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Q. Joe is an empire builder". That is, his goal is to produce and sell as much as possible. However, his stockholders impose constraint that he loses no money. He operates using production function y = f(x) and faces parametric prices p for his (single) output and (vector of) inputs. Production function is with positive marginal products.
(a) Set up Joe's problem and state rst-order conditions.
(b) Is no negativity constraint on profit binding? Why or why not?
(c) Interpret Lagrangian multiplier. What is its sign?
(d) Show that Joe's supply curve slopes upward.
(e) Show that Joe's output is a decreasing function of all input prices.
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