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There are two firms competing in quantity. Firm 1 and 2 set their quantities supplied, q1 and q2, respectively. The production costs are zero. The market price is given by
where a ∈ (0,1/2) and b ≥0. Note that the inverse demand function is kinked at the point (1 - a, a).
This is a simple one-shot game. The firms simultaneously set their quantities. The objective of each firm is to maximize its profit, that is,
1. Derive the pure strategy Nash equilibrium and the equilibrium profits when b = 0.
Ans. 0.5 each
2. Derive the pure strategy Nash equilibrium and the equilibrium profits when b > 0. Note that two pure strategy Nash equilibria may exist.
Ans. All or nothing
3. Dose an increase in b benefit the two firms? This means that you should explain whether or not at increase in the demand size benefits the firm.
Design an investigation that details the following six components: Note: If one or more of the following components do not apply to your investigation, explain why each does n
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Your division has been allocated $15M for capital projects for the coming year. You've been able to identify five potential projects, as outlined in the table below, each of which
Print out your results and bring them with you to the midterm as there will be additional questions on the midterm related to this analysis. You must hand in your take-home by the
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A girl named Alice fell asleep during a discussion about the difference quotient. She did not think it could possibly have anything to do with real life. While dreaming she saw
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