Presented by:

RAVI MUCHHAL

PGDM 1st trimester

Doon Business School

1Ravi Muchhal (R)

Each consumer has to face the problem of multiplicity of wants and limited

income.

In such state of affairs it is the desire of each consumer to maximize his

satisfaction in the presence of income constraint.

Whenever a consumer maximizes his satisfaction, he is satisfied with his

spending pattern, does not have any tendency to change his style of

expenditure, he is said to be in equilibrium in economics.

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(1) The satisfaction or utility can be measured into numbers. E.g. If a

consumer drinks a glass of milk, the satisfaction he derives from that glass

of milk can be represented into number like 1,2,4,5 etc.

It is the view of the economist that the satisfaction or utility is a cardinally

measureable quantity as length, weight and volume.

Therefore they accepted the existence of unit of measurement of utility

called “util”.

They believed that each consumer has a utilometer to measure the utility

into numbers when a consumer uses that units of a good.

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(2) Utility depends upon the units of one good which a consumer is

consuming. In other words utilities are independently determined as U=f(Q).

Where “U” stands for utility, while “Q” represents the units of the particular

good which a consumer is consuming.

Moreover, the utilities from different goods can be added. It shows by

additive utility function. U = U1(Q1) + U2(Q2)+....+Un(Qn)

Where U1, U2 are the utilities of commodity no. 1,2 etc, which are included

in the bundle or basket of goods which a consumer is purchasing. While

Q1, Q2 are the number of commodities.

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(3) The behaviour of all consumers remain a like. This means that what is

the behaviour of a representative consumer, the same is the behaviour of

rest of consumers during the consumption.

(4) Consumer is rational i.e. He is well aware of with his income and prices

of the good in the market.

(5) The money is a measure which is employed to measure the utility of the

goods and service. And there is no change in the marginal (extra) utility of

the money, it means that marginal utility of the goods may change while the

marginal utility of money remain the same.

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Before we explain this law, we clarify the meanings of utility and marginal

utility.

By utility we mean, the power of a good to satisfy human want. i.e. The

water has a power to quench one’s thirst. For our discussion, by utility we

mean “The satisfaction”.

As we discussed above that utility or satisfaction depends upon the units of

a particular good. It is as: U= f(Q) or TU=f(Q). This is called utility or total

utility function.

By “Marginal utility” we mean the net change in total utility by having

consumed an additional unit of a commodity.

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For example a consumer is using the units of apple, if the total utility of 1st

apple is 10 units while the total utility goes to 18 units if he uses the two

apples, then the net change in total utility or marginal utility is 8.

MU is the derivative of total utility function or it is the slope of TU curve, it is

as: U = f(Q).

Then its derivative will be MU = dU/dQ.

Now we introduce “Law of DMU”. This law is based upon a common reality

of life, “The more we have of any commodity, the desire to get any more of

it decreases”.

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“When a consumer goes on to use the units of good, the total utility derived

from the units of good increases at a decreasing rate.

In other words “along with successive and continuous use of any

commodity the marginal utility derived from the units of the commodity goes

on to fall”.

From the definition we deduce the following:

I. Along with increase in use of any commodity, TU increases at a decreasing rate, hence MU

decreases.

II. When the total utility reaches maximum , MU becomes zero. This situation is called point of

saturation.

III. When total utility itself falls, MU becomes negative.

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9Ravi Muchhal (R)

I. There should be a continuous use of the commodity which a consumer is

consuming.

II. All the units of the commodity in use must be similar.

III. The units of good must be a of a suitable amount.

IV. The taste of consumer should remain the same.

V. The income of the consumer should not change.

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According to law of equi. Marginal utility; “ A consumer is in equilibrium

when he spends his money income on different goods in such a way that

MU of the last units of money spent on each good is equal”.

This is explained with the help of a schedule and diagram. We assume that

a consumer has 5 rupees which he has to spend on two goods like “X” and

“Y”. The MU of different units of money are assumed as:

Units of Money

Mux Units of Money

Muy

1 16 1 14

2 12 2 10

3 10 3 6

4 8 4 4

5 6 5 2

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When a consumer decided to spend his 1st unit of money whether this will

go for good x or for good y. Obviously it will go for good x because here he

gets 16 utils.

While he get 14 utils if he spends it on good y. Then 2nd rupee will be spend

on good y because spending it on y yields 14 utils while spending it on x

yields 12 utils.

The 3rd rupee will be spent on x, because 12>10. The 4th rupee will be

spent on y and 5th will be spent on x yielding the 10 utils each.

In this way out of 5 rupee, 3 rupee will be spend on good x and the

remaining 2 rupee will be spend on good y. By such arrangements the MU

of the last rupee spent on each good has equalized as 10=10.

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Now we prove here that how this situation leads to maximization of

satisfaction.

Total satisfaction or total marginal utility when 3 rupee are spent on good x:

16+12+10 = 38.

Total satisfaction or total marginal utility when the remaining 2 rupees are

spent on good y: 14+10 = 24.

Total satisfaction or total marginal utility of 5 rupees: 38+24=62.

We assume that if the consumer plans to spend 4 rupee on x and remaining

1 rupee on y. This situation will not equate MU of the last unit of money

spent on each good.

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14Ravi Muchhal (R)

“An indifference curve is a curve which shows difference combinations of

two commodities like x and y which give a consumer an equal satisfaction”.

“An IC shows different bundles of two goods like x and y amongst which

consumer remains indifferent because of all such bundles yield a specific

level of utility”.

“An indifference curve is the locus of all points in the commodity space that

are equally attractive to the consumer”. That is the consumer is indifferent

between any two commodity bundles (points) that lie on the same IC curve.

U = f(x,y) = k

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Bundlesz Commodity x Commodity y MRSxy = dy/dx

A 1 11

B 2 8 3/1 = 3

C 3 6 2/1 = 2

D 4 5 1/1 = 1

E 5 4.5 0.5/1 = 1/2

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While the pairs giving less satisfaction to the consumer will lie below these

combinations or below this IC – all such is shown with the help of

indifference map.

Marginal rate of substitution MRSxy = dY/dx

Simply the rate of exchange between two commodities x and y is called

MRS. In proper words by “MRSxy we mean how many units of commodity

y the consumer has to forego to get an additional unit of commodity x while

the new combination of commodity x and y yields the same level of

satisfaction”.

Reference our previous schedule we see that as consumer moves from pair

A to pair B, he losses 3 units of y for an additional unit of x. Accordingly,

marginal rate of substitution of x for y is 3.

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MRS is also known as slope of an IC.

If we observe the indifference schedule and indifference curve, we find that

MRS goes on to fall. Such tendency of falling MRS is known as “Principle of

DMRS” between x and y.

It is well evident fact that as a consumer has more and more of any

commodity his desire to get any more of it decreases because of an

application of law of diminishing marginal utility.

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An IC shows different combinations of two goods x and y which yield and equal level of satisfaction. Now the question is this which combinations of two goods a consumer can afford to purchase.

This is concerned with the budget constraint line, price line or budget line of the consumer. It is defined as:

“Budget line is a curve which shows different combinations of two goods like x and y which a consumer can purchase, while the consumer’s income, price of x and price of y are given”.

It is as: xPx + yPy = I

Where x represents x commodity, Px is price of x, y represents y commodity and Py is the price of y while I is the income of the consumer.

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Y = I/Py – Px/Py (x).

Now by assuming different values of x, we can find the values of y and then

putting such values of x and y in the budget constraint equation, the

expenditure of the consumer will become equal to the fixed given income of

the consumer.

We suppose I = 10, Px = 2 and Py = 1. If x = 0,1,2,3,4,5. plotting values.

Pairs

X Y xPx + yPy = I

A 0 10 0(2) + 10(1) = 10

B 1 8 1(2) + 8(1) = 10

C 2 6 2(2) + 6(1) = 10

D 3 4 3(2) + 4(1) = 10

E 4 2 4(2) + 2(1) = 10

F 5 0 5(2) + 0(1) = 10

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The BL depends upon only two elements: the consumer’s money income (I)

and commodity prices (Px and Py). When either of these two elements

changes, the BL shifts to a new position. However the BL remains totally

unaffacted by a particular change: a proportional increase or decrease in

money income and all commodity prices. Such a change leaves horizontal

and vertical axis intercepts of the BL same.

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