ECOS3025 Lecture Notes - Lecture 2: Inverse Demand Function, Sunk Costs, Nash Equilibrium

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Industry consists of few firms that face strategic situation: what each firm does affects the response of. Firms set quantities (choose output levels) in a simultaneous-move game. Each firm takes output level of competitor as fixed and then chooses own output to maximize its profit. its competitors. The extent of market power depends on number of firms in the market as the number grows, the. Cournot-nash price converges to the perfectly competitive market outcome (marginal cost): assumptions: 2 firms (duopoly); homogenous products; demand curve known. The more rivals produce, the less firm produces (strategic substitutes in market). Fir(cid:373)s(cid:859) total (cid:272)ost fu(cid:374)(cid:272)tio(cid:374)s: (cid:2869)=(cid:883)(cid:882)(cid:1877)(cid:2869) and (cid:2870)=(cid:883)(cid:882)(cid:1877)(cid:2870): (cid:2869)(cid:4666)(cid:1877)(cid:2869);(cid:1877)(cid:2870)(cid:4667)=(cid:4666)(cid:889)(cid:882) (cid:1877)(cid:2869) (cid:1877)(cid:2870)(cid:4667)(cid:1877)(cid:2869) (cid:883)(cid:882)(cid:1877)(cid:2869). Fir(cid:373) (cid:1005)(cid:859)s profit-maximizing output level solves (cid:3117)(cid:3117)=(cid:889)(cid:882) (cid:884)(cid:1877)(cid:2869) (cid:1877)(cid:2870) (cid:883)(cid:882)=(cid:882): 2(cid:1877)(cid:2869)=(cid:888)(cid:882) (cid:1877)(cid:2870), (cid:1877)(cid:2869)=(cid:2869)(cid:4666)(cid:1877)(cid:2870)(cid:4667)=(cid:885)(cid:882) (cid:2869)(cid:2870)(cid:1877)(cid:2870) equation 1. Firm 1 maximizes its profit and chooses best output given firm 2 output, and similarly for firm 2. Thus substitute equation 2 into equation 1 : Cne occurs where the reaction curves of each firm intersect.

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