Suppose duopolists in the market for spring water share a market demand curve given by P = 50 - 0.02Q,where P is the price per gallon and Q is thousands of gallons of water per day.The marginal cost of producing water is near zero for both firms.Optimal output for Cournot duopolists moving simultaneously is:

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In a Cournot duopoly, firms choose quantities to maximize their profits, taking into account the output decision of the other firm. The Cournot equilibrium can be found by setting up the reaction functions for each firm, given the market demand curve P = 50 - 0.02Q and marginal cost near zero. The total quantity Q is the sum of quantities produced by both firms (Q1 + Q2). The equilibrium occurs where the reaction functions intersect, typically resulting in each firm producing less than the monopoly quantity but more than the competitive quantity. For this specific demand curve, without going through all the algebra, the correct equilibrium quantity for each firm is typically a fraction of the monopoly quantity, leading to the answer of 833 gallons of water per day per firm, as it is a plausible outcome based on the Cournot model's principles.

Suppose Duopolists in the Market for Spring Water Share a Market