Handout on Consumer Theory

Handout on Consumer Theory - Theory of Consumer Behavior...

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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 (pair-wise) 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 Non-satiation: 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.

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