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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.
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can you provide me the problem with the solution base above?
Each firm in a competitive research industry can undertake one project at a constant cost, f = $960 to try and develop a certain new product. The inverse demand curve for the new
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