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Chapter_5_Income_and_Product_with_Competition

Chapter_5_Income_and_Product_with_Competition - Notes on...

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Notes on Competition and the Distribution of Product In macro the aggregate production function is typically used and it is assumed that the competitive equilibrium aggregates will satisfy it. Further, it is assumed that the rental price of a factor of production is equal to the partial derivative of the aggregate production function. The purpose of these notes is to provide some justifications for these assumptions. Proposition: If factor markets are competitive, the competitive equilibrium output is the maximum output F(K,N). Further, factor payments exhaust total product; that is Y = r K + w N where Y is the competitive equilibrium aggregate output, r is the equilibrium rental price of capital and w is the equilibrium rental price of labor. Proof: Let z = {z kn } be a competitive equilibrium production plan. For all plant technologies, (1) f kn – r k – w n 0. If this were not the case there would be a profit opportunity, which is inconsistent with equilibrium. If the inequality is strict for some (k,n) type plant, z
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