Firms 1 and 2 produce differentiated products and choose their prices (p1 and p2) simultaneously. The following information describes firm 1's linear demand curve:

If both firms set p1 =p2 =0, firm 1 will give away q1 =60units.

Firm 1's demand q1 decreases by 2 units when they increase their own price p1 by $1. Firm 1's demand q1 increases by 1 unit when firm 2 increases the price p2 by $1.

There is no cost to production, so MC = 0.

a) Write firm 1's demand q1(p1,p2) as a function of both prices p1 and p2.

b) Write firm 1's profits 1(p1,p2) as a function of both prices p1 and p2.

c) What is firm 1's best response p1 as a function of firm 2's choice p2?

d) Assume the demand curves for firm 1 and firm 2 are symmetric. What are the Nash

equilibrium prices p1 and p2? What are the quantities and profits of each firm?