Chiang_Ch11_missing pages

Chiang_Ch11_missing pages - Ch.11TheCaseofMorethanOneChoice...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Ch. 11 The Case of More than One Choice  Variable 11.1 The Differential Version of Optimization  Conditions 11.2 Extreme Values of a Function of Two  Variables 11.3 Quadratic Forms - An Excursion 11.4 Objective Functions with More than Two  Variables [11.5 Second-Order Conditions in Relation to  Concavity and Convexity] 11.6 Economic Applications 11.7 Comparative-Static Aspects of  Optimization
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 11.1 The Differential Version of  Optimization Conditions • 11.1(a) First-order condition • 11.1(b) Second-order condition • 11.1(c) Differential conditions vs.  derivative conditions
Background image of page 2
3 11.2 Extreme Values of a  Function of Two Variables • 11.2(a) First-order condition • 11.2(b) Second-order partial derivatives • 11.2(c) Second-order total differential • 11.2(d) Second-order condition
Background image of page 3

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

View Full DocumentRight Arrow Icon
4 11.3 Quadratic Forms - An Excursion • 11.3(a) Second-order total differential as a  quadratic form • 11.3(b) Positive and negative definiteness • 11.3(c) Determinant test for sign  definiteness • 11.3(d) Three-variable quadratic forms • 11.3(e) n-variable quadratic forms • 11.3(f) Characteristic-root test for sign  definiteness
Background image of page 4
5 11.2(a) First-order condition yy xy xx y x yy xy xx y x f f f f f dy f dxdy f dx f z d dy f dx f dz y) f(x z s derivative partial Find 2 ) 3 : (SoC) conditions order - second the Find 0 ) 2 : (FoC) conditions order - first the Find , ) 1 function •Given the 2 + + = = + = =
Background image of page 5

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

View Full DocumentRight Arrow Icon
6 derivatives 2 2 2 2 2 ) ( ) 5 ) ( ) 4 ) ( ) 3 ) 2 ) , ( ) 1 y z y z y f y f y x z y z x f x f x z x z x f x f y z f x z f y x f z y yy y xy x xx y x = = = = = = = = = = = =
Background image of page 6
7 11.2(c) Second-order total differential ( 29 ( 29 ( 29 2 2 2 2 2 ) ( ) ( ) 3 ) 2 ) , ( ) 1 dy f dxdy f dx f dy f dxdy f dxdy f dx f dy y dy f dx f dx x dy f dx f dy y dz dx x dz dz d dy f dx f dy y z dx x z dz y x f z yy xy xx yy xy xy xx y x y x y x + + = + + + = + + + = + = + = + = =
Background image of page 7

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

View Full DocumentRight Arrow Icon
8 11.3(c) Second derivative as determinant [ ] definite negative definite positive is then , 0 and 0 0 If ) 3 ) 2 ) 1 2 2 2 2 2 < = = + + + = z d H f f f f f f H dy dx f f f f dy dx z d dy f dydx f dxdy f dx f z d xx xx yy yx xy xx yy yx xy xx yy yx xy xx
Background image of page 8
9 11.2(d) Second-order condition Condition Maximum Minimum Saddlepoint 1 st order Necessary Sufficient 2 nd  Order Necessary Sufficient  Condition                          ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 0 0 0 , 0 , 0 , , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 2 2 2 2 2 2 * * * * * * * * * * * * * * * * * * * * * * * * < < < ± < = = = = = = H
Background image of page 9

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

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/09/2011 for the course ECON 101 taught by Professor Richards during the Spring '11 term at Cambrian College.

Page1 / 38

Chiang_Ch11_missing pages - Ch.11TheCaseofMorethanOneChoice...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online