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Intergalactic Business Machines (IBM) and Compulsive Computers (CC) are the only two producers of the new Photon PCs. The market demand is P = 49,502 - Q IBM and CC (denote with a subscript of I and C respectively) have the following cost structure TCI = 50,000,000 + 2QI + 0.5QI 2 TCC = 70,000,000 + 2QC + QC 2
a) Set up the profit function for IBM, and solve for the FOC. Do the same for CC. The "conjectural variation" component should be present.
b) Assume both IBM and CC are Cournot firms. Solve for the Nash equilibrium (P, QI, πI, QC, πC). c) Suppose you are the CEO of IBM. Your "subjective" belief is that CC is a "wimp" in the sense that for every additional unit of output you produce, they will decrease their output by 0.5 units. Translate this into the "conjectural variation" term. Assume CC is still behaving as a Cournot firm. Solve for the new equilibrium.
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