Payoff matrix and profit maximising help

Hi there,

I need to revise for my upcoming examinations but the teacher has failed to put up solutions for the following two questions. I would be grateful for any help on this. many thanks.

<b>Question 1</b>

Consider the cost functions faced by a duopoly comprising two firms: A and B:

CA = 12 + qA, where CA denotes cost in dollars and qA is the quantity in kilograms

Firm B:

CB = 12 + qB , where CB denotes cost in dollars and qB is the quantity in kilograms

The demand function is given by

P = 100 – Q, where Q = industry output = qA + qB

REQUIRED:

a) Calculate the profit maximising level of output qA and qB for firms A and B, respectively.

b) Calculate the price P at the above level of output.

c) Calculate the profits made by each of the firms, Firm A and Firm B

d) If Firm A holds output at qA = 23, and Firm B also keeps output at qB = 23, Calculate the profits made by each of the firms, Firm A and Firm B

e) Point out the salient aspects of a comparison between output and profit levels in (c) and (d)

above.

f) Is the output level qA = qB = 23 a Nash equilibrium?

<b>Question 2</b>

Consider the following payoff matrix between two bakeries:

Please click here to see the table:

http://img849.imageshack.us/img849/659/shanti.png

Choose the best answer from the list below, and give reasons for your choice:

a) The Nash equilibrium is not a pareto optimum

b) The Nash equilibrium is a pareto optimum

c) Airline A’s dominant strategy is to cut price

d) Airline B has no dominant strategy.

Once again, many thanks in advance for anyone who can help. :)