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Unformatted text preview: Theory of Consumer Behavior Economics 201 G. Jehle I. Overview: There are three independent components to the theory of consumer choice:
Preferences, Constraints, Objectives. Each can be characterized separately in a manner
appropriate to the question at hand.
I.A. Preferences:
Preferences describe the agent’s innate ability to make choices, the
logical consistency of those choices, and the agent’s “tastes” for the objects of choice.
I.A.a. Axiomatic Structure: Preferences are structured axiomatically. Each axiom
formalizes an assumption about the agent’s binary (pairwise) comparisons between objects of choice. We let (P ) ≡ “ is strictly preferred to ”, (I ) ≡“is
indiﬀerent to”; A ≡ (x0 , y0 ), B ≡ (x1 , y1 ), and C ≡ (x2 , y2 ).
1. Axiom of Completeness: For any two bundles A and B :
either
or
or A (P ) B
B (P ) A
A (I ) B. 2. Axiom of Transitivity: For any three bundles A, B , and C :
if A (P ) B and B (P ) C, then A (P ) C,
if A (I ) B and B (I ) C, then A (I ) C. DEF: “The indiﬀerence curve through A”≡ {(x, y )  (x, y ) (I ) A}.
3. Axiom of Nonsatiation: If x0 ≥ x1 and y0 ≥ y1 and at least one inequality
holds strictly, then A (P ) B .
4. Axiom of Convexity: If A (I ) B and for C ≡ (x2 , y2 ) we have
x2 = θx0 + (1 − θ)x1
y2 = θy0 + (1 − θ)y1
and 0 < θ < 1, (i.e., C is on the chord connecting A and B ) then C (P ) A and
C (P ) B .
1 I.A.b. Utility functions: Axioms 1 and 2 suﬃce to permit all information on the
consumer’s preferences conveyed by the relations (P ) and (I ) to be summarized
and represented in the equivalent but more intuitive and familiar form of a “utility
function”.
DEF: The function u(x, y ) is a utility function representing the preferences (P ) and
(I ) if
u(x0 , y0 ) > u(x1 , y1 )
⇐⇒
(x0 , y0 ) (P ) (x1 , y1 ),
and
u(x0 , y0 ) = u(x1 , y1 )
⇐⇒
(x0 , y0 ) (I ) (x1 , y1 ).
I.A.c Indiﬀerence Curves: Deﬁned above, these may also be viewed as level sets or
level curves of the utility function. Axiom 1 insures indiﬀerence curves exist and
that some indiﬀerence curve passes through any point in the plane. Axioms 1,
2, and 3 imply indiﬀerence curves can not cross, that they are negatively sloped,
and that “preference increases northeasterly”. Axioms 1, 2, 3, and 4 imply, in
addition, that indiﬀerence curves are “convex to the origin”.
I.B. Constraints: Constraints restrict what choices the agent may make. The opportunity set is the set of feasible alternative choices given the agent’s circumstances. The
opportunity (or budget) set of the atomistic consumer facing ﬁxed prices px , py and
having income m, is given by
B ≡ {(x, y )  px x + py y ≤ m}.
I.C. Objectives:
The model of choice behavior is “closed” by making an assumption
regarding the agent’s objective or goal in the choice situation. Ordinarily, we will
assume the agent’s goal is to acquire that object preferred to all other feasible ones
or, equivalently, to maximize utility over the budget set. 2 ...
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This note was uploaded on 04/26/2010 for the course ECON 101 taught by Professor Staff during the Spring '08 term at Vassar.
 Spring '08
 Staff
 Economics, Microeconomics

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