Question

Given the Inverse Demand function as P = 1000-(Q1+Q2) and Cost Function of firms as Ci(Qi)...

Given the Inverse Demand function as P = 1000-(Q1+Q2) and Cost Function of firms as Ci(Qi) = 4Qi calculate the following values.
A. In a Cournot Oligopoly (PC, QC, πC)
i. Find the Price (Pc) in the market,
ii. Find the profit maximizing output (Qi*) and
iii. Find the Profit (πiC) of each firm.
B. In a Stackelberg Oligopoly (PS, QS, πS),
i. Find the Price (PS) in the market,
ii. Find the profit maximizing output of the Leader (QL*) and the Follower (QF*), and
iii. Find the Profit of the Leader (πLS) and the Follower (πLS) of each firm.
C. In a Bertrand Oligopoly (PB, QB, πB), (Hint: In Bertrand Oligopolies competition derives the prices all
the way down to the marginal cost)
i. Find the Price (PB) in the market,
ii. Find the profit maximizing output (Qi*) and
iii. Find the Profit (πiB) of each firm.

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