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Joe is an \empire builder". That is, his goal is to produce and sell as much as possible. However, his stockholders impose the constraint that...

Joe is an empire builder". That is, his goal is to produce and sell as much as
possible. However, his stockholders impose the constraint that he looses no money.
He operates using the production function y = f(x), and faces parametric prices
p for his (single) output and (vector of) inputs. The production function is with
positive marginal products.
(a) Set up Joe's problem and state the rst-order conditions.
(b) Is the nonnegativity constraint on pro t binding? Why or why not?
(c) Interpret the 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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