Chapter 14 Tradtonal Models of Imperfect Competton Now we wll relax some assumptons of perfect competton; the assumptons about the number (and sze) of frms n the ndustry, homogenety of products, and freedom of entry. Models of mperfect competton nclude a mxture of perfect competton and monopoly. A. Homogeneous Olgopoly (Assumptons) Few (large) frms sellng a sngle homogeneous product. Perfect competton on the buyer sde. The product obeys the law of one prce. No transacton or nformaton costs. Barrers to entry are prohbtve. All frms face the same cost structure (dentcal frms). Industry demand s P = f(q) (nverse demand functon), where Q = q 1 +q + +q n = =nq and q = output of frm. The prce depends on output of all frms. The frm wants to max = Pq -C(q ) = f(q)q -C(q ) = f(q 1 +q + +q n )q -C(q ).
Quas-Compettve Model Each frm assumes that ts decsons do not affect prce. It acts lke a prce taker (MR=AR=D=P). To max, π P C(q P MC (q ) ) Solve for q *. Also, MC = MC = MC for all. Assume constant MR=P C * MC MR D Q * = * = nq * Thus, the ndustry wll reach the compettve soluton (P=MC). The prce-takng assumpton leads to behavor as f MR=AR=D=P, that s, that the demand curve s horzontal when n fact t s not. How long could ths last before frms realze that they face downward slopng demand curves and restrct output to maxmze proft?
Cartel Model Frms realze ther effect on prce and collude to take advantage of ther market power. Colluson wll lead to a monopoly soluton because the frms coordnate ther outputs explctly to acheve maxmum for the ndustry. They realze that they are nterdependent and ther fortunes are ted together. They cooperate for the good of all. The cartel attempts to maxmze: π PQ C 1(q1) C(q)... C f(q1 q... qn)(q1 q... qn) C (q) Product Rule π P C (q) FOC s P (q1 q... qn ) P P Q MC (q Ths equals MR(Q) because by defnton t does not matter whch frm s quantty changes. ) P * MR(Q) MC (q) All frms produce the same q wth the Also, MC (q) MC(Q) same cost. Ths s the monopoly soluton. because all frms face the same costs. n (q n ) M MR Q * =nq * for D all. MC(Q)=MC (q )
Problems wth Cartels Colluson s llegal n most countres. Colluson requres substantal nformaton. Each member has an ncentve to ncrease q because P > MC. The cartel s unstable because each frm has an ncentve to cheat. It would requre a strong polceman to drect the cartel. OPEC ol cartel s a specal problem because Saud Araba has lower costs. Those outsde the cartel have ncentve to ncrease producton because prce s hgh (nterlopers).
Cournot Model Each frm recognzes that ts output affects prce, but thnks that changes n ts output wll not cause other frms to change ther output. P So but for. Conectural varaton assumed =. P q MC Max π = Pq C (q ) ; FOC For the Cournot model, q < Q for the cartel model. MR for Cournot > MR for Cartel. Cournot frm s output wll exceed the cartel frm s output because each frm s MR(q ) > MR(Q) for the cartel. But, because q (P/ ) wll be negatve, P>MC (q ). Thus, output wll occur between M and C at a pont such as A. M A The Cournot model followed to ts concluson C MC = MC ndcates that each frm wll produce the same q and n that total ndustry output wll be Q C. Q * MR D P where n = number of frms and C = the compettve ndustry output level (Footnote 3, page 43 of text). (q ) n 1
As n ncreases, Q approaches C. If n = 1, Q = 1/C, whch s the monopoly output for a horzontal MC curve. If n =, Q = /3C. $ Monopoly or Cartel M C MC = MC MR D Q = ½ C C Q LESSON: Output expands toward compettve output as n ncreases. Ths result also follows from the fact that as n ncreases q Ths gets smaller and P approaches. smaller as n gets larger because, wth more frms n the ndustry, an ndvdual frm has less market power (P/ gets smaller). P approaches MC (q ) as n gets larger.
Conectural Varatons Model So far we have not allowed for each frm to realze that ts q actons wll elct a q reacton from others n the ndustry. In realty, each frm wll have conectures about how other frms wll react to ts q actons. No nteracton would result n the Cournot soluton:,. If we relax ths assumpton, the FOCs for each frm to maxmze = Pq -C (q ): π q P P P q MC (q) Effect on P of a change n the frm s own output. Effect on P of the other frms output changes that result from my frm s output change. There s no general theory about the form and sze of the /. One could magne many possbltes. Thus, wthout some assumptons about frms conectures, we do not know much about where ths model wll lead. The soluton s ndetermnate and may be unstable. There s no theory of olgopoly??
Prce Leadershp - One possblty s to assume that the ndustry has a prce leader, maybe a low-cost frm or maybe the largest frm, and a resdual group of followers who are quas-compettors (frnge frms). The leader sees ts market as the excess demand below prce P 1 and above prce P (Q L = Q T -Q SC ). It equates ts MC L wth ts MR L and sells Q L at P L. Frnge frms sell Q SC at P L (dctated by leader and taken by the frnge). Total Q s Q T = Q L + Q SC. $ D T Compettve frms supply the quantty ndcated by pont A and the leader supples at P 1. MC L Compettve frms supply. D L P 1 P L P MC L Q SC Q L A Q T MC (frnge) D L MR L Q SC D T
MC = AC = Example: Cournot s Duopoly Assume two frms producng sprng water at zero margnal cost and that the demand for sprng water s: Q = q 1 + q = 1-P P = 1 - Q. Demand Quas-Compettve Soluton: The frm thnks ts decsons do not affect P. The frm acts as a Prce Taker, MR = P. Optmal M P = MC =. Optmal q 1 = 6 =q, =, Q = 1 at pont C. $ 1 6 4 3 R S Cartel Soluton: D = AR = P = 1 Q. All frms act MR C together as one. = PQ = (1 - Q)Q = 1Q Q = R 6 8 9 1 Q (C = ). FOC Q 1 Q MR MC. Optmal Q = 6, q 1 = 3 =q, P = 6, = 36 at pont M, 1 = 18 =. Cournot Soluton:, but P 1 Pq1 (1 q1 q)q1 1q1 q1 q1q Pq (1 q1 q)q 1q q1q q 1 1 1 q 1 q 1 q1 q because 1 FOC because 1 These FOCs are called reacton functons. They show how each frm reacts to the other frm s decsons. For equlbrum to exst, each frm must do what the other frm expects. Thus, solvng smultaneously gves pont R where optmal Q = 8, q 1 = 4 =q, P = 1 (q 1 + q ) = 4, 1 = 16 =, and = 3. Q Q 3 C 8 1 3 8
$ 1 6 4 3 MC = AC = π MR Demand M R S C 6 8 9 1 Q Von Stackelberg s Soluton: If one frm can predct accurately how the other wll react, but the reverse s not true, then the frst frm has an advantage. Say frm 1 knows that q (11). Ths s the reacton functon of frm solved for q. Frm 1can calculate: 1 1. Ths means that whatever frm 1 does, frm wll move n the opposte drecton by ½ and frm 1 knows t. 1 Pq1 (1 q1 q)q1 1q1 q1q q1 Pq (1 q1 q)q 1q q1q q π = -1/ 1 q1 q q 1 1 1 1.5q1 q 1 q1 q FOC because 1. 1 1 Frm 1 s reacton functon has changed. As before because Solve the reacton functons smultaneously to get optmal Q = 9 at pont S, q 1 = 6, q = 3, P = 3, 1 = 18, = 9, = 7. 1.
B. Dfferentated Olgopoly Assume there s a small number of frms n a product group (a group of goods whose cross-prce elastctes are very hgh wthn the group, but are relatvely low wth goods outsde the group). A product group s a group of goods that substtute well for one another. Barrers to entry are hgh. Each frm may spend money to dfferentate ts product. Methods of dfferentaton may nvolve advertsng, optons, qualty, locaton, etc. Use to represent the expendtures of frm on product dfferentaton. C C (q,z). Each frm s prce wll probably be somewhat dfferent, so that the nverse demand functon for the th frm wll be: p g(q,p,z,z ), where p and z are prces and dfferentaton expendtures by all other frms. We expect: p q, p p, p z, p z. The p =g (q p, z, z ) demand curve s shfted by p, z, and z. Profts are = p q C (q, z ), assumng z z p p (Other frms wll not change p or z z q z when frm changes q and z ).
Gven these assumpton, the FOCs are: π p C p q π p C q z z z The frst says MR = MC for q (typcal). The second says MRP = MIC for z. Ths means that the frm should ncrease dfferentaton expendtures (z ) untl the margnal contrbuton to revenues equals the margnal contrbuton to costs (.e., MRP nput = MIC nput). Relaxng the zero dervatve assumptons means that the demand curve for frm shfts frequently and, perhaps, unpredctably. Thus, the dfferentated model s even more complex than the homogeneous model because there are more varables and other frms react to changes n q and z. Therefore, few defntve conclusons are possble because of the unpredctable nterdependence among frms! Advertsng rotates and expands the demand curve. It 1) promotes product dfferentaton (rotaton), ) may expand the market for a frm, 3) may expand the total product group market, 4) should be undertaken to pont where MRP Adv = MIC Adv (Whether products are really dfferent or not doesn t matter much; ust percepton matters), 5) may be subect to economes of scale, whch gves advantage to large frms and creates barrers to entry, 6) may convey useful, truthful nformaton and, thus, mprove market effcency, and 7) may be false and confusng, thus, leadng to market neffcency (When not nformatve, t wastes resources. When only combatve or defensve n a fxed total market, t s neffcent). Judgments on advertsng are mxed.
Allow freedom of entry now: Freedom of entry means that long-run profts wll be zero under condtons of competton. Ths s true for olgopoly, also. Economc proft attracts entry! Even under free entry n olgopoly, there s no assurance that producton wll occur where AC s mnmzed (as wth perfect competton). It would be an accdent f a frm wth a downward slopng demand curve produced where AC s mnmzed. If t dd, t would have to make excess profts. =(P*-AC)Q* p * $ p * AC Q * Q * MR MC AC Q D Q D Mnmzng AC - Economc proft >, Q restrcted, prce hgh, transfer of consumer surplus to frm! In ths case, no excess capacty (Mnmum AC); but economc proft (frms have ncentve to enter). $ MC Non-mnmzng AC - Zero economc proft, Q stll restrcted AC because of negatvely sloped demand curve and the resultng separaton of MR=MC from p! In ths case, excess capacty MR (not at mnmum AC), but zero economc proft. When demand slopes downward, the frm must ether have excess or excess capacty or both. In both cases, Q s restrcted and p s elevated relatve to the perfectly compettve soluton (P=MC). The downward slopng demand curve for the frm may result from dfferentated products ( p q ) or n the case of homogeneous olgopoly few frms n ndustry ( P q ). Free entry wll result n zero profts, but olgopoly normally does not have free entry.
Monopolstc Competton Large n; many small frms. Free entry. Product dfferentaton means frm demand curve slopes downward slghtly (farly elastc) Economc profts are zero (free entry) The locaton of the demand curve depends on advertsng and the number of compettors and ther actons. Prces may dffer somewhat among frms. Because demand slopes downward, p > MC. The zero proft condton determnes the number of frms. A frm s demand curve wll shft because of entry and ext untl zero proft s earned. Excess capacty exsts n each frm (not at mnmum AC), whch s the prmary problem wth monopolstc competton. q s restrcted and p s hgh relatve to perfect competton (p=mc). $ Start wth d 1, wth q 1 demanded at p 1. p 1 MC AC p d q q 1 q d 1 Determned by MR 1 (not shown n graph) = MC. Excess proft s earned by frms n the ndustry, so other frms enter, eventually reducng demand for ths frm to d where zero proft s earned at q and p where MR =MC. Each frm n the ndustry has excess capacty (producng at hgher than mnmum AC).
Contestable Markets Some economsts have suggested that t s not the actual entry of frms that constrans profts. Rather, t s the threat of entry that may constran profts. If a market s contestable, frms already n the ndustry may lower profts to zero as a barrer to entry. Monopoles and olgopoles may be constraned to lower prces f they are n contestable markets (constraned by threat of entry). For example, OPEC may want ol prces to declne so the Unted States, Brton, and others do not develop alternatve sources of energy or ncrease ol exploraton. Thus, perfect competton may not be the only avenue to low or zero economc proft. Frms n contestable markets stll have excess capacty and restrct Q so that P > MR = MC. Contestablty may mean that frms may rad an ndustry by enterng even where P = AC ( = ) and attempt to garner a large market share quckly by under prcng exstng frms, movng down ther downward slopng AC curves (hopng to make a proft eventually). Ths actvty requres low fxed costs, low start-up cost, and low shut-down costs. These condtons are very restrctve. They mght occur where captal equpment could be leased, unsklled labor could be hred easly, and brands are not very mportant. Thus, equlbra for frms may not be stable f the market s hghly contestable. Exstng frms may have to lower and rase prces frequently to forestall entry. The entry forestallng prce may be the key proft constrant to exstng frms.