哈佛大学：《中级微观经济学》（英文版）Lecture 11 Competition and monopoly, some preliminary discussions

Economics 2010a Fa|2003 Lecture 11 Edward L. Glaeser

Economics 2010a Fall 2003 Lecture 11 Edward L. Glaeser

11. Competition and monopoly, some preliminary discussions Monopoly Pricing b. Cournot and Bertrand Oligopoly C. TWo Part Pricing d. Price Discrimination e. Regulation

11. Competition and Monopoly, some preliminary discussions a. Monopoly Pricing b. Cournot and Bertrand Oligopoly c. Two Part Pricing d. Price Discrimination e. Regulation

Standard monopoly result is quite straightforward Q is set to maximize P(Q)Q-C(Q)Which yields P(Q)Q+P(Q)=C(Q)or C(Q) 1+ o aP P(O) Cournot oligopoly-n firms-fixed entry choose q to maximize P(Q+∑9)Q-C(Q) or P(∑)+P(∑9)=CQ) or C"(Q=P(Q)(1+。如)

Standard monopoly result is quite straightforward Q is set to maximize P(Q)Q-C(Q) which yields: P’(Q)QP(Q)C’(Q) or C Q PQ  1  Q P P Q  1  1  Cournot oligopoly– N firms– fixed entry– choose Q to maximize: P Qi  ji Qj Qi  CiQi or P j Qj Qi  P j Qj  Ci  Qi or C Q  PQ1  Qi Q Q P P Q 

or P(Q)=C(Q)-5 thats the markup over marginal cost

or PQ  C Q   Qi Q that’s the markup over marginal cost

Claim: we know that industry profits are lower under cournot oligopoly than under monopoly(assuming identical cost curves) Is it possible that industry output will be lower under cournot oligopoly than under monopoly? Assume identical cost curves and write P(NO()O(N)+P(NO(ND)=C(O(N) Differentiation with respect ton then yields P(NOQ(N+OP (NO(O+NO(N)+ P(NO(O+NO(M)=C(Q@(M Solving this yields

Claim: we know that industry profits are lower under cournot oligopoly than under monopoly (assuming identical cost curves) Is it possible that industry output will be lower under cournot oligopoly than under monopoly? Assume identical cost curves and write: P NQNQN  PNQN  C QN Differentiation with respect to N then yields: P NQQ N  QPNQQ  NQ N  P NQQ  NQ N  CQQ N Solving this yields:

OP(NO)+O2P"(NO) C"(0)-(N+1)P(NO)NOP (NO) If0>P(NQ+OP (NO) then the expression is negative because the numerator is negative and the denominator is positive If P(No)+OP (No>0 then the numerator is positive-lf N(P(NQ+OP(N)>C(0-P(NO) and then the denominator is negative and the whole expression is again negative Second order conditions require that C"(O(N)-2P(NO)>QP (NO) Only if 0<N(P(NQ)+QP (NO)<C(O-P(NQ is the sign reversal possible. What's going on there?

Q N  QP NQQ2PNQ CQN1P NQNQPNQ If 0  P NQ  QPNQ then the expression is negative because the numerator is negative and the denominator is positive. If P NQ  QPNQ  0 then the numerator is positive–If NP NQ  QPNQ  CQ  P NQ and then the denominator is negative and the whole expression is again negative. Second order conditions require that CQN  2P NQ  QPNQ Only if 0  NP NQ  QPNQ  CQ  P NQ is the sign reversal possible. What’s going on there?

To show that overall industry output increases with n, we just need that Q+O(MN>O Or 1>O(N/Q or 1 NP(NO)-NOP"(NO) C"(0)-(N+1)P(NO)-NOP (NQ) or C(O-P(NQ)>0 And thats a fact- so we don t know what happens to individual output, but we know that aggregate output has to go up with the number of firms

To show that overall industry output increases with N, we just need that Q  Q NN  0 Or 1  Q NN/Q or 1  NP NQNQPNQ CQN1P NQNQPNQ or CQ  P NQ  0 And that’s a fact– so we don’t know what happens to individual output, but we know that aggregate output has to go up with the number of firms

Bertrand Competition - competition along prices yields marginal cost pricing Edgeworth conjecture-quantity precommitment bertrand price competition yields cournot outcomes Proved true(essentially) by Kreps Scheinkman rand journal 1983. Proof requires game theory

Bertrand Competition– competition along prices yields marginal cost pricing. Edgeworth conjecture– quantity precommitment  bertrand price competition yields cournot outcomes. Proved true (essentially) by Kreps  Scheinkman, Rand Journal 1983. Proof requires game theory

Obviously, every producer would be better off if they could restrict output to monopoly levels a large literature has thought about the sustainability of these cartels. One side has thought about making cheating observable- the other has thought about the ability of a cartel to punish Assume n independent producers, and an infinite time horizon Write profits as r(0,0 as profits based on own production and production of other firms

Obviously, every producer would be better off if they could restrict output to monopoly levels. A large literature has thought about the sustainability of these cartels. One side has thought about making cheating observable– the other has thought about the ability of a cartel to punish. Assume N independent producers, and an infinite time horizon. Write profits as  Q,Q as profits based on own production and production of other firms

OM is monopoly production (i.e. output that maximizes joint surplus that maximizes N(OM, OM) Oo is each firm acting independently, i. that maximizes T( 20, go just over the first argument Finally, @ c maximizes (@G, OM)just over the first argument Pofits under perfect monopoly are denoted OM, Q Repeated game literature(Abreu, Abreu Pearce and stachetti tells us that a monopoly outcome is not sustainable if

QM is monopoly production (i.e. output that maximizes joint surplus), that maximizes NQM,QM  QO is each firm acting independently, i.e. that maximizes  QO,QO just over the first argument. Finally, QC maximizes  QC,QM just over the first argument. Pofits under perfect monopoly are denoted  QM,QM Repeated game literature (Abreu, Abreu Pearce and Stachetti) tells us that a monopoly outcome is not sustainable if: