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Maximizing Profit Function

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Consider the problem of maximizing the profit function (pi)= pY -wL subject to the production function Y= L to the alpha (as the exponent) where alpha E (epsilon) (0,1). derive the profit function and confirm that Hotellings Lemma is met. What happens if alpha = 1?

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This solution discusses maximizing a profit function.

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First we'll check that Hotelling's Lemma is satisfied. The profit function relates factor prices to the maximum profit levels achievable at those output prices and factor prices. It is characterized by Hotteling's Lemma, which states that differentiating the profit function with respect to output price yields output quantity, while differentiating it with respect to price of a particular factor yields (the negative of) the ...

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