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 NQQ2PNQ CQN1P NQNQPNQ If 0 P NQ QPNQ then the expression is negative because the numerator is negative and the denominator is positive. If P NQ QPNQ 0 then the numerator is positive–If NP NQ QPNQ CQ P NQ and then the denominator is negative and the whole expression is again negative. Second order conditions require that CQN 2P NQ QPNQ Only if 0 NP NQ QPNQ CQ 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 NN 0 Or 1 Q NN/Q or 1 NP NQNQPNQ CQN1P NQNQPNQ or CQ 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 NQM,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: