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

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

View Full Document Right Arrow Icon
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.
Background image of page 1

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

View Full DocumentRight Arrow Icon
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.
Background image of page 2
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-
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
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 Right Arrow Icon
Ask a homework question - tutors are online