Producer_surplus_in_practice_630_430 - Producer Surplus in...

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Producer Surplus in Practice Consider a two-input, single-output production process. One of the inputs is assumed to be firm- owned and the other purchased. Input supplies are described by upward sloping input supply functions. Consider a technology that can be described by a generalized Cobb-Douglas production function: Q = G a α b β , 0 < α, β < 1 (1) P a = PαG a α-1 b β (2) P b = PβG a α b β-1 (3) where Q is production, a is the amount of firm-owned input, b is the amount of purchased inputs, G is the technological efficiency coefficient for production, α and β are the production elasticities, P is the price of output, P a the price of firm-owned inputs, and P b is the price of purchased inputs. The generalized Cobb-Douglas function allows only for a unitary elasticity of input substitution and so the input cost shares remain constant as relative input prices change. The economies of scale properties of the production process are determined by the sum of the production elasticities. The production process is characterized by constant, decreasing or increasing economies of scale depending on whether α + β is equal to, smaller than, or greater than one, respectively. Equations (2) and (3) are the profit-maximizing first-order conditions of a perfectly competitive industry. Collectively, equations (1), (2) and (3) represent the firm supply response curve. This particular formulation of supply has the advantage over a conventional supply curve in that supply response independent of input price changes can be determined. The associated cost function is (4) β α 1 BQ C(Q) + = where β α β b β α α a β α α β α β β α 1 P P β α β α G B + + + - + + - + = and P a and P b are the prices of inputs a and b, respectively. The marginal cost function gives, for each level of output, the change in total costs as output is increased: (5) β α AC(Q) Q C(Q) β α 1 BQ β α 1 MC(Q) 1 β α 1 + = + = + = - + The marginal cost function can be used to demonstrate the conditions under which the supply curve can be used as a basis for producer income measurement, and how these conditions depend on: (i) 1
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the returns-to-scale properties of technology; and (ii) price adjustments in input markets (we ignore the existence of a fixed factor in the analysis). The supply curve elasticity can be derived by setting P = MC and differentiate with Q, multiply by Q/P and inverting (assuming input prices are fixed): η s = (α + β)/(1 – α - β) If the firm (industry) operates under constant returns to scale, then α + β = 1. In this case, marginal cost is equal to average cost. Since in equilibrium, marginal costs equal output price, average costs also equals output price and income to producers is zero. The marginal cost curve is a horizontal line and producer surplus would be measured to equal zero. Perfect competition in combination with constant returns to scale and no fixed factor of production results in zero producer income. Assuming constant returns to scale is a very restrictive assumption because it means producer
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This note was uploaded on 02/22/2009 for the course ECON 4300 taught by Professor Degorter during the Spring '09 term at Cornell.

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Producer_surplus_in_practice_630_430 - Producer Surplus in...

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