The Firm That Stays Out
Two firms choose quantities q₁, q₂ ≥ 0 simultaneously. The market price is P = max(0, 120 − q₁ − q₂). Firm 1 has marginal cost 0 and firm 2 has marginal cost 70; there are no fixed costs. Firms maximise profit and play the Nash equilibrium. What is firm 1's equilibrium profit?
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Source: Original problem written for AxiomIQ.