2PropertiesDemand

2PropertiesDemand - Demand Properties: Summary Let u...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Demand Properties: Summary Let u represent a continuous preference relation % on R L + . In what follows assume that u is continuous and locally nonsatiated. For ( p, w ) >> 0, define d ( p, w ) = { x ∈ B ( p, w ) | u ( x ) ≥ u ( y ) for all y ∈ B ( p, w ) } , where B ( p, w ) = { x ∈ R L + | p · x ≤ w } . For ¯ u ∈ Range ( u ) and p >> 0, define e ( p, ¯ u ) = min x ∈ R L + p · x (1) subject to the constraint that u ( x ) ≥ ¯ u . Theorem 1. For every ¯ u ∈ Range ( u ) • e ( · , ¯ u ) is nonincreasing on R L ++ ; • e ( · , ¯ u ) is homogenous of degree 1 on R L ++ ; • e ( · , ¯ u ) is concave on R L ++ . Let h ( p, ¯ u ) be the set of solutions to (1). The next result follows from Theorem 1 and Shepard’s Lemma. Corollary 1. ( Properties of h ). For every ¯ u ∈ Range ( u ) • h ( · , ¯ u ) is homogeneous of degree 0 on R L ++ ; • If e ( · , ¯ u ) is C 2 (implying h ( p, ¯ u ) is single-valued and C 1 ), then the matrix...
View Full Document

This note was uploaded on 11/19/2010 for the course ECON 202 taught by Professor Schlee during the Spring '10 term at ASU.

Page1 / 2

2PropertiesDemand - Demand Properties: Summary Let u...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online