Advanced economics (lecture 4: consumption theory D) Ye Jianliang lecture for Chu Kechen Honors college
lecture4 for Chu Kechen Honors College Advanced Economics (lecture 4: consumption theory I) Ye Jianliang
Preference and choice Content Preference and rationality The rule of choice Budget Demand function 。 WAand demanded law lecture for Chu Kechen Honors College
lecture4 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 (acceptablealternatives set (or a consumption set)Xc界 A(weak) preference relation%: a binal relationship on x, for any x,yEX, x% ymeans x is at least as good as y A strict preference“x xxyex% y, but not y %x 。 An indifference relation“~ xxyex% y, and y %x lecture for Chu Kechen Honors College
lecture4 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 Its complete x,yEX, either x% y or y %x, or both o It's reflexive WxEX.x% x Its transitive x,y,zEX, if x% y and y% z, then x%z lecture for Chu Kechen Honors College
lecture4 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 is rational, then >is irreflexive and transitive is reflexive and transitive and symmetric If xsy%z,then x>z lecture for Chu Kechen Honors College
lecture4 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 >Is the mans preference rational when we observed several choice of him? Or if his preference was rational, what rules will his choice take? lecture for Chu Kechen Honors College
lecture4 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:(∞,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)∈B,forB∈B,C(.)≠ maybe contain more than one elements lecture for Chu Kechen Honors College
lecture4 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 BB B C B B B ( ) ,for B C(.)
2. The rule of choice Weak axiom of revealed Preference WarP or Wa):fx∈C(B) or certain∈B, andx,y∈ B for B'∈andx,y∈B,y∈C(B) then must x∈C(B) Revealed Preference“%*” x%”y台3B∈B,3x,y∈ B and x∈C(B) lecture for Chu Kechen Honors College
lecture4 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 “ ”: BB x y B , x C B ( ) BB 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. s his preference rationalif his choice is observed satisfy WA? lecture for Chu Kechen Honors College
lecture4 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(@, C"( ) We say " rational preference rationalization Co >Propersition3: if(9B, C(%) satisfied WA and o contain all subsets of x that is ternary and less than ternary example: Xx, z,9B=x,y,21,x, 2) C({xy})={x}C({y2})={y}C({x,-})={},C(. satisfied warp but there is no rationalization preference relation over it lecture for Chu Kechen Honors College
lecture4 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