104A_Utility

# 104A_Utility - ject to a budget constraint Reconciliation...

This preview shows pages 1–4. Sign up to view the full content.

Utility Theory . Classical Utility Theory . Utility (satisfaction level) from consump- tion bundle X : U ( X )= U 1 ( X 1 )+ · · · + U n ( X n ) . Measurable (up to an arbitrary origin and unit of measurement; i.e. cardinally measurable ). Marginal utility of good i : MU( X i )= dU i ( X i ) dX i . Optimization condition : MU i ( * X i ) P i = MU j ( * X j ) P j for all i, j.

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

View Full Document
Modern Utility Theory . A function U represents the preference or- dering if U ( ¯ X ) >U ( ˆ X ) ⇐⇒ ¯ X is preferred to ˆ X and U ( ¯ X )= U ( ˆ X ) ⇐⇒ ¯ X is indi f erent to ˆ X. If U represents the preference ordering, so does any transformation of U that pre- serves (a) and (b); i.e. utility is only ordinally measurable.
The consumer choice problem can be re- formulated as Maximize U ( X ) s.t. n ± i =1 P i X i I. The rational consumer acts as if he or she were maximizing a utility function sub-

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

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

Unformatted text preview: ject to a budget constraint. Reconciliation of classical and modern op-timality conditions (when n = 2): Δ U ( X ) = MU 1 ( X ) · Δ X 1 + MU 2 ( X ) · Δ X 2 . Along an indi f erence curve, Δ U ( X ) = 0, so that MU 1 ( X ) MU 2 ( X ) =-Δ X 2 Δ X 1 = MRS 12 ( X ) . In general, MU i ( X ) MU j ( X ) = MRS ij ( X ) for all i, j. So, the modern optimization condition, MRS ij ( * X ) = p i /p j for all i, j, can be written as MU i ( * X ) MU j ( * X ) = p i p j for all i, j ; or MU i ( * X ) P i = MU j ( * X ) P j for all i, j Exception : “corner solutions.”...
View Full Document

## This note was uploaded on 10/05/2010 for the course ECON 104A taught by Professor Thomas during the Spring '10 term at UC Riverside.

### Page1 / 4

104A_Utility - ject to a budget constraint Reconciliation...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online