Two firms compete simultaneously as follows. Firms A and B each selects an output

level QA or QB. Neither Firm observes the output selected by its rival. The cost of

producing Q units of output is 10Q for Firm A and 15Q for Firm B. When outputs

(QA, QB) are selected, the price per unit output (for each firm) is given by

P(QA, QB) = 100 5(QA + QB).

i) (5 points) For any output QA, find the profit-maximizing choice of output (Ie. Best

Response) of Firm B.

ii) (5 points).For any output QB, find the profit-maximizing choice of output (Ie. Best

Response) of Firm A and draw the best responses of each firm in (QA, QB) space.

iii) (5 points) Find the Nash Equilibrium choice of output of each firm

2. Two firms compete simultaneously as follows. Firms A and A each selects a price PA or

PB. Neither Firm observes the price selected by its rival. The cost of producing Q units

of output is 10Q for Firm A and 10Q for Firm B. When prices (PA, PB) are selected,

the price per unit output (for each firm) is given by

QA(PA, PB) = 100 + DPB 5PA,

QB(PA, PB) = 100 + DPA 5PB

where D is a positive number strictly below 5.

i) (5 points) For any price PA, find the profit-maximizing price (Ie. Best Response)

of Firm B. Do the same for firm A for a price PB.

ii) (5 points) Find the Nash Equilibrium choice of price of each firm. (It will depend

on D).

iii) (5 points) Describe what happens to the Nash Equilibrium in prices a) as D goes

to 0 and b) as D goes to 5.