Uncertain demand, Applied Statistics

Consider a Cournot duopoly with two firms (fi rm 1 and fi rm 2) operating in a market with linear inverse Demand P(Q) = x Q where Q is the sum of the quantities produced by both rms and x is a parameter that captures the level of demand in this industry. Firms have 0 cost of production. The demand for the good is uncertain: it is high, x = xH, with probability 1/3 and it is low, x = xL (< xH), with probability 2/3. Furthermore, information is asymmetric: rm 1 knows whether demand is high or low but rm 2 does not. All this is common knowledge. The two rms simultaneously choose quantities.

(a) What are the actions, types, beliefs and payo s of both rms?

(b) Suppose that 7xL > xH. Find the Bayesian Nash equilibrium of the game.

(c) Compare the quantities chosen by rms 1 and 2. Interpret the result.

Now, call q1-H and q2-H the quantities chosen by rms 1 and 2 if the demand is high under complete information (that is, when both know it). Also, call q1-L and q2-L  the quantities chosen by rms 1 and 2 if the demand is low under complete information (that is, when both know it).

(d) Find (q1-H ,  q2-H, q1-L , q2-L) Compare these quantities with the quantities determined in the case of incomplete information. Interpret the result

Posted Date: 3/14/2013 3:44:11 AM | Location : United States

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