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A perfectly competitive, profit maximizing firm hires capital and labor at competitive prices r and w. In the long run, the firm operates at minimum average cost. Total cost is the sum of the resource expenditures i.e. (rK +wL) and output (Q) is produced according to the production function: Q=K^α L^β average cost can therefore be expressed as:
AC = (rK +wL)/K^α L^β
a. Determine mathematically the amount of capital and labor that will minimize average cost.
b. Provide an explanation for your results in part a
c. Show second order conditions for the minimum
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