Utility theory Utility is defined as want satisfying power of the commodity. Marginal Utility-...
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Transcript of Utility theory Utility is defined as want satisfying power of the commodity. Marginal Utility-...
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
80
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
82
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.
83
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
n
n
C
C
B
B
A
A
P
MU
P
MU
P
MU
P
MU...........
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Ma r
gina
l U
t il i
t yM2
M1
Q3 Q2 Q3
MUx
Dx
P3
P3
P3
Q3 Q2 Q3
Pri
c e
Figure 4.3 : Derivation of Demand Curve
M3
86
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 Approach- assumptions
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.
89
25
20
15
10
5
05 10 15 2520
a
b
c
d
Commodity X
Com
mod
i ty
YFigure : Indifference Curve
90
Indifference Curve Map
• A number of indifference curves representing various levels if satisfaction form an indifference map
Figure : Indifference Map
Quantity of X
Quanti
ty o
f Y
Y
O X
IC4
IC3
IC2
IC1
91
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
X1 X2 X3 X4
0
Y1
Y1
Y1
Y1
Commodity X
Figure : Perfect Substitutes
B
A
IC2
IC1
Commodity X
Com
mod
ity Y
Figure ) Perfect Complimentary Commodity
93
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
y
xxy p
qp
py
yq
1
x
yyx p
qp
xp
yq
1
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Y/Py
Y/Px
Com
mod
ity
Y
Commodity X
Figure : Budget Line
95
Commodity X
0 M
N C IC3
IC2
IC1
A
B
Com
mod
ity
YFigure : Consumer Equilibrium
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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
At the point of consumer equilibrium, indifference curve is convex to the origin, i.e. MRS is diminishing
y
x
y
x
y
x
y
xxy
p
P
MU
MU
MU
MU
P
PMRS
xyMRS
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Derivation of Demand Curve Using IC Approach
P
Budget line shifts
New Equilibrium(E2)
Point of Tangency ofBLS & Higher IC
(Price Consumption Curve)
Join successive pointsOn QY axis to get DD
98
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 income effect
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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)
N
IC2
LM
IC1
Co
mm
odit
y Y
Commodity XX1 X2 X3
B1B B3
A
A1
0
Income Effect
SubEffect
102
HICKSIAN APPROACH – Normal Commodity (Price Rise)
IC1
IC2
L
N
M
A
0 X2 X3 B”X1 B
Income
Effect
Substitution
Effect
Commodity Y
Com
modit
y X
Income & Substitution Effect :
Hicksian Approach (Prise Rise)
Price Effect
B’
A’
103
Slutsky Approach – Income & Substitution Effect (Price Fall)
IC3IC2
IC1 MNL
0 X1 X2B X3
B1 B2
A
A1
Commodity X
Com
mod
ity Y
Income and Substitution effects SlutskyApproach
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TECHNIQUES OF DEMAND
FORECASTING
SURVEY METHODS
STATISTICAL METHODS
SURVEY METHODS
CONSUMER SURVEYDIRECT
INTERVIEW
OPINION POLL METHODS
COMPLETE ENUMERATI
ON
SAMPLE SURVEY
END-USE METHOD
EXPERT OPINION
MARKET STUDIES &
EXPERIMENTS
SIMPLE METHOD
DELPHIMETHOD
MARKET TEST
LABORATORY TESTS
STATISTICAL METHOD
TREND PROJECTION BAROMETRIC METHODECONOMETRIC
METHODS
GRAPHICAL METHOD
TREND FITTING / LEAST SQUARE METHODS
BOX-JENKINS METHOD
LEAD INDICATORS
COINCIDENTALINDICATORS
LAGINDICATORS
REGRESSION METHODS
SIMULTANEOUS EQUATIONS
FITTING TREND EQUATION
1. Linear Trend
S=a+bT
2. Exponential Trend
Y = a ebT
Log Y = Log a + bT
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
TABLE 1
S=a+bT
∑S=na +b∑T∑ST=a∑T + b∑T2
See table 1,
164=10a+55b
1024=55a+385b , by solving these two equations we get the trend
equation as
S=8.26+1.48T
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 Method1.Eliminate trend from time series data2.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
YEARPopulation(X)
SugarConsumed (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