Lecture 3 Models of non-cooperative oligopoly with homogenous products Cooperative oligopoly same as cartels Main assumption in the models discussed here: products are homogeneous: World without brands e Consumers as before assumed to be price takers e Two kinds of market structure o Competition in quantities o Competition in prices Competition in quantities o Cournot model(simultaneous move game)-solve for Nash equilibrium o Stackelberg model(sequential move game)-solve for subgame perfect Nash equilibrium Competition in prices o Bertrand model Model of cournot duopoly e Two firms
Lecture 3 Models of non-cooperative oligopoly with homogenous products • Cooperative oligopoly same as cartels. • Main assumption in the models discussed here: products are homogeneous: World without brands. • Consumers as before assumed to be price takers. • Two kinds of market structure: oCompetition in quantities oCompetition in prices • Competition in quantities: oCournot model (simultaneous move game)- solve for Nash equilibrium o Stackelberg model (sequential move game)- solve for subgame perfect Nash equilibrium • Competition in prices oBertrand model Model of Cournot Duopoly • Two firms
●7(q1)=c;q Inverse demand equation: p(Q=a-bQ ·Q= total output=q+q2 Profit for firm 1 1=P1-c1q1 o Through the demand equation quantity produced by firm 2 affects the profit of firm 1: strategic interaction alI a-bg-c BR=-=0→q 26 alI BR =0→q bq 26 Cournot Nash equlibrium o Mutual best response: Plug equation 2 into equation I or other way round. Cournot Nash equlibrium: 2c;+ 2C+ q1 36 36 Reaction functions plot here
• iii)( = qcqTC • Inverse demand equation: p(Q)=a-bQ • Q = total output = 21 + qq Profit for firm 1 −=Π qcpq 1111 • Through the demand equation quantity produced by firm 2 affects the profit of firm 1: strategic interaction. • )1( 2 0 12 1 1 1 1 − − − =⇒= ∂ Π∂ = b cbqa q q BR • )2( 2 0 21 2 2 2 2 − − − =⇒= ∂ Π∂ = b cbqa q q BR • Cournot Nash equlibrium: oMutual best response: Plug equation 2 into equation 1 or other way round. Cournot Nash equlibrium: • b cca q b cca q 3 2 , 3 2 * 12 1 * 21 1 − + = +− = • Reaction functions plot here
Graphical lllustration of asymmetric Cournot Nash equilibrium in the q1 a-c2 Reaction function of firm2 2b eaction function of firm 1 Cournot N ash eam a-C2/2b a-c1b
1 Graphical Illustration of asymmetric Cournot Nash equilibrium in the q1 q2
Homogeneous firms Cournot duopoly: CI=C2 Output produced by each firm in a symmetric Cournot duopoly d-c equilibrium q 36 e Total output produced in a-c equilibrium g 36 Equilibrium price p a-c ab+26c a+2c a-62 36 36 o Knowing the price in the market and quantity produced by each of the firms: can calculate the profit of each firm d-c 丌1 2 96
2 Homogeneous firms Cournot duopoly: 21 = cc • Output produced by each firm in a symmetric Cournot duopoly equilibrium * q = b ca 3 − • Total output produced in equilibrium * Q = b ca 3 2 − • Equilibrium price * p = 3 2 3 2 3 2 ca b bcab b ca ba + = + = − − • Knowing the price in the market and quantity produced by each of the firms: can calculate the profit of each firm • b ca 9 )( 2 * 2 * 1 − ππ ==
Homogeneous firms Cournot duopoly: Continued o Knowing the price: we can calculate the consumer surplus (CS) Welfare under a homogeneous firms cournot du uop (a-c =CS+兀1+兀2=CS+2 96 o Example: Demand curve Q=1000-1000p c=28cents
3 Homogeneous firms Cournot duopoly: Continued • Knowing the price: we can calculate the consumer surplus (CS) • Welfare under a homogeneous firms Cournot duopoly b ca CS CS 9 )( 2 2 * 2 * 1 − ππ +=++= • Example: Demand curve Q = −10001000 p = 28centsc