# Lagrangean Equation and Maximizing Subject

Not what you're looking for?

Consider the problems of maximizing u(x) subject to px = y and maximizing v(u(x)) subject to px = y, where v(u) is strictly increasing over the range of u. Prove that x* solves the first problem if and only if it also solves the second problem.

If this proof is in the Mas-Collel text or Varian text, let me know and I can look it up.

##### Purchase this Solution

##### Solution Summary

The solution applies the Lagrangean equation for maximizing problems. The Mas-Collel and Varian text is used as a proof.

##### Solution Preview

Please refer to the attachment.

Consider the problems of maximizing u(x) subject to px = y and maximizing v(u(x)) subject to px = y, where v(u) is strictly increasing over the range of u. Prove that x* solves the first problem if and only if it also solves the second problem. If this proof is in the Mas-Collel text or Varian text, let me know and I can look it up.

To solve the first problem: maximizing u(x) subject to px = y

Assuming x is a one variable commodity bundle,

Lagrangean equation: L = u(x) - b(px-y)

First order ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Pricing Strategies

Discussion about various pricing techniques of profit-seeking firms.

##### Basics of Economics

Quiz will help you to review some basics of microeconomics and macroeconomics which are often not understood.

##### Economics, Basic Concepts, Demand-Supply-Equilibrium

The quiz tests the basic concepts of demand, supply, and equilibrium in a free market.

##### Economic Issues and Concepts

This quiz provides a review of the basic microeconomic concepts. Students can test their understanding of major economic issues.

##### Elementary Microeconomics

This quiz reviews the basic concept of supply and demand analysis.