lecture5,for Chu Kechen Honors College,Advanced Economics (lecture 5: consumption theory I),Ye Jianliang,lecture5,for Chu Kechen Honors College,Preference and Choice,Content: Preference and rationality The rule of choice Budget Demand function WA and demanded law,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 “ ”:,lecture5,for Chu Kechen Honors College,1.Preference,Definition: preference on X is rational if: Its complete: Its reflexive: Its transitive:,lecture5,for Chu Kechen Honors College,1.Preference,Propersition1: if is rational, then: is irreflexive and transitive is reflexive and transitive and symmetric If,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 mans preference rational when we observed several choice of him? Or if his preference was rational, what rules will his choice take?,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.,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 “ ”:,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?,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.,lecture5,for Chu Kechen Honors College,3.Competive budget,Consumption set X and its price with the wealth w0. Definition: Walras (competive) budget set Proposition4: if X is concave, then is,lecture5,for Chu Kechen Honors College,4.Demand function,For any p and w are strictly positive, the corresponding demand set x(p,w) are nonempty, if x(p,w) is single point, we call it the Walrasian( Marshallian) demand function. x(p,w) is homogenous of degree zero and satisfied Walras law. That is px=w for all (we will prove them next lecture),lecture5,for Chu Kechen Honors College,4.Demand function,Wealth effects: Engel function: given price ,function over wealth Wealth expansion path: Wealth effects:,lecture5,for Chu Kechen Honors College,4.Demand function,Wealth effects: Commodity l is normal goods if Commodity l is inferior goods if The demand is normal if See the fig,lecture5,for Chu Kechen Honors College,4.Demand function,Price effects: Supply curve: Price effects: Giffen good: See the fig.,lecture5,for Chu Kechen Honors College,4.Demand function,Cournot Aggregation: if Walrasian demand function x(p,w) is HD0 and satisfied Walras Law , then: Engel Aggregation: if Walrasian demand function x(p,w) satisfied Walras Law, then:,lecture5,for Chu Kechen Honors College,5.WA and demand law,Walrasian demand function x(p,w) satisfied WA if for any we have: See the fig.,lecture5,for Chu Kechen Honors College,5.WA and demand law,Changing in price will change wealth too. But how can we tell the demand changing by price changing from wealth changing? Given a changing from ,and people will not get worse that is here wealth changing (compensation ) was called “Slutsky wealth compensation” and “(Slutsky) compensated price changing”.,lecture5,for Chu Kechen Honors College,5.WA and demand law,Proposition5: x(p,w) satisfied WA if and only if: and when , Prop.5 indicates, , or thats called “demand law ”, or “compensation demand law ”.,lecture5,for Chu Kechen Honors College,5.WA and demand law,Slutsky matrix (substitution matrix) Substitution effects is n.s.d Giffen good is necessary inferior good.,lecture5,for Chu Kechen Honors College,Assignment,If Then For then If Laspeyres quantity index is less than 1, then ,and if Paasche quantity index is large than1, then,lecture5,for Chu Kechen Honors College,Consumption set,lecture5,for Chu Kechen Honors College,Consumption set,lecture5,for Chu Kechen Honors College,Consumption set,lecture5,for Chu Kechen Honors College,