Book contents
- Frontmatter
- Contents
- Preface
- PART I SOME BACKGROUND
- PART II MODELING INDIVIDUAL CONSUMER AND PRODUCER BEHAVIOR
- Chapter 2 Individual consumer behavior: Direct and indirect utility functions
- Chapter 3 Individual consumer behavior: Expenditure and distance functions
- Chapter 4 Individual consumer behavior: Further useful relationships and formulations
- Chapter 5 Producer behavior
- Chapter 6 Consumer and producer behavior: More useful topics
- Chapter 7 Consumer theory with many constraints
- PART III APPLYING THE MODEL OF INDIVIDUAL BEHAVIOR
- Epilogue
- Bibliography
- Author index
- Subject index
Chapter 2 - Individual consumer behavior: Direct and indirect utility functions
Published online by Cambridge University Press: 11 September 2009
- Frontmatter
- Contents
- Preface
- PART I SOME BACKGROUND
- PART II MODELING INDIVIDUAL CONSUMER AND PRODUCER BEHAVIOR
- Chapter 2 Individual consumer behavior: Direct and indirect utility functions
- Chapter 3 Individual consumer behavior: Expenditure and distance functions
- Chapter 4 Individual consumer behavior: Further useful relationships and formulations
- Chapter 5 Producer behavior
- Chapter 6 Consumer and producer behavior: More useful topics
- Chapter 7 Consumer theory with many constraints
- PART III APPLYING THE MODEL OF INDIVIDUAL BEHAVIOR
- Epilogue
- Bibliography
- Author index
- Subject index
Summary
It is known that utility functions are themselves the consequences of assumptions, or axioms, imposed on individuals' rankings over commodity bundles. The literature usually begins by demonstrating the existence of a direct utility function U(q) and proceeds from there. It transpires that this is not a convenient strategy for analyzing demand functions of the form qi = xi(P,M), but is admirably suited for analysis of inverse demand functions of the form Pi/M= φi,(q). The key result here is known as the Hotelling-Wold identity. If one develops the observation that the maximum attainable utility in a competitive situation is determined by the prices faced and income received, one arrives naturally at the idea of an indirect utility function, V(P, M). Just as the Hotelling-Wold identity generates inverse demand functions from U(q), so a similar result, Roy's identity, generates demand functions from V(P, M). Under certain assumptions, of which convexity of preferences is a crucial one, U(q) and V(P, M) are dual functions – that is, they offer alternative ways of representing a given set of preferences. We are then free to choose whichever is more convenient for the purpose at hand, because both contain precisely the same information, the one in terms of quantities, the other in terms of prices.
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- Information
- Duality and Modern Economics , pp. 31 - 62Publisher: Cambridge University PressPrint publication year: 1992