Suppose two firms sell products in a particular market, but consumers do not regard the output of each firm as perfectly identical. The two firms face the following demand curves:

q1

= 30

– 4p1

+ 2p2 q2

= 60

+ 2p1

– 4p2 Each firm has the same constant marginal cost of production, so that c1

=

c2

= $15. Fixed costs are zero.

(a) Write out each firm’s profit function, of the form i

= (pi

– ci

) · qi

, for i =1, 2.

(b) Solve for each firm’s first-order condition, i

/ pi = 0, for i = 1, 2, and use it to solve for each firm’s reaction function.

(c) On a graph with p1 on the horizontal axis and p2 on the vertical axis, graph each firm’s reaction function.

(d) Use the equations of each firm’s reaction function from Exercise 2(b)

to solve for each firm’s equilibrium price pi

, level of output qi and profits i

.

(e) Do firms earn positive profits in equilibrium? Does this result confirm or contradict the Bertrand paradox? Explain your answer.