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1. (16 points) Assume the firm produces output using two factors, x, and x, , in the long run. Derive the firm's cost function and

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1. (16 points) Assume the firm produces output using two factors, x, and x, , in the long run. Derive the firm's cost function and graphically illustrate that cost minimization is a necessary but not sufficient condition for profit maximization within the context of a two-stage optimization

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