Consider the market where there is product differentiation with two firms. The firms are choosing prices p1 and p2 and have demands given by
q1 = 40 - 0.5 p1 + p2
q2 = 60 - 2 p2 + p1
a) Assuming zero marginal and zero fixed costs, what are the firms' best response functions, that is best price of firm 1 given price of firm 2, and best price of firm 2 given price of firm one.
b) What are the equilibrium levels of prices, and then the resulting quantities, and profits? (do not set p1 equal to p2 as this is not necessarily the case, in a) you get two equations in two unknowns, so please solve for p1 and p2 here.)
c) Why do the firms get different profits in b)? Don't they have the same costs? Please explain.