1 7. Suppose that for some reason we were interested in studying solutions to the following problem: A firm produces a single output y from N inputs x = (x1 , • • • , xN) . The firm is given a certain budget that it can spend on inputs, and the firm produces as much output as it can given that budget. Letting B be the budget and supposing the firm is described by a production function f (x ) and that the firm is competitive and faces factor prices w, we can define y* (w, B) = max{f (x) :w ·x ::.; B}. Devise a theory concerning this problem in the spirit of the results we have given concerning partial derivatives of y* and solutions to the problem just posed.

1 7. Suppose that for some reason we were interested in studying solutions to the following problem: A firm produces a single output y from N inputs x = (x1 , • • • , xN) . The firm is given a certain budget that it can spend on inputs, and the firm produces as much output as it can given that budget. Letting B be the budget and supposing the firm is described by a production function f (x ) and that the firm is competitive and faces factor prices w, we can define y* (w, B) = max{f (x) :w ·x ::.; B}. Devise a theory concerning this problem in the spirit of the results we have given concerning partial derivatives of y* and solutions to the problem just posed.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.4P

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