Neoclassical Theory of Consumption
Economics II: Microeconomics
VE Praha
September 2009
Micro (VE) Consumption theory 09/09 1 / 24
Economics II: Microeconomics
Consumers:
People.
Households.
Applications.
Firms:
Internal Organisation.
Industrial Organisation.
Equilibrium:
Holds.
Does not hold.
Micro (VE) Consumption theory 09/09 2 / 24
Microeconomics
Consumers:
People. Now
Households.
Applications.
Firms:
Internal Organisation.
Industrial Organisation.
Equilibrium:
Holds.
Does not hold.
Micro (VE) Consumption theory 09/09 3 / 24
Neoclassical theory of consumption
Basics
PEOPLE CHOOSE THE BEST THINGS THEY CAN AFFORD.
Micro (VE) Consumption theory 09/09 4 / 24
Neoclassical theory of consumption
Basics
PEOPLE CHOOSE THE BEST THINGS THEY CAN AFFORD.
Micro (VE) Consumption theory 09/09 5 / 24
Neoclassical theory of consumption
Basics
THE BEST THINGS:
Denition
Consumtion bundle is a complete list of the goods & services that are
involved in the choice problem that is investigated. (say, X and ).
Fact
Notation:
Strict preference: X ~
Indierence: X ~
Alternative notation:
Weak preference: X _
Micro (VE) Consumption theory 09/09 6 / 24
Neoclassical theory of consumption
Basics
Relationship between ~, ~,and _
Lemma
if X _ and _ X then ?
if X _ but not _ X then ?
Micro (VE) Consumption theory 09/09 7 / 24
Neoclassical theory of consumption
Basics
Relationship between ~, ~,and _
Lemma
if X _ and _ X then X ~
if X _ but not _ X then X ~
Micro (VE) Consumption theory 09/09 8 / 24
Neoclassical theory of consumption
Homo-economicus
The economic agent (or economic human)
Rational
Egoist (or self-interested)
Micro (VE) Consumption theory 09/09 9 / 24
Neoclassical theory of consumption
Homo-economicus
The economic agent (or economic human)
Rational
Egoist (or self-interested)
Micro (VE) Consumption theory 09/09 9 / 24
Neoclassical theory of consumption
Homo-economicus
The economic agent (or economic human)
Rational
Egoist (or self-interested)
Micro (VE) Consumption theory 09/09 9 / 24
Neoclassical theory of consumption
Rationality
Axiom
1
st
Axiom: Complete preferences
Either of X ~ Y
Y ~ X
X ~ Y
[or[
Either of X _ Y
Y _ X
both
Example
Buridans ass...
2
nd
Axiom: Reexive preferences
X ~ X [or[ X _ X
Micro (VE) Consumption theory 09/09 10 / 24
Neoclassical theory of consumption
Rationality
Axiom
3
rd
Axiom: Transitive preferences
If X ~ Y and Y ~ Z then X ~ Z
If X ~ Y and Y ~ Z then X ~ Z
or
If X _ Y and Y _ Z then X _ Z
Example
The Dutch-booking...
Micro (VE) Consumption theory 09/09 11 / 24
Indierence curves
e = (15, 25)
d = (10, 15)
e ~ c ~ a
I
1
~indierece curve
Micro (VE) Consumption theory 09/09 12 / 24
Indierence curves
I
0
: a ~ e
I
1
: b ~ e
Q : 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 (VE) Consumption theory 09/09 13 / 24
Indierence curves
I
0
: a ~ e
I
1
: b ~ e
Q : Do the axioms hold?
Proposition
Indierence curves
representing distinct levels of
preference cannot cross.
Proof.
Otherwise the transitivity
axiom is violated.
Micro (VE) Consumption theory 09/09 14 / 24
Indierence curves
I
0
: a ~ e
I
1
: b ~ e
Q : 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 (VE) Consumption theory 09/09 15 / 24
Indierence curves
Psych. Assumptions
Axiom
4
th
Axiom: Insatiable
(monotonic) preferences
If X Y then X ~ Y
If X > Y then X _ Y
5
th
Axiom: Convex preferences
(w) If X ~ Y then
X + (1 ) Y _ X
where (0, 1)
(s) If X ~ Y then
X + (1 ) 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 (VE) Consumption theory 09/09 16 / 24
Indierence curves: No-No-No Cases
Micro (VE) Consumption theory 09/09 17 / 24
Indierence curves: Special Cases
Micro (VE) Consumption theory 09/09 18 / 24
Marginal rate of substitution
Denition
Marginal rate of
substitution (MRS) is the
rate at which the consumer is
just willing to substitute one
good for the other
- MRS is the (absolute of the)
slope of an indierence curve
at a particular point:
x
2
x
1
or
dx
2
dx
1
Micro (VE) Consumption theory 09/09 19 / 24
Diminishing Marginal Rate of Substitution
Micro (VE) Consumption theory 09/09 20 / 24
Next lecture
Further studies in Neoclassical Theory!
Thank you!
Micro (VE) Consumption theory 09/09 21 / 24
Utility
measure of happiness
cardinal utility
ordinal utility
Denition
Utility function: A way of
assigning a number to every
possible consumption bundle,
such taht more preferred
bundles get assigned larger
numbers.
Micro (VE) Consumption theory 09/09 22 / 24
Utility
Theorem of Debreu
Theorem
Given the assumptions of Rationality and Monotonicity,
u () s.t. (x
1
, x
2
) ~ (y
1
, y
2
) ==u (x
1
, x
2
) > u (y
1
, y
2
) .
Proof.
Do not need for this course.
Micro (VE) Consumption theory 09/09 23 / 24
Utility
Monotonic transforations
Lemma
Any monotonic transformation of the original utility function is a utility
function representing the same preferences.
Proof.
1. Suppose u () is the utility function representing the preferences ~
P
.
(x
1
, x
2
) ~
P
(y
1
, y
2
) ==u (x
1
, x
2
) > u (y
1
, y
2
) (1)
2. And suppose that f (u) is a monotonic transformation of u () .
u (x
1
, x
2
) > u (y
1
, y
2
) ==f (x
1
, x
2
) > f (y
1
, y
2
) (2)
3. From (1) and (2) follows:
(x
1
, x
2
) ~
P
(y
1
, y
2
) ==f (x
1
, x
2
) > f (y
1
, y
2
) (3)
Micro (VE) Consumption theory 09/09 24 / 24
