Post on 19-Dec-2015
transcript
In Bertrand’s model of oligopolyA) Each firm chooses its quantity as the best response to
the quantity chosen by the other(s).B) Each firm chooses its price as the best response to the
price chosen by the other(s).C) The firms set quantities sequentially. The second firm’s
quantity is the best response to the first firm’s quantity.D) The first firm sets a quantity. The second firm follows
by setting a price.E) The firms jointly set the price that maximizes industry
profits.
Ex 42.2 (a joint project)
Two players, choose effort levels x1 and x2
between 0 and 1. Cost of effort to player i is xi
2
Part a) Total output is 3x1x2. They divide output equally.Payoff to Player 1 is:
Part b
• Total output is 4x1x2 and is split between two players.
• Cost of effort xi is c(xi)=xi
• Payoff to player 1 is:
Ex 58.2 (Cournot)
• Two firms, linear inverse demand function P=a-Q=a-q1-q2. Firms have constant marginal costs, c1 and c2
• Profit function for firm 1 is:
Ex 59.1 (Cournot 2)
• Linear inverse demand P=a-Q• Quadratic Cost function: C(qi)=qi
2
• What is profit function for firm 1?
Bertrand model
• Each player does best response to other’s price.
• Constant marginal cost • Buyers will purchase only from seller with
lowest price. If prices are equal, demands are split.
• What can be an equilibrium?
Player 2’s best response
• If Player 1 plays heads with probability p>1/2, what is Player 2’s best response?
• What if p<1/2?• What if p=1/2