Monopolistic competition

Transcription

1 Leture 08 arket Struture (II) A. Olgopoly. Spetrum of market struture Perfet ompetton onopolst ompetton Olgopoly onopoly ost markets are nether perfetly ompettve nor monopolst but they may fall somewhere n between along the spetrum. ypal market wll have more than one seller of the same or smlar produts, but not enough to justfy the assumpton that sellers smply take pres as gven. hus, eah frm wll have an ndvdual, downward slopng demand urve and s sad to have some level of monopoly power.. Olgopoly Olgopoly s from the Greek word olgospolen meanng few to sell. And t s refletng the nterdependene among frms, whh means olgopoly or mperfetly ompettve frm must take aount of ts rval s atons n makng ts own prng desons. So, studes of olgopoly an gve us good nformaton about ompettons among frms, strateg reaton or desonmakng proess and trend of market shares of frms. he most modern approah s to model suh frms as hoosng strateges or playng games wth one another. hs approah s alled game theory. 3. Early Generalzed odel Assumptons N frms produng homogeneous and standardzed produts. Input market s perfetly ompettve. No entry s allowed. From these assumptons, we an derve several thngs; ) Inverse demand funton s expressed as p f ( Q) () N, where Q q (market quantty). ) Proft of eah frm wll be π pq ( ) q ( q ),,, L, N () 3) FOC of proft maxmzaton s d π p q dp dq d( q) + 0 () dq dq dq dq f) dq means that a hange n produt of -th frm an affet the hange n total produt or dq hange n produts of other frms. ) We need to know the value of dq dq. Rewrtng ths, we an get dq dq dq N N N + dq dq dq Q Q q q j + q. Q q j (v) j j Intermedate roeonoms 3

2 dq dq : the rato of hange n produts of other frms to the hange n -th frm. Conjetural Varaton (C.V.) So, equaton (v) s now dq + λ (v) dq (hs s the most mportant fator n Olgopoly. We an fgure out dfferent types of olgopoly as λ hanges) Puttng asde the dsusson about λ, we need to derve the generalzed result by assumng that (ost struture) and λ are onstant aross ndvdual frms. herefore, 5) From () and (v), we an get p C q dp ( + λ ) dq p C q Q dp k ( + λ ). Lerner Index ( + λ) (v) p Q p dq ( k s market share of -th frm. s pre elastty of market demand) From (v), assumng that every frm has the same sze, then k N. p C ( + λ) (v) p N 6) So, Lerner Index or monopoly power an be determned by N,, and λ. Ex) In perfet ompetton, p C (Q N and ) In monopoly, N, λ 0. So, p C p For more generalzed ase, we an relax the assumpton that λ s onstant. So, assumng that λ and k an vary among the frms, then we get p C k( + λ ) (v) p 7) Let s thnk about the ndustry (But, assume that C AC ) Rewrtng equaton (), we an get π pq ( ) q ( q ) q,,, L, N (x) Let Π denote the ndustry proft or aggregate profts, then N π Π pq ( ) q q ( q) (x) 8) From (v), multplyng by q on both sdes and summng up from through N, we get pq q k( + λ ) q pq q. And p pq From equaton (x) and (x), k ( + λ ) q k ( + λ ) Q (x) Intermedate roeonoms 33

3 N, where HHI k Π R k ( + HHI λ ) ( + λ ) (Herfndahl-Hrshmann Index) (x) 9) From (x), l.h.s s alled Industral Rate of Return, whh an reflet the performane of the ndustry. N (why?) N ( + λ) ( p C) Q LI N pq 0) If C, k, and λ are onstant, HHI k Π R (x) In onluson,. As N, Conjetural varaton ( λ ) 0 Neglgble market share ( k ) 0 Low HHI ( HHI) 0 herefore, from (x), the value on r.h.s. wll go to zero, whh s analogous to the perfet ompetton wth p C.. If monopoly, N, k ( or 00%), HHI ( or 0000), and λ 0. (Pre-ost margn n monopoly) (ndustral rate of return) p C p Π R. Cournot Duopoly (Augustne A. Cournot, 838) ) Assumptons * λ dq / dq 0 * Eah frm determnes produts that maxmze ther profts takng the produts of rvals onstant. * arket demand s P a Q ( a > 0) and Q q + q (Q s the total quantty of sprng water sold n the market per unt of tme). * For smplty, C AC. ) odel * Frm assumes that frm s produng q and t produes q as the best response to q. * So, the eonom proft for frm s as follows, π ( P ) q ( a q q ) q. Δπ a q q 0 (). From (), we get the best response of frm to q of frm, Δq Intermedate roeonoms 3

4 a q q (): Reaton Curve of frm * In the same way, we get reaton urve of frm. a q q (): Reaton Curve of frm q ( a ) Frm ( a ) / ( a ) / 3 C Frm ( a ) / 3 ( a ) / ( a ) q * Cournot-Nash Equlbrum * * a q q 3 a + P* a q* 3 ( a ) π ( P * ) q * 9 * Suppose frm and frm dede to make a Cartel and at as olletve monopolst. hen what are the profts of two frms? And what s the monopolst produt? (R C) Gven demand urve s P a Q. R PQ ( a Q) Q. And R a Q, and C ( a ) R a Q C. So, Q m ( a ) If these two frms produe the same quanttes, then q q. a + ( a ) ( a ) And P m, π m, whh s bgger than proft at pont C ( π ). 8 9 * If the two frms make a Cartel and determne ther quanttes ooperatvely, then ther eonom profts are hgher than those of Cournot-Nash equlbrum. herefore, there s a good reason and motve to artelze or to ollude. Intermedate roeonoms 35

5 * But, why do we all C as an equlbrum pont, not? Or, why s not an equlbrum? Beause there s another motve to heat by nreasng quantty to earn more proft at pont. a * If frm produes q and keeps the Cartel but frm does not, then the proft funton a 3 of frm s as follows: π ( a q ) q ( ( a ) q ) q. Δπ 3 ( a ) q 0. Δq 3 q ** ( a ), whh maxmzes eonom proft of frm. Hene, frm breaks the artel 8 3a + 5 and produes more. arket pre of frm s produts s P and 8 9 π ( a ) > ( a ). 6 8 * Frm has a motve to heat frm. Ve versa. So, one-shot artel s unstable. * Cartel s easy to ollapse. But, f the artel s made among few frms for relatvely long perods, then t an be sustaned longer wth effent and severe punshment or penalty on the volators. 5. Generalzaton to Olgopoly P a Q, a > 0. n Q q π ( p ) q [ a ( q + q+ L+ q + q + + L + q n )] q d π [ a q q q q q q L + L n] 0 dq q+ L+ q + q + q+ + L + qn a Assumng that C AC, ( q q*) a a n ( a ) q* p* +,, π * n + n + ( n + ) If n, we get the same results n Cournot Duopoly. j 6. Bertrand s Paradox ) Assumptons * Eah frm s assumng that the pres of other frms are onstant n dedng the quanttes. * So, n ths model we an thnk about the motve to set a lower pre than any other frm. * Pre-underuttng and fnally up to most ompettve level. ) odel Unlke Cournot model, frms wll determne the pre. And quantty s deded n aordane wth the pre. * arket Demand: P a Q or Q a P ( a > 0 ) Suppose there are two floppy dskette ompanes DK and axell. Assumng that the dskettes are entrely dental n every aspet, then onsumers try to purhase a heaper one. Intermedate roeonoms 36

6 If P < P, Q a P Qand Q 0 If P P, Q a P Q ( ) If P > P, Q 0 and Q a P Q, where Q Q + Q. he unque (Nash) equlbrum s aomplshed f P P, and at ths level π π ( ) ( a ) 0. * he ratonale s as follows; At P P, no frm an set a pre lower than. If P >, then axell an domnate the market by settng P < P even slghtly. If P > P, π ( P ) 0 0 If P P, π ( P ) ( a P ) If P < P, π ( P ) ( a P ) * For example, f DK sets P P ( > 0 ), then ts proft wll be ( P )( a P + ). Smply, as approahes to zero, ts proft wll go to ( P )( a P ). If DK sets P P, proft s ( P )( a P ), whh s about half of ( P )( a P + ). Ex) Suppose a 000, 800, P 000, and P 999,. axell earns 0, and DK earns ( ) ( ) 99, 99. If P P000, π ( )( ), 7. Produt Dfferentaton ) odel * Small Car arket (Olgopoly) wo Frms: Ford (Frm ) and oyota (Frm ) wth Fous and Eho, respetvely. * For smplty, assume that CF ACF AC C. Demand fang Ford s assumed to be QF a PF + β P (). * If β > 0, the nrease n P wll nrease Q F. It means Fous and Eho are substtutes. * If β < 0, two produts are omplements. ) Analyss Let s get best response of Ford to P. π F ( PF ) QF ( PF )( a PF + β P) () dπ F a+ PF + β P 0 () dp F Intermedate roeonoms 37

7 a P he reasonable pre P F s PF + + β (v) (Ford s reaton urve to oyota s pre) For example, f oyota sells Eho at P, then Ford s best way to maxmze ts proft s to a sell Fous at PF + +β. Suppose the demand fang oyota s Q a P + β P (v) In the same way, we an get P P a P + + β F F (v) Ford oyota d B Pont a and : a+ a b P F Pont b and d: a+ β If 0< β <, then Fous and Eho have substtutablty n some degree. a+ At B, PF* P* β, 0< β <. And a ( ) QF* Q* + β β If β < 0, we get the same results. But reaton urves are downward slopng. If β >, P *, P * < 0. In prate, P * P * F F As β goes up, the substtutablty wll go up, whh means there are almost dental produts. So, t s same n the perfet ompetton prng. 8. Loaton Game Brands ompete more vgorously wth brands that are lose substtutes than wth those that onsumers vew as less lose substtutes. Consumers vew ertan brands as loser substtutes than others. Smply, ertan brands have partular ommon haratersts that other lak. hat s, eah brand s loated at a partular pont n produt haraterst spae. Or, produts sold at nearby stores are lose substtutes. hat s, eah frm s loated at a partular address or pont n geograph spae. Intermedate roeonoms 38

8 ) Hotellng s odel (99) * Consder a long, narrow ty wth only one street whh s mle long. * Consumers are unformly dstrbuted between 0 and. * Eah has to purhase one unt of produt. * wo stores are sellng almost dental produt at the same pre and try to maxmze profts. * Consumers wll purhase at the nearest store beause they have to nur transaton ost (travel, tme, watng, ). store store 0 a - b Loaton a ( a b ) b * Suppose two stores have to loate at the same tme before they start to sell. Consumers lvng on the left of store and half of onsumers lvng between store and wll hoose store. * Store s market share a+ 05.( a b) 05.( + a b) Store s market share b+ 05.( a b) 05.( a+ b) * he equlbrum n ths loaton game s where two stores are loated n the enter of ths lnear ty. a 05. ( b) * Intutvely, f store s at a 05., then the best response of store s to loate at b 05. to maxmze ts share. But, f store s at ( b ) > 05., then t has less 50% of total share. If store s at a 03., store an maxmze ts share by loatng at ( b ) 03., rght next to store. he equlbrum when there are two frms suggested to Hotellng that Buyers are onfronted everywhere wth an exessve sameness (99). he result that two frms n ether produt or geograph spae wll loate n the mddle s often referred to as the prnple of mnmum dfferentaton (K. Bouldng, 966). he prnple does not hold strtly when there are more than two frms. However, even when there are more than two frms, the equlbrum market onfguraton s haraterzed by bunhng. * Eonom Implaton: Adoptng ths model to produt Dfferentaton wo ompettve frms n duopoly wll have a strategy for medum onsumers as man target n desgn, harater or qualty. And the degree of dfferentaton s trval. Ex) Even n poltal sene, U.S. has two party polts system. Demorats and Republan. hey take publ pledge or ommtments whh are so smlar or vague whh are not easly dstngushable. 9. Stakelberg s Duopoly (Leader-Follower odel) In Cournot s duopoly, we assumed that λ 0. But, f the deson on produton s sequental or f there s a gap n ompettve power, then one frm ats as a leader and the others as followers. Stakelberg showed another duopoly model wth leader and followers. In hs model, leader ats as f the other frm s output s onstant, and followers, however, hoose optmal produts n response to leader s output. ) If leader/follower are predetermned * Frm (leader) and Frm (follower). Idental n almost every aspet. Intermedate roeonoms 39

9 * arket demand: P a ( q + q ), same demand n Cournot model. * C AC AC C a q * If q s determned, q that maxmzes π wll be: q () a q * And, Frm (leader) an expet that Frm wll produe q f Frm produes q. So, pluggng the reaton urve of Frm nto π, a q a q q q () dπ a a q 0, q* () dq π ( p ) q ( a q q ) q a * By the way, the Frm (follower) wll produe q n response to q*. a a a q * (v) 3( a ) * So, market produt Q q* + q* (v) ( a ) a * arket pre s P* a + 3 (v) * * * a + 3 ( a ) ( a ) * π ( P ) q 8 (v) * * * a + 3 ( a ) ( a ) * π ( P ) q 6 (v) ) If leader/followers are not ertan We know every frm wants to be a leader beause the leader s proft s always bgger than that of follower. So, f the leader and follower are not determned before they start game, we mght expet dfferent results. Eah frm has two strateges; Lead and Follow. * If two frm at as leaders ad produe q and q, a q* q*, P a ( q + q ), π ( P ) q ( P ) q π Idental to Perfet Competton (Stakelberg Warfare) * If two frms at as followers and produe q and q, q a q a, P +,π π ( a ) It s Cournot Duopoly 0 Intermedate roeonoms 0

10 q Frm a S W a 3 C a S Frm a a 3 a q C: Cournot-Nash Equlbrum Pont S : If Frm s a leader S : If Frm s a leader W: Stakelberg Warfare 0. Knked Demand Curves (by Paul Sweezy) P P A C A C B C R Demand Q A Intermedate roeonoms

11 Another hypothess about how olgopolst rvals may respond says that rvals math pre uts but do not respond to pre nreases. In ths stuaton, an olgopolst beleves that t wll not gan muh n sales f t lowers ts pre, beause rvals wll math the pre uts, but t wll lose onsderably f t rases ts pre, sne t wll be undersold by rvals who do not hange ther pres. he demand urve fang suh an olgopolst appears knked. he urve s very steep below the urrent pre, p, refletng the fat that few sales are ganed as pre s lowered. But t s relatvely flat above that pre, ndatng that the frm loses many ustomers to ts rvals, who refuse to math the pre nreases. he fgure also presents the R urve, whh has a sharp drop at the output level orrespondng to the knk. Why does the R urve have ths shape, and what are the onsequenes? Consder what happens f the frm wants to nrease output by one unt. It must lower ts pre by a onsderable amount sne, as t does so, ts rvals wll math that pre. Aordngly, the R t garners s small. If the frm ontemplates uttng bak on produton by one unt, t needs to rase ts pre only a lttle sne rvals wll not hange ther pre. hus, the loss n revenue from uttng bak output by a unt s muh greater than the gan n revenue from nreasng output by a unt. Wth a flat demand urve, pre and R are lose together. he drop n R means that at the output at whh the drop ours, extra revenue lost from uttng bak produton s muh greater than the extra revenue ganed from nreasng produton. hs has one mportant mplaton. Small hanges n C, from C to C, have no effet on output or pre. hus, frms that beleve they fae a knked demand urve have good reason to hestate before hangng ther pre.. Advertsng (Non-pre ompetton) ) ypes of Advertsng Persuasve advertsng of experene goods: fousng on mage makng for the ompany Informatonal advertsng of searh goods: fousng on nformaton of produts ) Optmal Advertsng odel R R( Q, α), where α 0 (advertsng expenses) π R( Q, α) C( Q) α. o solve for Q *andα * that an maxmze proft, FOCs wll be π R dc RQ C 0 Q Q dq π R Rα 0 α α Can you nterpret the result? Intermedate roeonoms