Finding statistical distribution of quantity and price

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Reference no: EM132201022

Question: You manage an airline that operates on the route from Tokyo to Paris. You have one competitor. You compete in quantities (Cournot duopoly). Assume that neither you nor your competitor has any fixed cost. Both your and your competitor's marginal cost (MC) can end up being either 2 or 6, depending on circumstances such as personnel turnover and oil price that you cannot foresee in advance. You need to decide how many planes to fly on the route, i.e., you need to decide on your quantity for the next year before you know the analogous decision of your competitor. Before you decide, you will be aware of your MC, but not of the MC of your competitor. You believe that your competitor's MC is going to be 2 with probability 1/2 and it is going to be 6 with probability 1/2. Assume that your competitor is in a symmetric position. The overall market demand is given by Q = 20 âˆ' P .

1. Suppose that the realization of your competitor's MC is independent of your own realization (for example, due to independent personnel turnover issues). Suppose your competitor produces Q1 if his MC is low and Q2 if his MC is high. What is your best response as a function of Q1 and Q2 if your own MC is low and what is it if your own MC is high?

2. Assuming that your competitor thinks alike, what are the Bayesian Nash Equilibrium values of output of each firm if its own MC is low and if its own MC is high? (Hint: assume the equilibrium is symmetric and hence the optimal values of output given a particular level of the MC is the same for both firms.)

3. What is the resulting statistical distribution of quantity and price?

4. Now suppose that the realization of your competitor's MC is the same as your own realization (for example, due to oil price shocks that are common to both firms). Repeat the analysis from parts (a)-(c).

Reference no: EM132201022

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