E1)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(Qdis quantity demanded), and that there are2firms competing in quantities. Both have no fixed costs and a constant marginal cost. Firm 1 has a marginal costc1, 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 optimalq1ifq2=100,a=4,b=0.01,c1=2, andc2=1. (Note that this is not necessarily an equilibrium.)

Q1=?

E2)Solve for the quantity produced by each firm and the equilibrium price. To verify that you have found the correct equilibrium, computeq1,q2, andpifa=4,b=0.01,c1=2, andc2=1.

Q*=?

Q2*=?

P*=?

E3)Find the equilibrium price and the quantity produced by each firm if they compete in prices (Bertrand competition). (Assume the parameters given above.) pis close to what value?

a)C1

b)None of the above

c)C2

d)C1+C2/2

e)0

E4) Q1 is close to what value?

a)0

b)None of the above

c)a/b-C/b1-C2/b

d)a/b-C1/b

e)a/b-C2/b

E5)Q2 is close to what value?

a)a/b-C1/b

b)a/b-C1/b-C2/b

C)a/b-C2/b

d)None of the above

e)0

E6)How does this equilibrium compare to the perfectly competitive case (if firms sold at their marginal cost as though they faced perfect competition)?

a)Bertrand competition results in an efficiency gain relative to perfect competition

b)Bertrand competition results in an efficiency loss relative to perfect competition

E7)Now, let's go back to the case where all firms have the same cost function. In class we saw the Cournot competition model for two firms. Now, we are going to get you through the Cournot model with three firms. Assume that demand for a good is given byp=abQd, and that there are3firms competing in quantity with a constant marginal costc

Q1=?

E8)In the three-firm case, what will be the equilibrium price and the total quantity produced in the market?

To verify that you have found the correct equilibrium, computepandQifa=4,b=0.01, andc=2.

p=?

Q=?

E9)How does this equilibrium compare to the perfectly competitive case?

a)Cournot competition results in an efficiency gain relative to perfect competition

b)Cournot competition results in an efficiency loss relative to perfect competition

E10)Intuitively, what will happen in this market when the number of firms goes to?

a)The market converges to perfect competition

b)None of the above

c)Efficiency losses become arbitrarily large

d)Cournot competition will become the more realistic model

e)Price will approach zero