Two firms produce differentiated products and the demand is given by

q1 = 8 - p1 + p2/3 ;

q2 = 8 - p2 + p1/3 .

Both firms have constant marginal cost c = $2. Firm 1 chooses p1 first, followed by firm

2's choice of p2.

a. Derive rm 2's best-response function and calculate equilibrium prices, quantities

and profits

b. Now suppose a third firm with the same marginal cost enters and the demand functions become

q1 = 8 - p1/2 + p2+p3/3 ;

q2 = 8 - p2/2 + p1+p3/3 ;

q3 = 8 - p3/2 + p1+p2/3

Firm 1 keeps its leadership and firms 2 and 3 make decisions simultaneously, after

observing p1. What are the equilibrium prices, quantities and profits for these firms?