Two firms compete by selling a differentiated product. Firm 1's product is

considered higher quality but is more costly to produce while firm 2's is the opposite. Specifically,

their demand functions are

q

1

=

20

p

1

+

0.5

p

2

and

q

2

=

10

p

2

+

0.5

p

1

with firm 1's marginal

cost being

MC

1

=

10 and firm 2's marginal cost

MC

2

=

5.

(a)

[35 points]

Solve for the Bertrand equilibrium prices of each firm.