7 utility

In This Lecture…

Concepts of Utility: Cardinal and Ordinal

Law of Diminishing Marginal Utility

Indifference Curve (IC) Analysis : Concept, Properties, MRS

In This Lecture…

Consumer’s Equilibrium : Budget Line and IC Curve Analysis, Price Effect, Income Effect, Substitution Effect, Effects of changes in Income and Prices.

Utility Theory Utility is the want satisfying power of a

good.There are two approach in this theory.

- Cardinal Utility Theory- Ordinal Utility Theory

Cardinal Utility Theory : Classical school believes that utility can be measured using an absolute/ quantitative scale like the other physical characteristics – height and weight – and are comparable.

A util is an artificial construct used to measure utility.

No Interpersonal UtilityComparison

Caution: The utility obtained by one person cannot be scientifically or objectively compared with the utility obtained from the same thing by another person because utility is subjective.

Total Utility Total utility is the total satisfaction a

person receives from consuming a particular quantity of a good. TUn = MU1 + MU2 + …….. + Mun

Marginal utility is the additional utility a person receives from consuming one extra unit of a particular good.MUn = TUn – TUn-1

or, MUx = Δ TUx

Δ X

Law of DiminishingMarginal Utility

As you consume more and more of a same commodity at a point of time the marginal utility derived from each successive unit goes on declining assuming that the utility each unit of money paid as price of commodity is constant.

Law of DMU can be explained by the relationship between TU and MU.

TU and MU

TU and MU Schedule

Quantity of X MUx TUx

0 - 0

1 8 8

2 6 14

3 4 18

4 2 20

5 0 20

6 -2 18

7 -4 14

8 -6 8

Contd..•Graphical Presentation:- TUx

TUx

O Quantity MUx

MUx=0 O MUx Quantity

TU and MUTU curve starts from the origin, reaches a

maximum point and starts declining. When TU is maximum, called saturation point,

MU is zero. Units of goods are consumed till saturation point.

When TU is rising, MU curve falls.When TU is falling, MU curve becomes

negative.The falling MU curve exhibits the law of

diminishing marginal utility.

Consumer’s Equilibrium

The consumer is in equilibrium when he maximizes his level of satisfaction with given income and market price.Assumption :-

Rational ConsumerCardinal UtilityIndependent UtilityMU of money is constant

Rationality

A rational consumer is the one who wants to get maximum satisfaction out of his given income.

Cardinal Utility

Utility can be cardinally measured, i.e. can be expressed in exact units.

Utility is measurable in monetary terms.

Independent Utility

The utility that the consumer derives from a commodity depends upon the quantity of that very commodity alone and is not affected by the consumption of other goods.

MU of Money is Constant

It means that importance of money remains unchanged.

MU of money is addition made to utility of consumer as he spends one more unit of money income. This is assumed to be constant.

Consumer’s Equilibrium – One Commodity Case

When a consumer buys a commodity he pays a price for it. For each unit he makes a sacrifice in terms of price. In turn he gets utility from each unit. We know that the utility of each successive unit goes on diminishing as we consume more and more of it according to law of DMU with the assumption that that the utility each unit of money paid as price of commodity is constant.


A rational consumer will be in equilibrium when he consumes that quantity at which utility value of money price is equal to marginal utility of the commodity.

Marginal Utility = Utility of Price of good Paid

MUX = MUM X PX

MUX = MUM

PX


Geometrically, Price, Utility

CONSUMER’S EQULIBRIUM

10 E MUx = Px (MUm)

MUx

O 9

Quantity

Here, MUm is constant and is equal to 10 utils.


If the consumer consumes more than equilibrium point, then the utility value of money price is higher than the marginal utility of the commodity and hence, consumer will be in disequilibrium.

If the consumer consumes less than equilibrium point, then the utility value of money price is lower than the marginal utility of the commodity and that there is the further scope of maximization of satisfaction/utility. Hence, consumer will be in disequilibrium.

Consumer’s Equilibrium – Two Commodity Case

In reality consumer spends his income on many goods.

A rational consumer will be in equilibrium when he consumes that quantity of Good X and Y at which utility value of money price is equal to marginal utility of the commodities.

Consumer’s Equilibrium – Two Commodity Case -

contd.Suppose a consumer spends on two

goods X and Y. Then he will be in equilibrium when,

MUX = MUM X PX ……………… (i)

MUY = MUM X PY………………. (ii)

Or, MUX / PX = MUM and MUY / PY = MUM

Or, MUX / PX = MUY / PY = MUM

This is subject to money income of the consumer being constant.

Consumer Equilibrium – Multiple Commodity Case

The analysis is based on the assumption that individuals seek to maximize utility.

Occurs when the consumer has spent all income and the marginal utilities per dollar spent on each good purchased are equal:

where the letters A–Z represent all the goods a person buys.

Ordinal Utility Theory

Modern school does not believe that utility can be measured using an absolute/ quantitative scale like the other physical characteristics – height and weight – and are comparable.

All desires of a consumer are not of equal importance or urgency. Due to resources being scarce, the problem of choice arises and that a consumer cannot satisfy all his desires. So some desires take precedence over others. It is consumer’s scale of preference that determines his expenditure pattern.

Ordinal Utility Theory – Indifference Curve Analysis It is consumer’s scale of preference that

the consumer determines his expenditure pattern in such a way that maximizes his level of satisfaction. For this Indifference Curves or IC curves are drawn.

IC curve is the diagrammatic representation of a set of combinations of two commodities that offers a consumer same level of satisfaction and that he is indifferent between these combinations given his level of income and price of the commodities.

IC curve is also known as Iso-utility curve.

IC Curve – Schedule

Satisfaction level at A = Satisfaction level at B = Satisfaction level at C = Satisfaction level at D

Combinations Apples Oranges

ABCD

1234

10754

IC Curve – Diagrammatic Representation

Oranges 10

8

6

4

IC Curve 2

0 1 2 3 4 Apples

IC Curve Map

A set of family of IC curves is called IC Curve Map.

Higher the IC curve from the origin the higher will be the level of satisfaction.

Level of satisfaction of F > Level of satisfaction of E > Level of satisfaction of A > Level of satisfaction of D > Level of satisfaction of C

Indifference Curve Analysis- Assumptions

Rationality : Consumers are assumed to be rational and aims at maximizing his benefits from consumption, given his income and price of good.

Ordinality : Utility is expected satisfaction that a consumer gets and is subjective in nature. He ranks utilities derived from the commodities and has a scale of preferance between different combination of two goods.

Indifference Curve Analysis – Assumptions Contd.

Consistancy of Choice : If consumer prefers good X over good Y in one time period, the consumer will not prefer Y over X in another in another time period.

Transitivity of Choice : If good X is preferred to good Y, and good Y is preferred to good Z, then good X is preferred to Z.

Convexity : IC curve is always convex to the origin due to diminishing marginal rate of substitution (MRS).

What is diminishing MRS?

MRS shows how much of one commodity is substituted for how much of another.

Combinations Apple OrangeA 1 10B 2 7C 3 5D 4 4

For combination B 3 oranges are sacrificed for 1 apple and C, 2 for 1 and D, 1 for 1..

It can be observed that as the consumer consumes more and more of a same good he is prepared to forego less and less of other as his desire for the former becomes less and less intense with more and more of it.

Therefore, MRS of apple to orange fall as he has more of apple.

What is diminishing MRS? Contd.

As more and more of good Y is substituted for X MRS starts to diminishes because X and Y are imperfect substitutes to one another.

Orange ΔY1/ ΔX1 > ΔY2 / ΔX2 > ………. > ΔYn/ ΔXn

ΔY1

ΔX1

ΔY2

ΔX2

O Apple

IC Curve - Characteristics

Downward Sloping to the right : It is because when the consumer decides to have more of one good he will have to reduce the number of consumption of other good to remain on the same level of satisfaction / IC curve.

The further away the IC curve from the origin the higher the level of satisfaction and are preferred by the rational consumer.

IC Curve - Characteristics

IC curves never intersect each other.

A B

C

Here, level of satisfaction at A = B and A = C . But B ≠ C

IC curves are always convex to the origin due to diminishing MRS.

Budget Line A rational consumer would always like to be

on the highest IC curve signifying highest level of satisfaction. But it is governed by the level of income of the consumer and prices of goods in the market.

Budget line is a line that shows the different possible combinations of two goods X and Y, which a consumer can buy given his budget and the prices of good X and Y.

Anywhere on the budget line a consumer is spending his entire income either on Good X or on Good Y or the combination of both X and Y.

Budget Line – Diagrammatic

Representation with exampleSuppose the income of a consumer is

$60, price of apples is $2 per unit and oranges $1 per unit.

Apples Oranges

0102030

6040200

Budget Line – Diagrammatic Representation with example

Contd. Good Y

60

50 Budget Line or Price Line

40

30

20

10

0 10 20 30 Good X

Consumer cannot go beyond Budget line as any point beyond it shows a non-attainable / non-feasible combination.

Shifting of Budget Line

Good Y Good Y A’ A A

O B B’ Good X O B’ B Good X

Budget line when money income increases Budget line when price of X increases

prices remaining unchanged – that is why price of Y and money income there is a parallel shift in budget line. remaining unchanged

Consumer’s Equilibrium

All bundles of goods are available to the consumer in the sense that he can buy them if he can. The consumer’s IC map establishes a rank ordering of these bundles.

The consumer’s budget space is established by his fixed money income and relative commodity prices; it shows bundles he can purchase.

Rational consumer selects the most preferred bundle of goods in his budget space.

Consumer’s Equilibrium Good Y

60 Equilibrium Point

50

40 Q IC4

30 IC3

20 IC2

10 IC1

0 10 20 30 Good X

Given the IC map consumer is in equilibrium when the budget line is tangent with the highest possible IC curve where he maximizes his level of satisfaction with his given income and the market prices.

Income Effect on Equilibrium

Good Y ICC (Income Consumption Curve) S P B A IC2

IC1

O Q R Good X

With a rise in the income of the consumer he attains a higher level of equilibrium from A to B. ICC traces the income effect. It shows how the changes in income of the consumer will affect the consumer’s purchases of good X and Y– price of X and Y, taste and income being constant

Price Effect on Equilibrium

The consumer will either be better off or worse off depending on the change in price of a good.

With a change in price of a good, the consumer will be at a higher level of satisfaction with a fall in price and will be at a lower level of satisfaction with a rise in price.


Good Y PCC (Price Consumption Curve)

P

C IC3

B IC2

A IC1

O Q R S Good X

With a fall in the price of Good X the consumer attains a higher level of equilibrium from A to B and B to C. PCC traces the price effect. It shows how the changes in price of good X will affect the consumer’s purchases of good X and Y – price of Y, taste and income being constant


Good Y PCC (Price Consumption Curve)

P

C B IC3

IC2

A IC1

O Q R S Good X

If PPC curve is backward sloping it indicates that good X is an inferior good because with a fall in price of X less of X is demanded. (PED<1)


Good Y IC1 PCC (Price Consumption Curve)

IC2

P IC3

B C A

O Q R S Good X

If PPC curve is forward sloping it indicates that good X is a superior good because with a fall in price of X more of X is demanded (PED>1)


Good Y IC1 PCC (Price Consumption Curve)

IC2

P IC3

C B A

O Q R S Good X

If PPC curve is horizontal it indicates PED = 1

Price Effect and Substitution Effect and

Income Effect A change in the price of a commodity

leads to a change in the relative prices of the goods – a change in terms at which a consumer can exchange one good for another (substitution effect) and a change in the real income of the consumer.

If the price of a good X falls then the real income of the consumer goes up leading to income effect and that the relative price of X to Y will be lower as well and consumers will substitute more of X to Y.

Substitution Effect

It is a change in quantity demanded resulting from a change in relative price while retaining the same level of satisfaction or on same IC curve.

Substitution Effect on Equilibrium

R Good Y A P C B IC2

IC1

O T S Q Good X

With a fall in the price of X consumer can move from C to A –

Income Effect or to B – Price Effect; and since the relative price of X is lower to Y, consumer can move from A to B by retaining the same level of satisfaction, nominal income being constant.

Substitution Effect on Equilibrium

R Good Y Income Consumption Curve (ICC) A Price Consumption Curve

(PCC) P C B IC2

IC1

O T S Q Good X

With ICC and PCC curves.

Movement from C to A – Income Effect Movement from C to B – Price Effect Movement from A to B – Substitution Effect.

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7 utility