Theory of Utility

8/8/2019 Theory of Utility

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P.K.BABY

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Consumer is assumed to be rational ..Utility Maximaisation

What is utility?

.. Cardinal utility

..measurable

Ordinal ..Not measurableorder of preferences

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Assumptions:Assumptions:Assumptions:Assumptions: ..rationality

..cardinal utility

..constant MU of money

..diminishing MU

..additive

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This School believes that Utility is Measurableand is a Quantifiable entity. Cardinal Approach gives exact measurement

etc.Assumptions of the Cardinal Marginal Utility1. Cardinal Measurement of Utility

2. Utilities are Independent3. Constant Marginal Utility of Money

4. Introspection


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TotalTotalTotalTotal UtilityUtilityUtilityUtility is the sum total of the units of utility

which an individual derives from the consumption of acommodity during a specified period of time.

MarginalMarginalMarginalMarginal UtilityUtilityUtilityUtility is the change in the total utility

resulting from a one-unit change in the consumptionof a commodity per unit of time.

It is the addition made to the total utility by the

consumption of the last unit considered just worthwhile.MU = Change in Total Utility

Change in Quantity Consumed


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Total Utility starts increasing by decreasingratio while Marginal Utility starts decreasing.

When Total Utility is at its maximum point and

t erea ter starts ecreasing, Margina ti itycomes to zero.

After the maximum point has been achieved

by total utility it starts decreasing whichcauses marginal utility to become negative.


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The German Economist H. Gossen who was

first to explain the law said that As the

consumer consumes more and more units of

units goes on diminishing. Marshall explains the law as The additional

benefit, which a person derives from an

increase of his stock of a thing, diminisheswith every increase in the stock that he

already has.


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Units Total utility Marginal utility1 10 10

2 15 5 (15-10)

3 19 4 (19-15)

4 22 3 (22-19)

5 23 1 (23-22)

6 23 0 (23-23)

7 21 -2 (21-23)


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Explanation: As more and more quantity of a

commodity is consumed, theintensit if desire decreases and

also the utility derived from theadditional unit.


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Assumptions: All the units of a commodity must be same

in all respects

There should be no change in taste duringthe process of consumption

There must be continuity in consumption

There should be no change in the price ofthe substitute goods

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Mux = Px


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This law states that the consumermaximizing his total utility will allocate

his income among various commodities

the last rupee spent on each commodity

is equal.

The consumer will spend his money

income on different goods in such a waythat marginal utility of each good is

proportional to its price


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Under Law of Equi-marginal utility consumer

equilibrium can be stated in the following

.

MUx = MUy = Mun = MUmPx Py Pn


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Suppose consumer is buying two Goods X and Y and

marginal utility of them are given asUnits of X & Y MU x MU y

1 33 36

Suppose the prices of good X & Y are Rs. 3 & Rs.4 respectivelyand total income is Rs.20. The above table can bereconstructed by dividing the marginal utilities of good X by Rs.3 and marginal utilities of good y by Rs. 4.

3 27 28

4 24 24

5 21 20

6 18 16


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Units of Money MU xP x

MU yP y

1 11 9

2 10 83 9 7

4 8 6

5 7 5

6 6 4


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The aim: to analyze how a rational consumer

chooses between two goods.

For instance, how the change in thewage rate will affect the choice

between leisure time and work time.

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Assumptions:Assumptions:Assumptions:Assumptions: ..rationality

..utility is ordinal

..diminishing MRS ..TU depends on quantities consumed

..consistency and transitivity

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An indifference curve is a line that shows all

the possible combinations of two goods

between which a person is indifferent.

,

consumption ofdifferent combinations oftwo goods that will give the same utility

(satisfaction) to the person.

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Pizza (X)

Soft

Drinks

(Y)

Comb-

ination10

12

oftime

A

1 10 A

2 6 B

4 3 C

7 1 D

0

2

4

6

8

0 2 4 6 8

Pizza per unit of time

SoftDrinksperu

nit

20

B

C

D


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For instance, inFigure a personwould receivethe same utilitysatisfaction

Y(Wor

k)

Same Utility in two points

from consuming5 hours of workand 3 hours ofleisure, as theywould if they

consumed 2hours of workand 6 hours ofleisure.

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Good X (Leisure)

IC

0

5

3

2

6


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The marginal rate of substitution isthe amount of one good (i.e. work)

that has to be given up if the

consumer is to obtain one extra unitof the other good (leisure).

Slope of IC X

YMRSxy

=

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IC slopes downward from left to right

an IC does not touch either x or y axis.

convex to origin

diminishing RS a higher IC represents higher level of

satisfaction than lower one

IC can not intersect each other

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Y(Wor

k)

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Good X (Leisure)

IC4

0

IC5

IC3

IC2IC1


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y y

25

xx

Perfect Substitutes Perfect Complements

IC

IC


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Y = px qx + py qy If qx = 0,

Spends Y/py on Y

PriceofY

Y/py

px qx + py qy

If qy = 0, Spends Y/px on X

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0

Price of X

Y/px

Same costat differentprice combinations


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Py/Qy

Shifts Parallelwhen income changes

27o

Px / Qx

Income Rs. 100

.


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Py/Qy

28

Px / Qx

Px = 15 Px = 10

Px = 5


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Py/Qy

29

Reduction in price of Y

Px / Qx


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Slope of IC,

RSx =

Py/Q

y

MUx/MUy Slope of budget

line, Px/Py

MRSx,y =

Px/Py

30Px / QxQx

Qy

IC1

IC2IC3

E


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Thank you.

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Theory of Utility

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