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 BB 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 “ ”: 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 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