Microeconomics
M.A. first semester
Unit 2 : Consumer Behavior
Preference ordering: the consumption decision;
consumer’s equilibrium ( with indifference curve
approach); changes in price and derivation of
compensated and uncompensated demand curves;
comparative statics of consumer behavior; types of
goods; concept of duality in consumer theory; the
expenditure function; the indirect utility function;
estimating cost of living; Lancasterian demand
theory and linear expenditure system; revealed
preference theory
Preference ordering; and
consumption decision
Utility:
is the power of goods and services to satisfies the human
wants. There are two hypothesis about the measurement of
utility.
1. Cardinal utility analysis (Marshallian utility hypothesis)
2. Ordinal utility hypothesis (Hicksian utility analysis)
Utility may be total and marginal utility.
Total utility is the sum of all the utilities derived with
consuming all the available quantity of a commodity.
TU= ∑ MU = MU1 +MU2+……..+MUn
Marginal utility is an additional utility derived with consuming
an additional unit of the commodity
MU= dTU/dQ
Cardinal utility analysis
(Marshallian utility analysis)
This hypothesis is based on the assumptions of the cardinal
measurement of utility, constant marginal utility of money,
introspective approach of analysis, law of diminishing
marginal utility, independent utility.
There are two cases in which consumers equilibrium can be
explain
one commodity case law of diminishing marginal utility.
Two commodity case law of Equi- marginal utility/ law of
substitution
Consumers demand any goods and services because of
the utility held in the goods. So consumers’ preferences
is depend on the utility of goods and services.
Ordinal utility analysis/ Hicksian
approach/ Indifference Curve approach
It is invented by Edgeworth and Fisher independently
Pareto, Johnson, Slutsky also has the contribution to
use of indifference curve in the various aspect of
consumer behaviour
English economists, J.R. Hicks and R.G.D Allen a
paper “A Reconsideration of the theory of Value”
Hicks reproduced the indifference curve theory of
consumer’s demand in his book ‘Value and capital’ in
1939 with the decomposition of price effect into
substitution effect and income effect.
Indifference curve:
It is a locus of various combinations of two goods the
gives same level of satisfaction to the consumer. It
means a consumer is in indifferent among the
combinations of goods and services because of each
and every combinations of these goods gives same level
of satisfaction to the consumer.
Assumptions
1. Rational consumer
2. Consumer consumes only two goods say X and Y
3. Ordinal measurement of utility/ preference hypothesis/
Weak ordering preference hypothesis
4. Diminishing Marginal rate of substitution
5. Consistency and transitivity
6. Non-satiation
Utility/
combinatio Good
Goods X MRS satisfec
isoquant
ns sY
tion
A 1 15 - 200
B 2 11 1:4 200
C 3 8 1:3 200
D 4 6 1:2 200
Indifference curve E 5 5 1:1 200
16
Series1; 15
14
12
11
10
Labor
8 8
6 6
5
4
0
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
Capital
Diminishing marginal rate of
substitution (MRS):
MRS is a rate at which units of two goods
are substituted to each other to maintain
same level of satisfaction to the consumer.
It is the ratio of the change in units of one
good (say X) with the change in unit of
another good (say, Y)
U=f(X,Y)
-△Y MUY
….(i) IC utility function
…(ii) when consumer sacrifices some
+△X MUX
units of good Y total utility will change
….(iii) when he changes some unit of good
-△Y MUY = +△X MUX
X, total Utility will change
-△Y/△X =MUX/MUY = MRSXY ..... (iv) slope of IC
Properties or characteristics of Indifference Curve
1. It has negative slopes. Or IC always slopes
downwards from left to the right.
2. It is convex to the origin.
3. Indifference Curves never intersect to each
other.
4. Higher IC represents higher the utility and lower
IC represents lower satisfaction.
5. It never tough any axis.
6. ItY must not be parrellal Good Y
Good
a
b
IC2
IC1
IC c
0 Good X
0 Good X
Budget line / price line
It shows the budget of the consumer
It is locus of various combination of two goods that can
be purchased by the consumer with spending his/ her
limited resources (budget)
The slope of the budget line is depends on the prices of
the commodities so it is also known as the price line.
The budget line equation is
B = Px.X +Py.Y……..i)
Where
B = budget of the consumer (money income of the
PX = price of the good X,
consumer)
Py = price of good Y
X = unit of good X, Y = unit of good Y
Cont……
Let B = Rs100. Py= Rs10, and Px =Rs20 then
budget line is drawn as 100=20X+10Y
when Y = 0, X= B/Px = 100/20 = 5 a point of
budget line
When X=0, Y=B/Py = 100/10= 10 another point of
budget line, then Good y
10
Slope of budget line is
B = Px.X +Py.Y
dY/dX= - Px/Py
0
5 Good x
Cont…..
Causes of shift in budget line
a. Change in budget/ money income of the
consumer
I. When money income increase it shift
rightward
II. When money income decrease it shift
leftward
b. Change in prices of the goods
i. If price of goods decreased it shift
rightwards
ii. If price of goods increased it shift leftwards
Cont……a. shift in budget line due to change in
income
Let B = Rs100. Py= Rs10, and Px =Rs20 then
budget line is drawn as 100=20X+10Y
when Y = 0, X= B/Px = 100/20 = 5 a point of
budget line Good y
12
When X=0, Y=B/Py = 100/10= 10 another point of
budget line, then
If the income of the consumer10
Increases to Rs 120 8
Then budget line will shift to the
Rightwards
If the income of the consumer
Decreases to Rs 80 it shift the
budget line leftwards
0 4 5 6 Good x
Cont…b. shift in budget line due to change in price
of goods
Let B = Rs100. Py= Rs10, and Px =Rs20 then
budget line is drawn as 100=20X+10Y
when Y = 0, X= B/Px = 100/20 = 5 a point of
Good y
budget line
When X=0, Y=B/Py = 100/10= 10 another point of
budget line, then
10
If prices of the goods increases
It shift the budget line leftwards
(Inwards)
If the prices of the goods
Decreases it shift the budget line
Outwards (rightwards)
0 5
Good x
Consumer’s equilibrium:
A consumer is said to be in equilibrium when he is buying
such a combination of goods as leaves him with no
tendency to rearrange his purchases of goods.
A consumer is able to get maximum satisfaction with
spending his limited money income.
Assumptions:
1. Consumer is a rational person
2. Consumer has a given indifference map exhibiting his
scale of preferences for various combinations of two
goods.
3. Perfect information about the market to the consumer
4. Good are homogeneous and divisible
5. Taste and preferences remains same.
6. He has fixed amount of money to spend on the two goods.
He has to spends his whole of his money on the two goods
7. Prices of goods are constant
Conditions for equilibrium
Necessary condition (1st order condition):
Price line must be tangent to the indifference
curve (or the slope of the budget line equals
-△Y/△X =-MUX/MUY = MRSXY = -Px/Py
slope of the indifference curve. i.e
Sufficient condition (2nd order condition):
At the point of tangency the IC curve must be
convex to the origin
Consumer’s equilibrium under indifference
curve approach:
Good Y
A
f
e
Y1
IC3
g
IC2
IC1
0 X1 B Good X
Differences in Preferences and Consumer’s
equilibrium and Choice of Goods
Good Y
Good Y
IC3
IC1 IC2 IC3
A A
e1
Y1 IC3
f
IC2
e
Y
IC1
B
0
0 X1 B X Good X
Good X
a) Amit’s Preferences b) Rajiv’s Preferences
MUx - λPX = 0
Consumer’s equilibrium (mathematically)
…..(7)
U=f(X,Y) Utility function……. (1)
B = Px.X +Py.Y Budget constraint..(2)
λPY = 0 ….(8)
MUy -
Introducing lagrangian Multiplier B - Px.X - Py.Y
z= f(X,Y) + λ(B - Px.X - Py.Y)……(3)
= 0 ….(9)
rewriting
these equations
…..(7)
For maximization set first order MUx = λPX
…..(8)
Partial derivatives with respect to MUy = λPY
X,Y and λ is zero B - Px.X - Py.Y = 0
….(9)
Consumer’s equilibrium: corner
solution
1. Convex indifference curve and corner
equilibrium
2. Concave indifference curve and corner
equilibrium
3. Corner solution in case of perfect substitutes
and perfect compliments
Indifferent curve analysis of demand:
Income, Substitution and Price effects
Income Effect (Income Consumption Curve):
it is the analysis of consumer’s reaction
(preferences of consumer) when income of
the consumer is changed.
If income of the consumer increased he can
purchases more commodity of the goods and
services and vice versa.
It is the explanation of consumer’s equilibrium
as changed in the income of the consumer.
ICC is the locus of equilibrium of consumer as
changes in the income of the consumer.
Income effect:
Good Y
ICC1: X is necessary
Good Y
P4 Y is Luxury
ICC2: is equal
to one for both good
P3
ICC
P2
Q4
ICC3 : X is luxury
P1 Q3 IC4 Y is necessity
Q2
IC3
Q1
IC1 IC2
O L1 L2 L3 L4 Good X Good X
Income effect:
ome consumption curve in case of good Y is inferior
Good X
ICC1: X is inferior
Good Y
P4 Y is normal
P3
P2
IC1 IC2 IC3 IC4
P1
Q1 Q2 Q3
Q4
ICC ICC2 : X is norma
Y is inferior
O L1 L2 L3 L4 Good X Good X
Change in price and derivation of
compensated and uncompensated
demand
Price effect and curve curve (price
price consumption
effect):
It analyze the change in consumer’s behavior due the
change in prices of goods and services. Consumer’s
reaction on the purchases of goods and services when
Good Y
prices of goods and services changes.
It explains the
A
change in consumer’s
equilibrium as changes PCC
e1 e2 e3
in prices of the
IC3
commodities IC1 IC2
B2
0 B B1 Good X
Shapes of Price Consumption curve
A.
Good Y
PCC
Good Y
PCC
e3 A PCC
e1 e2
IC3 PCC
IC2
IC1
O B B1 O
B2
Good X
Good X
In case of changes in the price of good X
( continuously decreases in the price of good X given
the price of good Y)
PCC1
Good Y
PCC2
PCC3
O
Good X
Substitution effect:
Substitution effect is the analysis of consumer’s reaction on
the purchases of the commodity when relative price change
keeping real income constant.
It explains the consumer’s equilibrium as change in the
relative price with the given level of real income of the
consumer.
Real income refers to the purchasing power of the consumer
There are two approaches to keep the real income constant
1. Slutsky substitution effect: Slutsky says that consumer’s
real income should compensated in such a way that
consumer is able to purchase exactly the same
combination of goods and services if he desire.
2. Hicksian substitution effect: Hicks says that consumer’s
real income should adjust in such a way that consumer
should achieve same level of satisfaction. It mean
consumer should be in equilibrium at initial equilibrium.
Slutsky’s substitution effect
a. For a price decline b. for price rise
case
Good Y
Good Y
A
e3
A
G IC1
IC3
e2
e1 e1
e2
e3 IC2 IC1
IC2
IC
3 O
O X1 B X2 F C X2 C X1 G B
Good X
Good X
Hicksian substitution effect
a. For a price decline b. for price rise
case
F
Good Y
Good Y
A
A e3
G
e1
e2
e3
e2
IC2 e1
IC1 IC2 IC1
O X1 X2 B F C O X2 C B
X1 G
Good X Good X
Decomposition of price effect into
income and substitution effect
P.E.= I.E. + S.E. Hicksian Method
Or e1 to e2=e2e3+e1e3 Or
x1x2=x2x3+x1x3
Compensating variation F b. Equivalent
variation ICC
Good Y
Good Y
A
ICC A
G e3
e1 PCC
e2
e3 PCC
e1 e2
IC2
IC1 IC2
IC1
O X1 X3 B C O X1 X3 C B
X2 F X2 G
Good X
Good X
Decomposition of price effect into
income and substitution effect
P.E.= I.E. + S.E. Hicksian Method
Or e1 to e2=e2e3+e1e3 Or
x1x2=x2x3+x1x3
Incase of Giffen good
Good Y
A e2
IC2
G
e1
e3
PCC
IC1
ICC
OX2 X1 X3 B F C
Good X
Decomposition of price effect into income
and substitution effect Slutsky method
a. Compensating variation b. Equivalent
variation F
Good Y
Good Y
A
e3
A
G IC1
IC3
e2
e1 e1
e2
e3 IC2 IC1
IC2
IC
3 O
O X1 B X2 F C X2 C X1 G B
Good X
Good X
Demand curve derivation: compensated
and uncompensated demand curve
Uncompensated Or ordinary demand curve
Good Y
A PCC
e1 e3
e2
IC3
IC1 IC2
O x1 B x2 x3 B1 Good X
B2
Do
Price of X
P1
P2
P3
Do
O Good X
Uncompensated demand curve Giffen good case
Uncompensated Or ordinary demand curve
e3
Good Y
A PCC
IC3
e2
IC2
e1
IC1
Ox3 x2 x1 B Good X
B1 B2
Do
Price of X
P1
P2
P3
Do
O x3 x2 x1 Good X
Ordinary and Compensated demand curve: Hicksian
Method
a.
A
Good Y
PCC
F e1
e2
e3
IC1
IC2
O Good X
x1 B1x3 x2 G B2
Dc
Price of X
P1
P2 Do
Dc
O
x1 x3 X2 Good X
Ordinary and Compensated demand curve: Slutsky’s
Method
a.
A
IC1
Good Y
F e1
e3 e2
IC3
IC2
O Good X
x1 B1x3 x2 G B2
Dc
Price of X
P1
P2 Do
Dc
O
x1 x3 X2 Good X
Indirect utility function
U= f(X,Y) direct utility function
Generally we deal as utility is the function of
quantities of goods and services consumed
by the consumer. It means if quantities of
goods and services changed the utility also
changed. That is called direct utility
function.
If we deal as utility in terms of prices and
money income that is called indirect utility
functions.
B = Px.X +Py.Y Budget constraint..(2)
U=XY Utility function……. (1)
z= XY + λ(B - Px.X - Py.Y)……(3)
Introducing lagrangian Multiplier
For maximization set first order
Partial derivatives with respect to
∂z/∂x= Y - λPx. = 0 …..(4)
X,Y and λ is zero
∂z/∂y= X - λPy. = 0 ….(5)
∂z/∂λ= B - Px.X - Py.Y = 0 ….(6)
MUx = Y - λPX …..(7)
MUy = X - λPX ….(8)
B - Px.X - Py.Y = 0 ….(9)
Mux
=0
rewriting these equations 7 and 8
Y = λPX …..(7)
X = λPY …..(8)
solving these equations 7and 8 we get
MUx/Muy =MRSxy= Y/X =λPx/λPy
MRSxy=Px/Py …(10)
this is the first order condition for the consumer’s
equilibrium
X=Py.Y/Px and Y= Px.X/Py
Putting X in budget equation we get
B = Px (Py.Y/Px) + Py Y
B= Py.Y + Py.Y
B=2Py.Y
Y*= M/2Py…….(i) this is the Marshallian (ordinary)
demand function for the good Y
Solving for X
Y=Px.X/Py
B=Px.X + Py(Px.X/Py)
B= Px.X + Px.X
B=2Px.X
X*= M/2Px…….(ii) this is the Ordinary demand function
for good X
Putting the value of X* and Y*
In utility function we get
U=(B/2Px.) (B/2Py)
U*= B2/4Px.Py …. This is called
Expenditure function: how much money is needed to get given level
of satisfaction (utility) when the prices of goods and services are given
Money=Budget=Expenditure M=B=E
Minimum expenditure function
V= U*
B2/4Px.Py = U*
B2 = 4Px.Py U*
B = 2√ (Px.Py. U*)…….. Expenditure function
E(Px.Py. U*)= 2√ (Px.Py. U*) this is the Marshallian
expenditure function
Roy’s Identity Xm = - (dV/dPx)/ dV/dB is equal to X*= B/2Px
V= B2/4Px.Py
dv/dPx= - (Px-2 B2)/4Py = -B2 / 4Px2Py then dv/dB=2B/4Px.Py
Xm = - (dV/dPx)/ dV/dB = - (-B2 / 4Px2Py)/2B/4Px.Py
Xm or (X*) = B/2Px Roy’s identity is satisfied.
Roy’s Identity Xm = - (dV/dPx)/ dV/dB is equal to
X*= B/2Px
V= B2/4Px.Py
dv/dPx= - (Px-2 B2)/4Py
= -B2 / 4Px2Py
then
dv/dB=2B/4Px.Py
Xm = - (dV/dPx)/ dV/dB = - (-B2 / 4Px2Py)/2B/4Px.Py
= B2 / 4Px2Py)/2B/4Px.Py here 2 and 4 and
B and B is cancel out
Xm or (X*) = B/2Px Roy’s identity is satisfied
Minimisation B = Px.X +Py.Y Budget …(1)
z= B - Px.X - Py.Y+ λ(U - XY)……(3)
Subject to U=XY Utility function constraint … (2)
rewriting
these equations
For maximization set first order
Partial derivatives with respect to
∂z/∂x= Px - λY. = 0 …..(4)
X,Y and λ is zero
∂z/∂y= Py - λX = O ….(5)
solving these equations we get
∂z/∂λ= U - XY= 0 ….(6)
Px/Py=Y/X
Y = Px.X/Py
X =Py.Y/Px
putting Y in Utility function
U = X(Px.X)
X2 = U.Py/Px
U = Px.X2 /Py
X* = √ (U.Py/Px) …….(i)
these equations are called
similarly Y*= √( U.Px/Py) ……(ii)
Hicksian demand function
or Ordinary demand function
for the goods X and Y
respectively
Expenditure function:
Says what amount of money is needed to achieve a
utility if the n prices are given by the price vector
In another words how much money is needed to get
given level of satisfaction (utility) when the prices of
goods and services are given
M= Px.X + Py.Y Budget line equation
From the our previously example if we put the value of
X* and Y* which are derived for the Hicksian demand
function we get expenditure functiosn.
M = Px. √ (U.Py/Px) + Py. √( U.Px/Py) it is the
Expenditure function
