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8/13/2019 Ordinal Approach
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Ordinal Approach or
The concept of Scale of Preferences or
The Indifference Curve Technique Originated by Francis Ysidro
Edgeworth in 1881 and Refined by
Pareto in 1906.
Application in the demand analysis at
the hands of J.R. HICKS and R.G.D.Allen in 1934.
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The Ordinal Approach In Utility Theory
The ordinal theory suggests thatutility is only relativelydiscernible
but notquantifiable.
U is the level of satisfaction than
an amount of satisfaction.
Utility is a series of assigned
numbers to rank options by the
consumer preference. The
assigned numbers reveal what is
morepreferred but cannot tell
how much the difference is.
Utility can only be ranked by anorder or a scale of preferenceto
show the degree of willingness of
a consumer.
Hicks uses Significancerather
than Utility.
Combinations
between Apples
and Bananas
Level of
Satisfaction
Derived
Ranking
Order of
Preference
a) 12 Apples
+
12 Bananas
Highest First
b) 10 Apples
+
19 Bananas
Lesser than
(a)
Second
c) 5 Apples
+
5 Bananas
Lesser than
(b)
Third
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Scale of Preferences - Characteristics
Drawn by a consumer in his mind consciously or
unconsciously. Based on subjective valuation of goods made by
the cust on the basis of his liking, habits, tastes,desires, intensity of wants, etc.
Independent of Price and consumers income. It represents Ordinal comparison of the level of
satisfaction derived by the consumer fromdifferent combinations of goods.
S of P differs from person to person. S of P considers the significance of the
commodity in the context of their stocks.
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Indifference ScheduleAn Indifference
schedule is a list of alternate combination in
the stocks of two goods which yield equalsatisfaction to the consumer.
Indifference Curve-An Indifference curve is
the locus of points representing all thedifferent combinations if the two goods (say
X and Y) which yield equal utility or
satisfaction to the consumer. Indifference Map-An Indifference map is a
set of indifference curves.
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Hypothetical data for an IC Map
Combination of Goods
(Units)I II III
X Y X Y X Y
1 10 2 15 3 20
2 6 4 10 5 14
3 3 6 6 7 7
4 1 8 3 9 7
U1(IC1) U2(IC2) U3(IC3)
Third OrderPreference
Second OrderPreference
First OrderPreference
QTofco
mmY
Y
X
U1
U3
U2
O
QT of comm X
d
c
b
a
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ASSUMPTIONS
A consumer is interested in buying two goods in
combination. He is able to rank his preferences & give a
complete ordering of the scale of preferences.
Non-satiation, i.e, the consume always prefers
more quantities of goods to lesser quantities. He is rational and his choices are transitive.Itmeans, if he prefers combination a to b and b to c,then he must also prefer a to c.
Height of the IC indicates the level of satisfaction.
IC are drawn as continuous curves assuminginfinitesimal amount of changes in the combinationof 2 goods i.e. perfect division of the goods underconsideration.
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The Indifference Curve Theory
Based on these assertions, Edgeworth F.
Y. ( 1845 - 1926 ) first suggested the
indifference curve to represent the level of
preferencea consumer has when twogoods are consumed with different
amount, but each combination of these
two goods yields the same level ofpreference.
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The Properties of the Indifference Curve
IC slope downwards from left to right , i.e.vely sloped, indicating if X increases in
combination X and Y , there should be a
decrease in Y amount to be on the samelevel of satisfaction.
They are convex to origin.
They cant intersect each other.
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The Marginal Rate of Substitution
Def: The MRS of Xof Y refers to the amount
of Y that must be given up per unit of X
gained by the consumer to keep the level if
satisfaction unchanged.
MRSxy= x/ y, where
MRSxy = the MRs of X for Y
Y = a small change in the quantity of Y
X = a small change in the quantity of X
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Comm Y Comm X MRS =
x / y
10 25 -
11 20 -5/1=-5
12 16 -4/1=-4
13 13 -3/1=-3
14 11 -2/1=-2
Hicks replaces the lawof DMU by the principle
of DiminishingMarginal Rate ofSubstitution.
As the consumer
increases the quantityof X then its MUdecreases and % ofsubstitution will be lessas the point movesdownwards on the ICcurve
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Budget Constraint Or Budget Line
DEF: The Budget line is the locus of points representing all the different
combinations of the two goods that can be purchased by the consumer,given his money income and the prices of the two goods.
What a consumer can actually buy depends on the income at hisdisposal and the prices of goods he wants to buy.
I and P are 2 objective factors which form the budgetary constraint of theconsumer.
The consumption or purchase possibility of the consumer is restricted tothe budget constraint.
The slope of the budget line is called the marginal rate of substitution inexchange = PX / PY.
The concept of relative price is important because a rise in relative pricewould encourage the producer to put more resources in production. The
concept also conveys the market information of relative scarcity of thoseresources.
The budget line rotates when the relative price changes.
The shift of the line means that either the income changes or there is achange in the price of both goods.
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Alternate Purchase
Possibilities
Units
of Y
Units
of X
A 5 0
4 2
3 4
2 6
1 8
B 0 10
QtofY
s
z
XO
Y
b
a
Qt of x
c
A
B
Given income = Rs. 50
If P of Y = Rs 10/ unit
If P of X = Rs 5/ unitAB= Budget
( Price, Income) Line
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Changes in Income.
Px, Py constant
X
A3
O B3B1 B2
A1
A2
C
ommo
fY
Comm of X
Changes in
Price of Y
Changes in
Price of X
Comm of X
Comm of X
Y
A1
O XB3B1 B2
A2
A1
OB
Y
Changes in
money income,
Prices
and the BL Commo
fY
Commo
fY
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Assumptions of the Consumer Equilibrium
Consumer Has fixed amount of money income.
Intends to buy combination of 2 goods, X and Y.
Has definite tastes and preferences.
Hence has definite scale of preferences. Expressed
through IC Map. S of P remains same through out the analysis.
Is rational and mazimizes his satisfaction
Each of the goods X and Y is homogenous(identical characteristics) and divisible, sovarious combinations of these goods canbe sold.
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The consumer Equilibrium
Point e is theequilibrium
point given the
Budget line.
Satisfaction
is max
when the MRS
of x for
y is just equal
to the price
of x to the
price of y.Qt. of comm X
Qt.ofcommY
b
a
eM
N
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Consumer Optimum or Equilibrium
The CE is attained when , given, his budget constraint, theconsumer reaches the highest point in the IC.
The indifference curve and the budget line together constitute the consumptionbehaviour.
Graphically speaking, the two curves meet at a point where the indifference curveis tangent by the budget line to get an unique or internal solution. This point of
tangency represents the highest level of preference obtained by a person given afixed amount of money income.
This point is also the point of optimum condition or utility maximization.
In mathematics, the slopes of the indifference curve and the budget line arethe same.
Slope of the budget line = M R S in exchange = PX / PY
Slope of the indifference curve = M R S in consumption = Y / X
In equilibrium, PX / PY = Y / X
file:///C:/Documents%20and%20Settings/Icbm-Sbe/Desktop/MUlecture.ppt#636,1,Slide 1
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Alfred Marshall
Sir John R. Hicks
Vilfredo Federico
Damaso Pareto
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Francis Ysidro Edgeworth
Sir Roy George Douglas Allen