Post on 04-Jan-2022
Neoclassical Theory of Consumption
Economics II: Microeconomics
V�E Praha
September 2009
Micro (V�E) Consumption theory 09/09 1 / 24
Economics II: Microeconomics
Consumers:
People.Households.Applications.
Firms:
Internal Organisation.Industrial Organisation.
Equilibrium:
Holds.Does not hold.
Micro (V�E) Consumption theory 09/09 2 / 24
Microeconomics
Consumers:
People.� NowHouseholds.Applications.
Firms:
Internal Organisation.Industrial Organisation.
Equilibrium:
Holds.Does not hold.
Micro (V�E) Consumption theory 09/09 3 / 24
Neoclassical theory of consumptionBasics
PEOPLE CHOOSE THE BEST THINGS THEY CAN AFFORD.
Micro (V�E) Consumption theory 09/09 4 / 24
Neoclassical theory of consumptionBasics
PEOPLE CHOOSE THE BEST THINGS THEY CAN AFFORD.
Micro (V�E) Consumption theory 09/09 5 / 24
Neoclassical theory of consumptionBasics
THE BEST THINGS:
De�nitionConsumtion bundle is a complete list of the goods & services that areinvolved in the choice problem that is investigated. (say, X and Υ).
FactNotation:Strict preference: X � ΥIndi¤erence: X � ΥAlternative notation:Weak preference: X � Υ
Micro (V�E) Consumption theory 09/09 6 / 24
Neoclassical theory of consumptionBasics
Relationship between �,�,and �
Lemma
if X � Υ and Υ � X then ?
if X � Υ but not Υ � X then ?
Micro (V�E) Consumption theory 09/09 7 / 24
Neoclassical theory of consumptionBasics
Relationship between �,�,and �
Lemma
if X � Υ and Υ � X then X � Υ
if X � Υ but not Υ � X then X � Υ
Micro (V�E) Consumption theory 09/09 8 / 24
Neoclassical theory of consumptionHomo-economicus
The economic agent (or economic human)
RationalEgoist (or self-interested)
Micro (V�E) Consumption theory 09/09 9 / 24
Neoclassical theory of consumptionHomo-economicus
The economic agent (or economic human)
Rational
Egoist (or self-interested)
Micro (V�E) Consumption theory 09/09 9 / 24
Neoclassical theory of consumptionHomo-economicus
The economic agent (or economic human)
RationalEgoist (or self-interested)
Micro (V�E) Consumption theory 09/09 9 / 24
Neoclassical theory of consumptionRationality
Axiom1st Axiom: Complete preferencesEither of X � Y
Y � XX � Y
jorjEither of X � Y
Y � Xboth
ExampleBuridan�s ass...
2nd Axiom: Re�exive preferencesX � X jorj X � X
Micro (V�E) Consumption theory 09/09 10 / 24
Neoclassical theory of consumptionRationality
Axiom
3rd Axiom: Transitive preferences
If X � Y and Y � Z then X � ZIf X � Y and Y � Z then X � Zor
If X � Y and Y � Z then X � Z
ExampleThe Dutch-booking...
Micro (V�E) Consumption theory 09/09 11 / 24
Indi¤erence curves
e = (15, 25)d = (10, 15)
e � c � aI 1 �indi¤erece curve
Micro (V�E) Consumption theory 09/09 12 / 24
Indi¤erence curves
I 0 : a � eI 1 : b � eQ : Do the axioms hold?
Question :(a) I 0 � I 1 � I 2;(b) I 0 � I 1 � I 2; or(c) I 2 � I 1 � I 0
Micro (V�E) Consumption theory 09/09 13 / 24
Indi¤erence curves
I 0 : a � eI 1 : b � eQ : Do the axioms hold?
PropositionIndi¤erence curvesrepresenting distinct levels ofpreference cannot cross.
Proof.Otherwise the transitivityaxiom is violated.
Micro (V�E) Consumption theory 09/09 14 / 24
Indi¤erence curves
I 0 : a � eI 1 : b � eQ : Do the axioms hold?
Question :(a) I 0 � I 1 � I 2;(b) I 0 � I 1 � I 2; or(c) I 2 � I 1 � I 0
Micro (V�E) Consumption theory 09/09 15 / 24
Indi¤erence curves
Psych. Assumptions
Axiom
4th Axiom: Insatiable(monotonic) preferences
If X � Y then X � YIf X > Y then X � Y
5th Axiom: Convex preferences
(w) If X � Y thenαX + (1� α)Y � Xwhere α 2 (0, 1)(s) If X � Y thenαX + (1� α)Y � X
Question :(a) I 0 � I 1 � I 2;(b) I 0 � I 1 � I 2; or(c) I 2 � I 1 � I 0
Micro (V�E) Consumption theory 09/09 16 / 24
Indi¤erence curves: �No-No-No�Cases
Micro (V�E) Consumption theory 09/09 17 / 24
Indi¤erence curves: Special Cases
Micro (V�E) Consumption theory 09/09 18 / 24
Marginal rate of substitution
De�nition
Marginal rate ofsubstitution (MRS) is therate at which the consumer isjust willing to substitute onegood for the other- MRS is the (absolute of the)slope of an indi¤erence curveat a particular point:
∆x2∆x1
ordx2dx1
Micro (V�E) Consumption theory 09/09 19 / 24
Diminishing Marginal Rate of Substitution
Micro (V�E) Consumption theory 09/09 20 / 24
Next lecture
Further studies in Neoclassical Theory!
Thank you!
Micro (V�E) Consumption theory 09/09 21 / 24
Utility
measure of happiness
cardinal utility
ordinal utility
De�nitionUtility function: A way ofassigning a number to everypossible consumption bundle,such taht more preferredbundles get assigned largernumbers.
Micro (V�E) Consumption theory 09/09 22 / 24
UtilityTheorem of Debreu
TheoremGiven the assumptions of Rationality and Monotonicity,9u (�) s.t. (x1, x2) � (y1, y2) () u (x1, x2) > u (y1, y2) .
Proof.Do not need for this course.
Micro (V�E) Consumption theory 09/09 23 / 24
UtilityMonotonic transforations
LemmaAny monotonic transformation of the original utility function is a utilityfunction representing the same preferences.
Proof.1. Suppose u (�) is the utility function representing the preferences �P .
(x1, x2) �P (y1, y2)() u (x1, x2) > u (y1, y2) (1)
2. And suppose that f (u) is a monotonic transformation of u (�) .
u (x1, x2) > u (y1, y2)() f (x1, x2) > f (y1, y2) (2)
3. From (1) and (2) follows:
(x1, x2) �P (y1, y2)() f (x1, x2) > f (y1, y2) (3)Micro (V�E) Consumption theory 09/09 24 / 24