ECON100A_4

ECON100A_4 - REVIEW 3IMPORTANTUTILITY FUNCTIONS Linear...

This preview shows pages 1–12. Sign up to view the full content.

1/4/2008 1 REVIEW –  3 IMPORTANT UTILITY  FUNCTIONS Linear: U(x 1 ,x 2 )=ax 1 +bx 2 Cobb-Douglass: U(x 1 ,x 2 )=ax 1 α x 2 β Leontief: U(x 1 ,x 2 )=min[x 1 /a, x 2 /b]

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

View Full Document
1/4/2008 2 Linear: U(x 1 ,x 2 )=ax 1 +bx 2 Perfect Substitutes MRS constant X 1 X 2 c/b c/a Slope=-a/b U(x 1 ,x 2 )=c
1/4/2008 3 Cobb-Douglass: U(x 1 ,x 2 )=ax 1 α x 2 β Diminishing MRS Willingness to trade depends on how much of each good is possessed X 1 X 2 U(x 1 ,x 2 )=c

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

View Full Document
1/4/2008 4 Leontief: U(x 1 ,x 2 )=min[x 1 /a, x 2 /b] Perfect Complements Goods must be used in fixed preportions MRS = 0 or undefined X T X M 1 4 (1,4) (2,8)
1/4/2008 5 MATH REVIEW Constrained Optimization

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

View Full Document
1/4/2008 6 Example 1 Unconstrained–one independent variable max x f(x) We assume nice properties (continuity, second order conditions) F.O.C. for interior solution: A. f(x)=0 B. f’(x)=0 C. f”(x)=0 X f(x) X*
1/4/2008 7 Example 1a Unconstrained–one independent variable max x 2x-4x 2 X*= A. 4 B. 2 C. ¼ F.O.C.: 2-8x=0 X f(x) X*

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

View Full Document
1/4/2008 8 Example 2 Unconstrained–Two independent variables We assume nice properties (continuity, second order conditions) F.O.C. s for interior solution: A. B. f’(x)=o X f(x) ) , ( max 2 1 , 2 1 x x f x x 1 2 1 2 1 2 ( , ) ( , ) 0, 0 f x x f x x x x = =
1/4/2008 9 Example 2a Unconstrained–Two independent variables F.O.C. s for interior solution: 8+y-2x=0 x-2y=0 X f(x) 2 2 , 8 max 2 1 y x xy x x x - - +

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

View Full Document
1/4/2008 10 Example 3 - Constrained Optimization Optimum is where these are equal: slope of level curve of function x 1 x 2 Slope of constraint x 1 +x 2 =10 Also must be on line x 1 +x 2 =10 10 . . max 2 1 2 1 , 2 1 = + x x t s x x x x X 1 X 2 10 10 x 1 +x 2 =10 X 1 * X 2 *
1/4/2008 11 More General Form Given “nice” assumptions, optimum is x 1 * , x 2 * that equate: slope of level curve of f at x 1 * , x 2 * slope of constraint g at x 1 * , x 2 * c x x g t s x x f x x = ) , ( . . ) , ( max

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.

This note was uploaded on 03/15/2010 for the course ECON 100A taught by Professor Babcock during the Winter '07 term at UCSB.

Page1 / 37

ECON100A_4 - REVIEW 3IMPORTANTUTILITY FUNCTIONS Linear...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online