浙江大学：《高级微观经济学》课程PPT教学课件（英文版）Lecture 4 consumption theory I

Adyanced econonics (lecture 5: consumption theory I) e Jianliang lecture 5 for Chu Kechen Honors College

lecture5 for Chu Kechen Honors College Advanced Economics (lecture 5: consumption theory I) Ye Jianliang

Preference and choice Content Preference and rationality The rule of choice Budget Demand function WAand demanded law lecture 5 for Chu Kechen Honors College

lecture5 for Chu Kechen Honors College Preference and Choice ➢ Content: ⚫ Preference and rationality ⚫ The rule of choice ⚫ Budget ⚫ Demand function ⚫ WA and demanded law

1. Preference An(acceptable) alternatives set (or a consumption set)XCR ° A(weak) preference relation“% a binary relationship on X, for any x,ye X, x%ymeans x is at least as good as y A strict preference> xxyex% y, but not y %x 。 An indifference relation“~” x>y分>x%y,andy%x lecture 5 for Chu Kechen Honors College

lecture5 for Chu Kechen Honors College 1.Preference ➢ An (acceptable) alternatives set (or a consumption set ) ⚫ A (weak) preference relation“ ”: a binary relationship on X, for any , means” x is at least as good as y”. ⚫ A strict preference “ ”: ⚫ An indifference relation “ ”: k X  + % x y,  X x y % x y x y y x  % % ,but not x y x y y x  % % ,and

1. Preference Definition: preference on x is rational if It's complete x,yEX, either x y or y% x, or both It's reflexive WxEX. x%x Its transitive x,y,EX, if x y and y% z, the en x 0 lecture 5 for Chu Kechen Honors College

lecture5 for Chu Kechen Honors College 1.Preference ➢ Definition: preference on X is rational if: ⚫ It’s complete: ⚫ It’s reflexive: ⚫ It’s transitive: % x y x y y x , ,either or , or both X % %  x x x X, % x y z x y y z x z , , ,if and , then X % % %

1. Preference Propersition1: if 9 is rational, then x is irreflexive and transitive c is reflexive and transitive and symmetric 。fx>y%z, then x>z lecture 5 for Chu Kechen Honors College

lecture5 for Chu Kechen Honors College 1.Preference ➢ Propersition1: if is rational, then: ⚫ is irreflexive and transitive ⚫ is reflexive and transitive and symmetric ⚫ If % , then x y z x z %

2. The rule of choice We can only observe what a man choice under a certain constrain >s the mans preference rational when we observed several choice of him? Or if his preference was rational, what rules will his choice take? lecture 5 for Chu Kechen Honors College

lecture5 for Chu Kechen Honors College 2.The rule of choice ➢ We can only observe what a man choice under a certain constrain. ➢ Is the man’s preference rational when we observed several choice of him? ➢ Or if his preference was rational, what rules will his choice take?

2. The rule of choice Choice construct: a choice under certain budget:(@B, C( Budget set: BaRand B≠andB∈B,isa budget family, represented a limited list of all possible choice under certain system, nature, technology and other social environments that the decision-maker must take Choice rule:C(B)cB,forB∈B,C()≠ maybe contain more than one elements lecture 5 for Chu Kechen Honors College

lecture5 for Chu Kechen Honors College 2.The rule of choice ➢ Choice construct: a choice under certain budget: ⚫ Budget set: and , is a budget family, represented a limited list of all possible choice under certain system, nature, technology and other social environments that the decision-maker must take. ⚫ Choice rule: , maybe contain more than one elements. ( , (.)) B C B B    X and BB B C B B B ( ) ,for  B C(.)  

2. The rule of choice Weak axiom of revealed preference VaRP or Wa):fx∈C(B) for certain∈B, andx,y∈ B for b'∈andx,y∈B',y∈C(B then must x∈C(B) Revealed Preference“%*” x%y分彐B∈,3x2y∈B,andx∈C(B) lecture 5 for Chu Kechen Honors College

lecture5 for Chu Kechen Honors College 2.The rule of choice ➢ Weak Axiom of Revealed Preference (WARP or WA) : if for certain , and for and , then must ➢ Revealed Preference “ ”: BB x y B ,  x C B  ( ) BB x y B ,   y C B  ( ) x C B  ( )  % x y B x y B x C B , , ,and ( ) %        B

2. The rule of choice > Choice set C(B,%)={x∈B:x%y,vy∈B} Proposition 2: if are rational, then choice construct(@B, C"(%)satisfied WA Prop 2 indicate that if the decision-maker have rational preference, than his choice satisfied WA Is his preference rational if his choice is observed satisfy WA? lecture 5 for Chu Kechen Honors College

lecture5 for Chu Kechen Honors College 2.The rule of choice ➢ Choice set ➢ Proposition2: if are rational, then choice construct satisfied WA. ➢ Prop.2 indicate that if the decision-maker have rational preference, than his choice satisfied WA. Is his preference rational if his choice is observed satisfy WA? ( , (., )) C  B % % C B x B x y y B ( , ) { : , }  % % =   

2. The rule of choice >Definition: for (@B, C"( % ) We say rational preference rationalization co Propersition3: if(9B, C( %)satisfied WA and og contain all subsets of x that is ternary and less than ternary example: X-x,v, 2,08=x,y,y2i,x, 2)) C({x,y})={x},C({=})={y}C({x,})={},(∞,C() satisfied Warp but there is no rationalization preference relation over it lecture 5 for Chu Kechen Honors College

lecture5 for Chu Kechen Honors College 2.The rule of choice ➢ Definition: for , we say “rational preference rationalization ➢ Propersition3: if satisfied WA and contain all subsets of X that is ternary and less than ternary. ⚫ example: X={x,y,z}, B ={{x,y},{y,z},{x,z}}, C({x,y})={x},C({y,z})={y},C({x,z})={z},(B , C(.)) satisfied WARP, but there is no rationalization preference relation over it. ( , (., )) C  B % % C(.) ( , (., )) C  B % B