcng. Varatons Prc comptton at th post-ntry stag. Multpl ncumbnts dtrrnc s a publc good ; prc > margnal costs; Glbrt and Vvs (1986) show that scond ffct domnats and hnc dtrrnc s vn mor lkly wth many ncumbnts. Stratgc typs and typs of stratgs Consdr th cas n whch th ncumbnt accommodats ntry Proft functons ncumbnt: Π ( q, q, k ) ntrant: Π ( q, q, k ) Frst-ordr condton for ncumbnt s x ant dcson dπ Π dq dq π = = + dk q dq dk k 0 6

7 Th frst lmnt on th rght-hand sd consttuts th stratgc ffct, and sgn Π q = sgn Π q ) so (assumng ( ) ( ) sgn Π (.. ) = sgn dq sgn dq strat ff q dk dq Around th opn loop pont ( Π k =0 ) w hav Π k < 0. Consquntly, a ngatv (rsp. postv) stratgc ffct wll lad to ovrnvstmnt (rsp. undr-nvstmnt). Dfntons Π Frm s tough (rsp. soft) f sgn dq < 0 q dk (rsp. > 0 ); Stratgs ar stratgc substtuts (rsp. complmnts) f racton dq functons ar ncrasng (rsp. dcrasng), or sgn > 0 (rsp. < 0 ). dq Ex ant nvstmnt maks th ncumbnt frm Though Soft Stratgc complmnts Puppy Dog Fat Cat Stratgc substtuts Top Dog Lan and Hungry Lool Entry dtrrnc: only toughnss/softnss dtrmns stratgy (ffct on compttor s profts). Entry accommodaton: typ of stratgs mattrs also (ffct on own proft). Quantty comptton: Top Dog n both cass. Prc comptton: Top Dog f dtrrnc, Puppy Dog f accommodaton. Exampls: gnrc advrtsng and prc comptton: xcssv advrtsng whn accommodatng ntry (Fat Cat); brand advrtsng and quantty comptton: xcssv to dtr ntry (Top Dog); locaton (product dffrntaton): Th Prncpl of Dffrntaton (Puppy Dog); larnng-by-dong: xcssv producton to dtr ntry (Top Dog); 7

8 most-favourd-customr-claus wth prc comptton (Puppy Dog) Ext Industrs n dcln fght to survv. War of attrton Two symmtrc frms supplyng a homognous good. Producton cost pr unt of tm: C( q ) = f + Brtrand comptton: p1 = p = c Monopoly gross profts (not ncludng fxd costs): Π m m, Π > f At any pont n tm, ach frm may choos to lav th markt (rcvs 0 profts aftrwards cannot r-ntr). W ar lookng for a symmtrc qulbrum (n mxd stratgs). Lt x () t b th probablty that a frm lavs th markt at tm t. Thn th othr frm wll b ndffrnt btwn stayng n an lavng ovr th nxt prod of tm dt f cq m Π f fr f dt + xdt = 0 x = Π m r f. Concluson bfor xst happns, both frms run dfcts (ovr a prod wth stochastc lngth); xpctd profts ar zro (x post th rmanng frm arns postv profts); wlfar loss both bfor (du to duplcaton of fxd costs) and aftr xt (bcaus of monopoly prcng); n th a cas of prc colluson (mayb tact) th xt rat would b lowr, and hnc wlfar would b lowr also (du to both hghr prc and mor duplcaton x ant) Wll small frms xst bfor larg frms? If contracton s not an opton, larg frms wll lav frst (Ghmawat and Nalbuff, 1985). 8

9 If contracton s possbl, larg frms wll contract bfor xt taks plac (Whnston, 1986, and Ghmawat and Nalbuff, 1987). 9