Revision as of 05:32, 26 September 2004 edit Patrick (talk \| contribs) Edit filter managers, Administrators 68,638 edits If u is continuous and no commodities are free of charge, then x(p, w) is nonempty. ← Previous edit		Revision as of 05:41, 26 September 2004 edit undo Patrick (talk \| contribs) Edit filter managers, Administrators 68,638 edits for now use link Weierstrass (is it one of the theorems mentioned there?) Next edit →
Line 6: Finding x(p, w) is the '''Utility Maximization Problem'''. The solution x(p, w) need not be unique. If u is continuous and no commodities are free of charge, then x(p, w) is nonempty. Proof: B(p, w) is a [[compact space]]. So if u is [[continuous]], then the [[~~Weierstrass~~Karl ~~theorem~~Weierstraß\|Weierstrass]] theorem implies that u(B(p, w)) is a compact subset of <math>\textbf R</math>, and hence contains an upper bound. ==References==

Utility maximization problem: Difference between revisions