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Suppоse there аre three firms prоducing а hоmogeneous good, eаch with a cost function given by , . Firms are playing an infinitely repeated game, facing a market demand given by , where . Both firms discount profits with a common discount factor . Suppose that competition is through prices. a) (10 points) If firms were to collude, what would market price and total market output be? If firms were to split production and profits into equal parts, how many units would each firm be producing? Hint: Set up the monopolist’s problem. b) (4 points) What would each firm’s profits for the period be? And what will be the total discounted profit for each firm? c) (6 points) For which value of will a firm be indifferent between honoring a collusive agreement or cheating on it?
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