The social welfare under stochastic demand
Cang, Ngyuen Minh
Carrick, Paul M.
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The purpose of this paper is to continue to develop the social welfare model of Brown and Johnson (The American Economic Review, March, 1969, page. 119). We introduce a normal distribution (u,o(2)) with mean u, variance o(2) as the characterization of the risk that additively enters the product demand function facing the firm. The optional price still equals the short run marginal operating cost. We observe the optimal output when the mean or variance of risk increases, using the least-square method we estimate the linear relation between the optimal output and mean or variance of risk. In the second model we introduce the expected monopoly profit and observe how both the optimal price and output vary as the mean or variance of risk changes. As the final step, we compare the results of two kinds of models, and find that which the least affected by risk.
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