Question

1)Consider the following variation of what biologists call the chicken game:

Two drivers drive towards each other on a collision course

They have to choose whether to swerve or not

If they both swerve then each one of them will get a payoff of zero.

If no one swerves then both die which will give them a payoff of -100 (the value of their lives)

If one driver swerves and the other does not, the one who swerved will be called a "chicken," meaning a coward. The one who swerves will get a payoff of -1, while the one that drove straight will get a payoff of 1.

The matrix form of this game is given below.

Swerve Straight

Swerve a,b c,d

Straight e,f g,h

What values do these payoffs take?

a=?

b=?

c=?

d=?

e=?

f=?

g=?

h=?

2)Acme and Tartine are identical bakeries and are the only suppliers of baguettes in San Francisco. They have agreed to form a cartel: they jointly sellQ=16baguettes and chargep=9.

Each bakery shall produce half of the joint quantity. Acme is tempted to cheat on the cartel agreement and increase its own production by2 units. Acme knows that if they cheat, there is a 50% chance Tartine will catch them and force them to pay a fine ofF that is taken out from their profits. If the market demand curve isQ=342P and the marginal cost of producing baguettes is constant and equal to1(assume there are no fixed costs), how big doesFhave to be to make Acme indifferent between cheating and not?

F=?

3)In lecture we saw the Cournot competition model for two firms with the same cost function. Now, we are going to consider asymmetric cost functions. Assume that demand for a good is given byp=abQd (Qd is quantity demanded), and that there are2 firms competing in quantities. Both have no fixed costs and a constant marginal cost. Firm 1 has a marginal costc 1, and firm 2 has a marginal costc2. We have thata > c1> c2.

Find the reaction functions of firms 1 and 2 in this market: how the optimal quantity produced depends on the quantity produced by the other firm.

To verify that you have found the correct reaction functions, compute the optimalq1 ifq2 =100,a=4,b=0.01,c1=2, andc2=1. (Note that this is not necessarily an equilibrium.)

q1=?

Solve for the quantity produced by each firm and the equilibrium price.

To verify that you have found the correct equilibrium, compute q1,q2, andpifa=4,b=0.01,c1=2, andc2=1

q*1=?

q*2=?

p*=?