Chapter 9: Oligopoly Models PDF

9 ter model of Oligopoly - sweezy oligopoly demand...

9 ter model of Oligopoly - sweezy oligopoly demand 1. C kinked curve model) explain sticky prices - - A prices that infrequently products/services d fferentiated $ Sticky ------ price D Q P - Relevant if competitors respond to price As Relevant if competitors ~ respond to price As their scompetitors keep prices fixed) Pet Q PSteep $ & which demand curve is more elastic ? flatter curve -3 e : in sweezy model , competitors DF match decreases but I match ph price Q plastic demand w/ a flatter curve  · im - - · * Ps Q firm faces demand PhTRd Ds wha wer price the inelastic ↑ - w/ a higher price the firm faces elastic demand p&TRd DF ↑ um - no incentive for the firm to D its price b/C Its TR will decrease W firm keeps its price constant for extended periods of time - sticky price Recall of the 2X of : the slope marginal rev curve is slope inverse demand curve MC z $ MCz MC , ·~ Q corresponds to "Kink" it max output is the same despite sticky price Marginal costs MR curve has a vertical Segment MC can change w/in a range & I affect the It max output (output changeina > - If I Q change in On HW 9 1 need 2 values you. 5) ? 8 ? & MR Q notirms - homogeneous/differentiated product > - firms believe competitors & respond to their actions barriers to entry - Find reaction function Hey : - function that determines a firms It max output given the output of a Competitor 2 firms Duopoly ex : - for 2 firms quantity D / & M Coke pepsi Market inverse demand function : P = 80 - 2Q $ A +C = Mc = 20 1. Find reaction function of each firm. 2 Find It max output of each firm !3 4. industry Q = Q p Coke ; Op = Op Pepsi P = 80 - 2Q p 80 2(Q, Qp) = - + P 80 2Q) 28p = - - P - Q ↓ P - Qc - Coke : TR , = PQ , = 800 , -2Q? - 20pQc = MR , = 80-40-  Set MR c = MC c 80 40 2Qp 20 - - = 40 = 60 - 2Qp ) Q 15-0 , =. 50p Coke's reaction function peps is reaction function Qp = 15 - 0. 5Qc > ) Qc 15-0 5 (15-0 59. OP= IS-0 =.. , Q = 15 - 7 5. + 0. 25Qc 5 0. 750, = 7. Q) = 10 Industry - 80 2Q TR p Q = $40 20 = $800 p. = - = - / Q Qp TC ATC Q $20 =500 + = - =. 20 , - p = 80 - 2(10 + 10) T = TR - TC $40 p = Assume a monopoly P = 80 - 2Q Mc = ATC = $20 TR = P. Q = 800 = 202 Set Mr = MC 80-4 = MR = 80 - 40 = 20 4Q = 60 a = 15 P = 80 - 2(15) P = $50 TR = P - Q = 50 x 15 = $750 $20 = TC = ATC - Q = x 15 T = TR - TC Assume Perfect Competition - Mc = ATC = $20 = MR = P TR = P xQ = $20 x 30 = $600 -600 P = 80 - 2Q TC = ATC +Q = 20 + 30 = 20 = 80-2Q T = TR - TC 20 = 60 Q = 30  #gopely Monopoly Q T 20 15 P $20 $40 $50 TR * 600 * 800 $750 * TC $600 400 $308 # $0 $400 $450 ex : Cournot Duopoly 2 firms - Firm - Firm 2 Market Inverse Demand Function P = 24 - Q Mc , = $g Mc = $4 Find 1. reaction function of each firm. 2 E*Q of each firm 3. Exp 4. TR of each firm Firm 2 P = 24 - (a , - Q2) Set MRz = MC 2 Tr p -0 0 240 0 02 =. = - , , , , , MR Try = P Qy = 2402 P, 02 - 9 ? , 24-20 - R - - = 24-Q-2 : MR2 R = Set MR , = MC , Mc = $8 24 a, 4 24 202 = 20. 02 8 - - = - - 20. = 16 - 02 202 = 20 - Q, 10-0 5 Q Q2 =. , Q 8 = 0 502 -. reaction function Firm 1 =24-4s S Q , = 8- 0 5. (10-0. 50 , Q = 8 - 5 + 0 25Q. , , 3 0 750 = TR. TR , Q, = 4 Q2 = 10 - 0. 9(4) Q2 = S elberi homogeneous/differentiated - * Leader/ Follower ↳ takes the leader's output as a given barriers to entry - (Market) · 20 100 " ex : p = - 40 p = 100 - 2(Q , + Q2) +C = , Mc = 4 p = 100 20, 202 T = 402Mc = 4 - - * start w/ follower Try = P - Q2 = 10092 - 20 , 02 - 202 MRz 100-20-4, :R = Set Mrz = Mc z 100 20. 4 402 = - - 402 = 96 - 20 , Q2 = 24 - 0 50 7.. , 100 p 20. 202 - = - p = 100 - 20. - 2(24 - 0 50. , ) P = 100 - 20. - 48 + Q, P = 52 - Q, 2 Tr = P. Q = 520 -0 , , , , & 5(24) = MR 52-2 , 24 0 R = -... =. , z Q2 = 12 Set MR , = MC , 52 - 20 = 4 20, = 48  P = 100 - 2Q P = 100 2(a , + Q2) - p = 100 - 2(24 + 12) P = $28 Tr , = P. Q , = $28x24 TR , = $672 Tc. = 4. 0 , = 4(24) = 96 T , = Tr , - T) = $672 996 - = 576 , TRz = P. Q = $28 + 12 = $336 = TC 4 12 $48 +02 4 = = + = = # = Trz - T) = $356 - 948 = $288 = Cartel of firms coordinate output decisions group that formally price - = & to Collusion-cooperate reduce output charge a higher price cartels usually found w/ industrus w/ inelastic demand P ↑ inelastic Try. P 0 E C Oll producing & exporting countries -.. > $ Problems : , 11 0 1. In most countries they are illegal 2 Coordination is difficult ↑.. 3 cheat huge incentive to % & the output under a cartel is the same output at a would be produced by a monopoly trans homogeneous - firms competition engage price - in barriers to entry - - firms produce & constant MC P Ultimately , Pz = =.... = MC set Mc = P # Mak a ~ estable - all firms have access to same information firms cannot existing their - lower prices => quickly there costs - are no sunk - irrecoverable Firms in a contestable market have no market power - cannot they Z charge a price above MC If econ it exists > - P * competitors enter until = Mc Economic T = 0 *