MICROECONOMICS 2
THEORY OF CONSUMER BEHAVIOR
LECTURE 1 & 2
Outline




Introduction to consumer’s problem

Utility Maximization Problem

Expenditure Minimization Problem
Building blocks in the model of consumer’s problem

Consumption Set

Feasible Set ( ⟹ Budget Set)

Consumer Preferences and Binary Relation ( ⟹ Preference Relation)

Preference Axiom
Preference axioms and Preference Relation

Rationality

Lexicographic Orderings
Utility function

Existence of Utility Function

Invariance of the Utility Function

Properties of Preferences and Utility Functions
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
2
Economic Model




Economic Model of Human Behavior (i.e. Homo Economicus)

Simplified representation of reality

Model’s power stems from the elimination of irrelevant detail, which allows the economist to focus on the essential
features of the economic reality he/she is attempting to understand

In microeconomics we are dealing with individual agents on how they make their decision rationally based on their
self-interest
When Economic Model is valid?

Intrumentalism: The power of prediction

Realism: The validity of the assumption of the model
How to test the validity of an economic model?

Empirical or Statistical

Other?
In this lecture, the goal is to provide you with the theory so that you could understand and explain the
behaviour of agents
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
3
Introduction to Consumer’s Problem
The Consumer’s Problem
Utility Maximization
Expenditure Minimization
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
4
Introduction to Consumer’s Problem (Cont’d)
The Consumer’s Problem
Utility Maximization
Expenditure Minimization
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
5
Consumption Set

Consumption set, X, represent the set of all alternatives, or complete consumption plans, that the
consumer can conceive – whether some of them will be achievable in practice or not.

Capture the universe of alternative choices over which the consumer’s mind is capable of
wandering, unfettered by consideration of the realities of his present situation.

The consumption set is sometimes also called the choice set

Usually, we’ll simplify things and just think of the consumption set as the entire non-negative
orthant, 𝑋 = ℝ𝑛+

Let x𝑖 ∈ ℝ represent the number of units of good I

We assume that only non-negative units of each good are meaningful and that it is always possible to
conceive of having no units of any particular commodity.

We assume there is a finite, fixed, but arbitrary number n of different goods

We let 𝒙 = (𝑥1 , … , 𝑥𝑛 ) be a vector containing different quantities of each of the n commodities and call x a
consumption bundle or a consumption plan.

A consumption bundle 𝐱 ∈ 𝑋 is thus represented by a point 𝐱 ∈ ℝ𝑛
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
6
Consumption Set (Cont’d)
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
7
Feasible Set and Budget Set

Feasible set B capture those alternatives that are achievable given the economic realities the
consumer faces

The feasible set B then is that subset of the consumption set X that remains after we have
accounted for any constraints on the consumer’s access to commodities due to the practical,
institutional, or economic realities of the world

We will simply say that B ⊂ X

e.g.: time constraints, quota, budget constraint

A budget set B is a set of feasible consumption bundles, represented as 𝐵 𝒑, 𝜔 = {𝒙 𝜖 𝑋|𝒑𝒙 ≤ 𝜔}


𝒑 is an n-dimensional positive vector interpreted as price

𝜔 is a positive number interpreted as the consumer’s wealth
Properties of Budget Set B

Non-empty

Closed

Bounded

Convex
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
8
Consumer Preferences and Binary Relation

We represent the consumer’s preferences by a binary relation ≿ defined on the consumption
set, X
If 𝒙𝟏 ≿ 𝒙𝟐 , we say that ‘𝒙𝟏 is at least as good as 𝒙𝟐 ’, for this consumer

We require only that consumers make binary comparisons, that is, that they only examine two
consumption plans at a time and make a decision regarding those two.
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
9
Preference Axiom: (1) Completeness & (1a) Reflexive

Consumer preferences are characterised axiomatically.

In this method of modelling as few assumptions as possible are set forth to characterise the
structure and properties of preferences. The rest of the theory then builds logically from these
axioms

These axioms of consumer choice are intended to give formal mathematical expression to
fundamental aspects of consumer behaviour and attitudes towards the objects of choice.
‘Can make a choice’
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
10
Preference Axiom: (2) Transitivity
‘Consistent’
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
11
Preference Relation
These two axioms
together imply that the
consumer can
completely rank any
finite number of
elements in the
consumption set, X,
from best to worst,
possibly with some ties.
This enable the
consumer to construct
such a ranking by saying
that those preferences
can be represented by a
preference
relation
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
12
Rational Preference Relation
Preference relation ≿ is a rational preference ordering if it is complete and transitive
However it is not enough to make a well-behaved preference
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
13
Rational Preference Relation
Hypothetical
preferences satisfying
Axioms 1 and 2
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
14
Trivia
Are Axiom 1 and Axiom 2 enough to define a Utility Function?
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
15
Lexicographic Orderings

In lexicographic orderings, the preference depends first on the amount of good 1. Good 2 affects
the relative ordering of the bundles only if amounts of good 1 are equal in the two bundles

Consumer likes good 1 very much that he/she will choose the bundle that offers the most good 1,
no matter how much good 2 there is. Only when both bundles have the same units of X will the
agent start comparing the number of units of good 2 across bundles
𝑥1 ≿ 𝑥 2
(𝑥11 , 𝑥21 ) ≿ (𝑥12 , 𝑥22 )
if either
𝑥11 > 𝑥12 , or 𝑥11 = 𝑥12 and 𝑥21 ≥ 𝑥22
Maximize first component. In case of tie, maximize second component

The lexicographic ordering is a preference relation that is complete and transitive, but does not
have utility representation
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
16
Trivia
Only rational preference relation can be represented by a utility
function. But is it enough to define a utility function?
What other axioms are needed to define a utility function?
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
17
Preference Axiom: (3) Continuity
‘No sudden
preference reversal’
Hypothetical
preferences satisfying
Axioms 1, 2, and 3
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
18
Preference Axiom: (4’) Local Non-Satiation
‘No zones of
indifference (thick
indifference curve)’
‘No bliss point’
Hypothetical
preferences satisfying
Axioms 1, 2, 3 and 4’
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
19
Preference Axiom: (4) Strict Monotonicity
‘More is better than less’

Weak Monotonicity
If bundle 𝑥 has more of every good than bundle 𝑦 then 𝑥 is
strictly preferred to 𝑦
𝒙𝒊 > 𝒚𝒊 for every 𝒊 implies 𝒙 ≻ 𝒚
Strict Monotonicity
If bundle 𝑥 has more of at least one good and no less of any
good than bundle 𝑦 then 𝑥 is strictly preferred to 𝑦
𝒙𝒊 ≥ 𝒚𝒊 for every 𝒊 and 𝒙𝒊 > 𝒚𝒊 for some 𝒊 implies𝒙 ≻ 𝒚
Under monotonicity we can not have upward sloping indifference curve

Weak monotonicity implies non-increasing indifference curve while strict monotonicity implies decreasing
indifference curve

It is also implies that the ‘preferred to’ sets be ‘above’ the indifference sets and that the ‘worse
than’ sets be ‘below’ them

Strict monotonicity imply local non satiation
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
20
Preference Axiom: (4) Strict Monotonicity (Cont’d)
Hypothetical
preferences satisfying
Axioms 1, 2, 3 and 4
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
21
Preference Axiom: (5’) Convexity & (5’) Strict Convexity
‘Consumer likes
extreme bundles less’
Hypothetical
preferences satisfying
Axioms 1, 2, 3, 4, and 5
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
22
Preference Axiom: (5’) Convexity & (5’) Strict Convexity
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
23
Utility Function
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
24
Utility Function
Concave and convex functions – Supplements:
https://www.youtube.com/watch?v=s0dZVmPN3Ww&t=5s
https://www.youtube.com/watch?v=MyaeAZEi-iE&t=722s
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
25
Marginal Rate of Substitution

MRS measures the rate at which the
agent is willing to substitute one
good for another

MRS diminishes with 𝑥1 if and only if
preferences are strictly convex
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
26
Discussion: The Non-Standard Preferences
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
27
Discussion: The Non-Standard Preferences
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
28
Discussion: The Non-Standard Preferences
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior
29
MICROECONOMICS 2: THEORY OF CONSUMER BEHAVIOR
LECTURE 1 & 2
1. Geoffrey A. Jehle and Philip J. Reny, Advanced
Microeconomic Theory, 3rd edition, Prentice Hall, 2011,
Essex. (JR)
2. Hal R. Varian, Intermediate Microeconomics, W.W
Norton & Company, New York, 2006. (HV2)
Ashintya Damayati (Universitas Indonesia) Microeconomics 2: Theory of Consumer Behavior