Transcript Utility theory

Utility theory
Utility is defined as want satisfying power
of the commodity.
•
•
Marginal Utility- Increase in the total utility as
a result of consumption of additional unit of
commodity.
MUn = TUn – TUn-1 MU = TU/Q
Total Utility – Sum of the utilities an individual
derives from the total consumption of his
commodity
TU n = U1 + U2 + U3 +………… Un
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Approaches to measurement of
utility• Cardinal Utility approach
• Ordinal Utility approach
 Indifference Curve Approach
 Revealed Preference Hypothesis
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CARDINAL UTILITY
APPROACH
• Utility can be measured in monetary units
by the amount of money consumer is
ready to sacrifice for another unit of
commodity.
• Measurement of utility can be done in
subjective unit called utils
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ORDINAL UTILITY APPROACH
• The utility is not measurable.
• Consumer should be able to determine the
order of preferences among different
bundle of goods.
• Consumer need not know in specific units
the utility of various commodity to know his
preferences.
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CARDINAL - Assumptions
Rationality
Cardinal Utility
Diminishing Marginal Utility
Constant Utility of Money
Utility is additive
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Consumer Equilibrium
• When a consumer pays price for the commodity
he is consuming, he compares the utility he
derives from the additional unit of commodity
with the utility he sacrifices in terms of price paid
for the unit of commodity
MU = P
In case there are more than two commodities the
equilibrium condition may be expresses as
MU n
MU A MU B MU C


 ...........
PA
PB
PC
Pn
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Marginal Utility
M3
M2
M1
MUx
Q3
Q2
Q3
Price
P3
P3
P3
Dx
Q3
Q2
Q3
Figure 4.3 : Derivation of Demand Curve
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Criticism of Cardinal Approach
 Satisfaction derived from various commodities
cannot be measured objectively
 Money used for measurement is not correct as
it is not constant and the value of money keeps
fluctuating.
 It is psychological concept, therefore the very
law is questionable.
 The cardinal approach considers the effect of
price changes on the demand curve ( price
effect). This assumption is unrealistic as the
price effect may include income and
substitution effect
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Ordinal Utility Approachassumptions




Rationality
Utility is Ordinal
Diminishing Marginal Rate of Substitution
The total utility of the consumer depends
on the quantity of the commodity
consumed i.e.
U=f (q1 q2 ….qn)
 Consistency and transitivity of choice
 Non satiety
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Indifference Curve
An indifference curve may be defined as
the locus of points giving particular
combination or bundle of goods which
yield the same utility or level of satisfaction
to the consumer so that he is indifferent as
to
the
particular
combination
he
consumes.
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Commodity Y
Figure : Indifference Curve
25
a
20
b
15
c
10
d
5
0
5
10
15
20
25
Commodity X
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Indifference Curve Map
• A number
of
indifference
curves
representing various levels if satisfaction
form an indifference map
Figure : Indifference Map
Quantity of Y
Y
IC4
IC3
IC2
IC1
O
Quantity of X
X
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Properties of Indifference Curve
Indifference curve have negative slope
Indifference Curve are Convex to Origin
Indifference cannot touch or Intersect each
other
Higher Level of Indifference Curve
Represents Higher Level of Satisfaction
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DIFFERENT SHAPE OF
INDIFFERENCE CURVE
Perfect Substitutes
Perfect
Complimentary
Figure : Perfect Substitutes
Commodity Y
Commodity Y
Figure ) Perfect Complimentary Commodity
Y1
Y1
Y1
Y1
B
IC2
IC1
A
0
X1
X2
X3
X4
Commodity X
Commodity X
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Consumer Equilibrium
• Budget Constraint-Income acts as a
constraint in the attempt for maximizing
utility and is known as budget constraint.
Y = px qx+ py q y
qy 
qx 
1y p x q x

py
py
1y
p x

pyqy
px
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Commodity Y
Figure : Budget Line
Y/Py
Bu
dg
et
Li
n
e
Y/Px
Commodity X
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Figure : Consumer Equilibrium
Commodity Y
A
N
C
IC3
IC2
IC1
0
M
B
Commodity X
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Two conditions must be fulfilled for the
consumer to be in equilibrium
 Scope of Indifference Curve (MRS) should be
equal to the slope of budget line
MRS

xy 
Px
Py
MRSxy 
MU x
MU y
MU x
Px

MU y
py
 At the point of consumer equilibrium, indifference
curve is convex to the origin, i.e. MRS is
diminishing
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Derivation of Demand Curve Using
IC Approach
P
Budget line shifts
New Equilibrium
(E2)
Point of Tangency of
BLS & Higher IC
(Price Consumption
Curve)
Join successive points
On QY axis to get DD
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Derivation of Demand Curve Using
IC Approach
Change in the consumption basket as a
result of Changes in price is called price
effect.
The total price effect comprises of two
components
(a) substitution effect
(b) income Effect
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• When the price of a commodity changes,
the price of the substitute remaining the
same, the price ratio changes (given
constant money income). The change in
the relative price induces substitution of
cheaper good for the expensive one. This
change is referred to a substitution
effect.
• If the price of a commodity decreases, the
consumer’s real income increases. The
change in the consumption basket due to
change in the real income in called
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•
•
There are two methods followed for splitting
the total price effect into income effect and
substitution effect.
Hicksian approach
Slutsky approach
Hicks assumes constancy of real purchasing
power of the consumer by keeping the consumer
on the same satisfaction level.
Slutsky keeps real purchasing power constant in
the sense that the consumer could purchase the
original combination of commodities.
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HICKSIAN APPROACH – Normal
Commodity (Price Fall)
Figure : Income & Substitution Effect:
Hicksian Approach (Price Fall)
A
Commodity Y
A1
L
M
Sub
Effect
0
X1 X2
N
IC 2
IC 1
Income
Effect
X3
B
B1
B3
Commodity X
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HICKSIAN APPROACH – Normal
Commodity (Price Rise)
Income & Substitution Effect :
Commodity X
Hicksian Approach (Prise Rise)
A’
A
N
M
L
IC2
IC1
0
X2
X1 B”
X3
Substitution
B’
B
Commodity Y
Income
Effect
Effect
Price Effect
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Slutsky Approach – Income &
Substitution Effect (Price Fall)
Income
and
Approach
Substitution
effects
Slutsky
A
Commodity Y
A1
0
L
IC1
N
M
IC2
X1
X2
B
X3
IC 3
B1
B2
Commodity X
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TECHNIQUES
OF DEMAND
FORECASTING
SURVEY
METHODS
STATISTICAL
METHODS
SURVEY
METHODS
CONSUMER
SURVEY
DIRECT
INTERVIEW
COMPLETE
ENUMERATI
ON
SAMPLE
SURVEY
OPINION POLL
METHODS
END-USE
METHOD
EXPERT
OPINION
SIMPLE
METHOD
DELPHI
METHOD
MARKET
STUDIES &
EXPERIMENTS
MARKET
TEST
LABORATORY
TESTS
STATISTICAL METHOD
TREND PROJECTION
BAROMETRIC METHOD
GRAPHICAL
METHOD
TREND FITTING /
LEAST SQUARE METHODS
BOX-JENKINS METHOD
LEAD
INDICATORS
COINCIDENTAL
INDICATORS
LAG
INDICATORS
ECONOMETRIC
METHODS
REGRESSION
METHODS
SIMULTANEOUS
EQUATIONS
FITTING TREND EQUATION
1. Linear Trend
S=a+bT
2. Exponential Trend
Y = a ebT
Log Y = Log a + bT
TABLE 1
YEAR
SALES
T
T2
ST
1992
10
1
1
10
1993
12
2
4
24
1994
11
3
9
33
1995
15
4
16
60
1996
18
5
25
90
1997
14
6
36
84
1998
20
7
49
140
1999
18
8
64
144
2000
21
9
81
189
2001
25
10
100
250
n=10
∑=164
∑T=55
∑T2=385
∑ST=1024
S=a+bT
∑S=na +b∑T
∑ST=a∑T + b∑T2
See table 1,
164=10a+55b
1024=55a+385b ,
S=8.26+1.48T
by solving these two equations we get the trend equation as
For 11th year
S = 8.26 + 1.48 (11) = 24,540 tonnes
BOX JENKINS METHOD
• Used for short term projection
• Uses stationary time series data
Steps in Box Jenkins Method
1.Eliminate trend from time series data
2.Make sure there is seasonality in
stationary time series data (if value of one
or more coefficients are different from
zero, it reveals seasonality in time series
data)
3. Apply models to it.
(1)Auto-regressive model
Yt = a1Yt-1 + a2Yt-2 +…..+anYt-n + et
et is random portion of Y which is not explained by
the model
(2) Moving Average model
Yt = m + b1et-1 + b2et-2 +….+bpet-p + et
(3) Auto regressive moving average model
Yt = a1Yt-1 + a2Yt-2+..+anYt-n+b1et-1+b2et-2+…+ bpet-p
+ et
YEAR
Population
(X)
Sugar
Consumed
(Y)
X2
XY
1992
10
40
100
400
1993
12
50
144
600
1994
15
60
225
900
1995
20
70
400
1400
1996
25
80
625
2000
1997
30
90
900
2700
1998
40
100
1600
4000
∑n=7
∑X=152
∑Y=490
∑X2=3994
∑XY=12000
Simple Regression Method
Y = a + bX
∑Y = na + b∑X
∑XY = ∑Xa + b∑X2
See table
490 = 7a +152 b
12,000= 152a + 3994b
By solving these equation we get
Y = 27.44 + 1.96 X
Multi- variate method
QX = a - bPx +cY +dPy+jA
Simultaneous Equation Model
Yt = Ct + It +Gt + Xt
Ct = a + bYt