{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chiang_Ch12

# Chiang_Ch12 - 1 Ch 12 Optimization with Equality...

This preview shows pages 1–6. Sign up to view the full content.

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

View Full Document

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

View Full Document

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: 1 Ch. 12 Optimization with Equality Constraints • 12.1 Effects of a Constraint • 12.2 Finding the Stationary Values • 12.3 Second-Order Conditions • 12.4 Quasi-concavity and Quasi-convexity • 12.5 Utility Maximization and Consumer Demand • 12.6 Homogeneous Functions • 12.7 Least-Cost Combination of Inputs • 12.8 Some concluding remarks 2 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 128 8 2 14 8 ) 14 13 8 14 2 4 60 ) 12 11 14 2 2 1 1 4 60 ) 10 9 2 2 2 1 2 ) 8 7 2 1 ; 2 ) 6 5 2 4 ; 2 4)- 3 functions both of als differenti l order tota- first the Taking 128 ; 14 ; 8 ) 10 8 maximum 4 ; 4 32 7)- 6 2 32 ) 5 2 30 ; 2 2 30 4)- 3 function utility the into ng substituti and for x Solving 2 4 60 2 2)- 1 B constraint budget and function U utility Given ation differenti total and substition by solving : Constraint a of Effects 1 . 12 * 1 1 * 2 2 2 2 1 2 1 2 1 2 1 2 1 2 1 1 2 1 1 2 * * 2 * 1 2 1 2 1 1 2 1 1 1 2 1 1 1 2 2 1 1 2 1 = + =- = + =- = + + =- + =- = +--- = +- =- =-- = = + + = = = =-- = =- =- =- = +- =-- = + = * U U x x x x x x x x x dx dx x x dx dx dx dx dB dx dx x dx x dU U x x dx U d x dx dU x x U x x x x x U x x B x x x U 3 ( 29 ( 29 y." and x values critical the find which to from equations two provide will 2), (eq. constraint with the together 10), (eq. condition The " ; ) 10 9 ; ) 8 7 B ; U ) 6 5 ; ) 4 3 , ; , 2)- 1 B constraint budget and function U utility Given 352) p. W, & (C- Constraint a of Effects 1 . 12 x x y y x y x y x y x y y x y x y x y x g f g f g g f f g g dy dx f f dy dx dy dx g g d dy dx f f d dy g dx g dB dy f dx f dU y x g B y x f U approach ferential Total dif = =-- =- =- = =- = + = = + =- = = 4 [ ] [ ] ( 29 ( 29 ( 29 ( 29 ( 29 128 8 2 14 8 2 ) 18 14 2 32 60 ) 17 2 8 4 60 ) 16 8 ) 15 64 8 ; 2 2 2 4 60 ) 14 13 2 2 ; 2 2 ) 12 11 2 2 4 2 ) 10 9 2 4 ; 2 1 1 U ) 8 7 ; 2 4 ; 2 ) 6 5 60 2 4 ; 2 2 1 2 1 U 4)- 3 60 2 4 ; 2 2)- 1 B constraint budget and function U utility Given 352) p. W, & (C- Constraint a of Effects 1 . 12 1 2 1 * * 2 2 * 1 1 1 1 1 2 1 2 1 2 1 2 1 2 2 1 1 2 1 2 1 2 1 1 1 2 2 1 2 1 1 2 1 2 1 2 1 1 2 1 = + = + = =- = + = = =- + =-- =- =---- =- =-- =- = + =- = + = = + + =-- = + = =- + = + = x x x U x x x x x x x x x x dx dx x x dx dx dx dx dB dx dx dx x x d dx dx dB dx dx x dx x dU x x B x x x x x x x B x x x U approach ferential Total dif 5 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 4 ; 128 ; 8 2 14 8 ) 17 15 14 ; 2 8 4 60 ) 14 13 8 ; 2 2 2 4 60 ) 12 11 2 2 ; 2 1 2 1 4 1 ) 10 9 2 1 ; λ2 ) 8 7 2 1 4 1 ; λ4 2 ) 6 5 2 4 60 ) 4 2 4 60 2 3) function Lagrangian 2 4 60 B 2 2)- 1 B constraint budget and function U utility Given on substituti with Lagrangian : constraint a of effect The 12.1 * * * 2 2...
View Full Document

{[ snackBarMessage ]}

### Page1 / 66

Chiang_Ch12 - 1 Ch 12 Optimization with Equality...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online