lecture17

# Bounded the sets dimensions are finite lecture 17

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ssociating points in a set with another set of points. – Closed: The set contains its edge. – Convex: If the set contains two points, it also contains all points on the line connecting the two points. – Bounded: The set’s dimensions are finite. Lecture 17 Econ 11--Spring 2001 Example for a Univariate Mapping 13 – A continuous function is a continuous mapping. – The set X = [0,1] is closed, bounded, and convex. • A fixed point of f(x) is a point x* such that f(x*)= x*. • On a graph of f(x), it’s fixed points are on the 45o line. Lecture 17 Example: Brouwer’s Fixed Point Theorem f (x ) Econ 11--Spring 2001 14 Back to Walras’ Economy • The next step to finding an equilibrium is to “normalize” the n prices so that they add to one. 45o line 1 – For the new price set, divide each price by the sum of all the prices. P′ = Pj ∀j j f(x*) n ∑P i i =1 – Redefining prices in this way will not change demand because of zero degree homogeneity. x* Lecture 17 1 Econ 11--Spring 2001 x 15 Lecture 17 Applying Brouwer’s FP Theorem Econ 11--Spring 2001 An Equilibrium Exists • After normalizing prices, the pr...
View Full Document

## This note was uploaded on 02/11/2012 for the course ECON 51 at Stanford.

Ask a homework question - tutors are online