Payoff matrix and profit maximising help
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.
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
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
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)
f) Is the output level qA = qB = 23 a Nash equilibrium?
Consider the following payoff matrix between two bakeries:
Please click here to see the table:
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. :)