ordinal approach

8/13/2019 Ordinal Approach

1/18

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.


2/18

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


3/18

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.


5/18

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


11/18

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.


12/18

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


13/18

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


14/18

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.


15/18

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


16/18

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


17/18

Alfred Marshall

Sir John R. Hicks

Vilfredo Federico

Damaso Pareto


18/18

Francis Ysidro Edgeworth

Sir Roy George Douglas Allen