Long Type Questions
Therefore,
a utility maximizing consumer exchanges his money income for the commodity so
long as MUx > MUm. As assumed earlier, marginal
utility of commodity of X is subject to diminishing returns, whereas marginal
utility of money income (MUm) remains constant. Therefore, the consumer will exchange his
money income for commodity X so long as MUx > Px (MUm). The utility maximizing
consumer reaches his equilibrium with the level of his maximum satisfaction
where
Consumer’sequilibrium in a single-commodity case is illustrated graphically in the given
figure. The horizontal line Px (MUm) shows the constant
utility of money weighted by Px, the price of commodity
X, and MUm curve represents the diminishing marginal utility of
commodity X.
Figure
shows the consumer’s equilibrium : One Commodity Case
In
figure, PT is budget line and IC1, IC2 and IC3 are three
indifference curves. Given the budget line, the consumer may get maximujn
satisfaction by IC2. This is consumers’ point C, budget line AB is tangent to
indifference curve IC2. This is consumers’ equilibrium point. At this point, consumer
purchases OH amount of X and OE amount of Y.
Conclusion : Cardinal approach is based on various unrealistic assumptions, therefore ordinal approach is superior to cardinal approach.
Question 3. Explain the characteristics of indifference curve analysis.
(ii)
Indifference Curves are Convex to Origin : The convexity of indifference curves
implies:-
Convexity
of the indifference curve is based on the postulate of diminishing marginal
rate of substitution.
Let
us now see what happens when two indifference curves IC1 and IC2, intersect at point B.
Consider two other points – point F on indifference curve IC1 and IC2, and point E on
indifference curve IC2, both falling on vertical line.
(iv)
Higher Indifference Curves Represent a Higher Level of Satisfaction Than the
Lower Ones : An indifference curve placed above and to the right of another
represents a higher level of satisfaction than the lower one. The reason is
that an upper indifference curve contains all along its length a larger
quantity of one or both the goods than the lower one. And, a larger quantity of
a commodity is supposed to yield a greater satisfaction than the smaller
quantity of it, provided MU > 0
Comparison of Lower and Upper Indifference Curves
For
example, consider the indifference curves IC1 and IC2. The vertical movement
from point a on the lower indifference curve, IC1, to point b on the upper
indifference curve, IC2, means increase in quantity of Y by ab, the quantity of X
remaining the same (OX). Similarly, a horizontal movement from point a to d
means a greater quantity of commodity X, quantity of Y remaining the same. A
diagonal movement from point a to c means larger quantities of both X and Y.
Unless the utility of additional quantities of X and Y are equal to zero, these
additional quantities will yield additional utility. Therefore, the level of
satisfaction indicated by the upper indifference curve (IC2) would always be greater
than that indicated by the lower indifference curve (IC1).
Thus, inspite of the fact that cardinal and ordinal approaches are based on different assumptions regarding the measurability of utility, both arrive at the same conclusion.
Therefore,
a utility maximizing consumer exchanges his money income for the commodity as
long as MUx > MUm. Marginal utility of commodity
of X (MUx) is subject to diminishing returns, whereas marginal utility of
money income (MUm) remains constant. Therefore, the consumer will exchange his
money income for commodity X as long as MUx > Px (MUm). The utility maximizing
consumer reaches his equilibrium with the level of his maximum satisfaction
where
MUx = Px (MUm) (Where MUm = 1)
Let
marginal utility of money for you = 5 utils (referring to your satisfaction
from your standard set of goods available for a rupee)
Units of X |
MUx |
1 |
40 |
2 |
28 |
3 |
16 |
4 |
10 |
5 |
0 |
6 |
-5 |
(ii)
Limited Money Income : Consumers have limited money in order to spend on goods
and services, which they have chosen to continue using.
(iii)
Maximisation of Satisfaction : Every rational consumer intends to maximize his
satisfaction from his given money income.
(iv)
Utility is Cardinally Measurable : The cardinalists assume that utility is
cardinally measurable, i.e. it can be measured in absolute terms and in
cardinal numbers.
(v)
Diminishing Marginal Utility : The cardinalists assume that the utility gained
from successive units of a commodity consumed decreases as a consumer consumes
more and more units of it.
(vi)
Constant Utility of Money : The marginal utility of money remains constant
whatever the level of consumer’s income and each unit of money has utility
equal to 1.
(vii)
Utility is Additive : Cardinalists maintain that utility is not only cardinally
measurable but also it is additive. The additivity of utility can be expressed
through a utility function.
(i)
Rationality : A consumer is considered a rational being. His goal is to
maximize his total satisfaction. Given his income and prices of goods and
services he consumes, his decisions are consistent with his objective. Apart
from this, they have full knowledge about their circumstances and circumstances
which are essential for a rational decision.
(ii)
Ordinal Utility : Unlike cardinal utility approach, ordinal utility approach
assumes that utility is only ordinally measurable by consumer’s subjective
evaluation. That is, a consumer is able to express only the order of his
preferences.
(iv)
Non-satisfaction : Non-satisfaction means that the consumer is not able to
reach the point of saturation in case of any commodity and he is not
oversupplied with goods in question. Therefore, a consumer always likes a
larger quantity of all the goods.
Uncompromising
means that the consumer is not able to reach the point of saturation in the
case of any object and the question of excess amounts of goods does not arise.
Therefore, a consumer always likes a large amount of all the items.
(v)
Diminishing Marginal Rate of Substitution : The marginal rate of substitution
is the rate at which a consumer is willing to substitute one commodity (X) for
another (Y) so that his total satisfaction remains the same. This rate is given
by ∆Y/∆X. The assumption is that ∆Y/∆X goes on decreasing, when a consumer
continues to substitute X for Y.
(i)
The law of diminishing marginal utility is of crucial significance in
explaining determination of the prices of commodities. The discovery of the
concept of marginal utility has helped to explain the contradiction of money
which troubled Adam Smith in ‘The Wealth of Nations’. Adam Smith was greatly
perplexed to know why water which is so very essential and useful to life has
such a low price (indeed no price), while diamonds which are quite unnecessary,
have such a high price. This value paradox is also known as Water-Diamond
Paradox. But modern economists can solve it with the help of marginal utility
concept. According to the modern economists, the total utility of a commodity
does not determine the price of a commodity and it is the marginal utility
which is crucially, an important determinant of price. Now, the water is
available in abundant quantities so that its relative marginal utility is very
low or even zero. Therefore, its price is low or zero.
(ii)
Another important use of marginal utility is in the field of fiscal policy. In
the modern welfare state, the Government redistributes income so as to increase
the welfare of the people. This redistribution of income through imposing progressive
income taxes on the rich sections of the society and spending the tax proceeds
on social services for the poor people is based upon the diminishing marginal
utility. The concept of diminishing marginal utility demonstrates that transfer
of income from the rich to the poor will increase economic welfare of the
community.
In
the beginning, the consumer gives up 4 units of Y for the gain of one additional
unit of X, and in this process, his level of satisfaction remains the same. It
follows that one unit gain in X fully compensates him for the loss of 4 units
of Y. It means that at this stage, he is prepared to exchange 4 units of Y for
one of X. Therefore, at this stage, consumer’s marginal rate of substitution of
X for Y is 4. Thus, we may define the marginal rate of substitution of X for Y
as the amount of Y whose loss can just be compensated by a unit gain in X. In
other words, marginal rate of substitution of X for Y represents the amount of
Y which the consumer has to give up for the gain of one additional unit of X so
that his level of satisfaction remains the same.
In
the table, when the consumer moves from combination B to combination C on his
indifference schedule, he forgoes 3 units of Y for additional one unit gain in
X. Hence, the marginal rate of substitution of X for Y is 3. Likewise, when the
consumer moves from C to D, and then from D to E in his indifference schedule,
the marginal rate of substitution of X for Y is 2 and 1 respectively.
Relation
of Marginal Rate of Substitution (MRSxy) with Marginal Utilities
It
follows from above that marginal rate of substitution of good X for good Y is
equal to the ratio of marginal utilities of the two goods.
Suppose
when two indifference curves IC1 and IC2, intersect at point B.
Consider two other points – point F on indifference curve IC2 and point E on
indifference curve IC1 both falling on vertical line.
Since
OD of X is common to both the terms, it means that FD of Y is equal to ED of Y.
But, this is not so. Figure shows FD > ED. Therefore, combinations B and C
cannot be equal in terms of utility in the objective introspection of the
consumer. The intersection, therefore, violates the transitivity rule which is
a logical necessity in indifference curve analysis.
The
greater the decline in marginal rate of substitution, the more the convexity of
the indifference curve. The less the ease with which two commodities can be
alternative for each other, the more will be the decline in marginal rate of
substitution. At the highest, when two goods cannot at all be substituted for
each other, that is, when the two goods are perfect complementary goods, as for
example bread and butter, the indifference curve will consist of two straight
lines with a right angle bent which is convex to the origin. Perfect
complementary commodities are utilized in a certain fixed ratio.
The
left hand portion in figure of an indifference curve shows the perfect
complementary goods through vertical straight line which indicates that an
endless amount of Y is necessary to substitute one unit of X, and the right
hand side portion in figure of an indifference curve shows horizontal straight
line which means that an endless amount X is necessary to substitute unit of Y
all means that the two perfect complements are utilized in a certain fixed
ratio and cannot be substituted for each other.
Figure
shows that two perfect complements are consumed in the ratio, 3X : 2Y.
Complements are thus those goods which are used jointly in consumption so that
their consumption increases or decreases simultaneously. Pen and Ink, Right
Shoe and Left Shoe, Automobile and Petrol, Sauce and Hamburger, Typewriter and
Typists are important examples of perfect complements.
Short Answer Type Questions
(i)
More Part of Goods is Better Than the Least: It is believed that the consumer
will always like a greater amount of quality goods, provided the other
accessories remain unchanged in their disposal.
(ii)
Preferences or Indifferences of a Consumer are Transitive : Suppose there are
three combinations of two goods A, B and C. If the consumer is indifferent
between A and B and C, it is then assumed that he will be indifferent between A
and C too. This condition implies that consumer’s tastes are quite consistent.
This assumption is known as Assumption of Transitivity.
(iii)
Utility is Ordinal : It is truly believed that consumers can evaluate different
combinations of the objects according to their liking.
(iv)
Diminishing Marginal Rate of Substitution : This principle is related to the
logical requirement that the particular desires are saturated and various goods
are not the right choice for each other.
Initial
line is MN, when the income decreases, the line M1N1 move downwards.
1.The consumers’ behaviour is assumed to be discretional.
2.Utility is measurable, and currency is used to measure it.
3.The marginal utility of currency is assumed to be invariable.
4.The process of consumption is continuous.
5.The income, habits, interest, and fashion trends of the
consumer do not change with time.
6.The units of utilised commodity should be of appropriate size
and homogeneous in context of their properties.
(ii)
Indifference Curves are Convex to Origin : The convexity of indifference curves
implies :
(iii)
Indifference curves do not intersect nor are tangent to one another.
(ii)
Utility cannot be measured in objective terms. It cannot be quantified and
cannot be measured by any measuring rod. However, some economists maintain that
utility can be measured in terms of money.
(iii)
Utility is not absolute but it is relative in view of its subjective nature. It
is relative to a person’s need. Therefore, it varies from person-to-person.
(iv)
Utility is abstract in the sense that it cannot be seen or touched.
1.Cardinal analysis, 2.Ordinal analysis.
(ii)
Goods are often available in large indivisible units. Because the goods are
indivisible, it is not possible to equate the marginal utility of money spent
on them.
(ii)
Indifference curves are convex to origin. Indifference curves for normal goods
are not only negatively sloping, but are also convex to the origin.
1. The consumer’s surplus cannot be measured
exactly because it is difficult to measure the marginal utility of different
units of a commodity consumed by a person.
2. In the case of necessaries, the marginal
utilities of the earlier units are infinitely large. In such case, the
consumer’s surplus is always infinite.
3. There is no simple rule for deriving the utility
scale of articles which are used for their prestige value (e.g., diamonds).
(i)
TU curve represents total utility. It slopes upwards upto point ‘G’. Point ‘G’
represents maximum total utility at the 5th unit. After point ‘G’, TU slopes
downwards, meaning thereby, that at the 6th unit marginal utility becomes
negative and total utility begins to fall.
(ii)
MU curve represents marginal utility. It slopes downwards from left to right.
It means that marginal utility of successive units goes on diminishing.
Above
graph makes it clear that budget line shifted towards Y-axis but it is constant
on that point on X-axis.
Where ∆TU = change in total utility, and ∆C = change in consumption by one unit
Substituting
the given values, we get MUx/8 = 40 implying that, in a state of equilibrium, Rohan’s MUx must be equal to 320.
If, having consumed 8 ice creams, Rohan’s MUx = 320 he must stop
consuming more. However, if MUx > 320 he should
consume more ice creams till MUx reduces to 320 and
in terms of its money worth is equal to Px = 40.
Question
37. Estimate the value of total utility and marginal utility from the
following table
Units Consumed (Commodity X) |
TUx |
1 |
200 |
2 |
390 |
3 |
570 |
4 |
740 |
5 |
900 |
Units Consumed |
TUx |
Marginal Utility |
1 |
200 |
200 |
2 |
390 |
190 |
3 |
570 |
180 |
4 |
740 |
170 |
5 |
900 |
160 |
Question
38. Convert this table into a diagram which shows the relation of total utility
and marginal Utility.
Units Consumed |
TUX |
Marginal Utility |
1 |
200 |
200 |
2 |
390 |
190 |
3 |
570 |
180 |
4 |
740 |
170 |
5 |
900 |
160 |
Figure
shows the relation between total utility and marginal utility
Question
39. Rita has ₹ 88 with her. She intended to purchase goods X and Y with
her money. The market price of X and Y per unit is ₹ 8. The marginal utility
schedule of goods X and Y is given below. Find out how many units of X and Y
should Rita purchase so that she will get maximum satisfaction.
Units of
Commodity |
MUy |
muy |
1 |
88 |
40 |
2 |
72 |
36 |
3 |
64 |
24 |
4 |
56 |
20 |
5 |
48 |
16 |
6 |
40 |
12 |
7 |
32 |
8 |
8 |
24 |
4 |
9 |
16 |
0 |
10 |
8 |
0 |
Consider
combination X = 6 and Y = 1, here also MUx = MUy. But it is not an
equilibrium point because here all income is not spent i.e., affordable in
terms of consumer’s income.
Here,
consumer’s expenditure exceeds his income i.e., 72 ( = 9 × 8) + 40 ( = 5 × 8) =
112 > 88.
Basis of
Comparison |
Total Utility |
Marginal Utility |
Meaning |
Total utility means total gain acquired
by a person from consumption of goods and services. |
Marginal utility meants the
amount of utility a person gains from the consumption of each gradual unit of
a commodity. |
Conclusion |
Suffers from diminishing
returns. |
Consumption decreases for each
additional unit. |
Certainly
OT > OS. Implying that at C a consumer gets more of Good-1 and the same
amount of Good-2 as at B. We know according to his monotonic preferences, a
rational consumer gets more satisfaction from more of good. Accordingly, C on
IC2 (or any other point on IC2) must offer the consumer
greater satisfaction than B on IC1 (or any other point
on IC1). Hence, it is proved that a higher IC implies a higher level
of satisfaction.
In
figure, AB = BC. For the sake of simplicity, AB = GE. To have additional GE, the
consumer is willing to give up QG. Subsequently, to have additional HF = GE,
the consumer is willing to give up only EH. Apparntly EH < QG. Implying that
.as we move along on IC (which is convex to the origin), we find that a
consumer is willing to give up less and less amount of Good-2 for a unit more
of Good-1. Implying that MRS tends to diminish.
IC1 and IC2 are intersecting at
point a. Points a and b are on IC2, implying a = b in terms
of the level of satisfaction. Likewise, points a and c are on IC2, implying that a = c. If
a = b, and a = c, then we can infer that b = c. But c is definitely better than
b. Because point c offers the same amount OS of Good-2 as to point b, but
greater amount of Good-1. At c, consumer is getting sc amount of Good-1 while
at b he is getting only sb amount of Good 1 sb < sc, apparently. So that
point c must be offering a higher level of satisfaction to the consumer than
point b. The intersecting IC1 and IC2 however, reveal that
b and c are equal. This must be wrong and hence proved that ICs never touch or
intersect each other.
1. A higher IC (which is to the right and above
another IC) offers a higher level of satisfaction.
2. ICs are convex to the origin, so that MRS tends
to diminish.
3. ICs are negatively sloped, or they slope
downward.
4. ICs never touch or intersect each other.
Question
45. The total utility schedule of individual ‘A’ is given below. Derive
his marginal utility schedule.
Units Consumed |
Total Utility |
0 |
0 |
1 |
30 |
2 |
45 |
3 |
58 |
4 |
68 |
5 |
75 |
Answer:
Units Consumed |
Total Utility |
Marginal Utility |
0 |
0 |
0 |
1 |
30 |
30 |
2 |
45 |
15 |
3 |
58 |
13 |
4 |
68 |
10 |
5 |
75 |
7 |
Question
46. Marginal utility schedule of individual ‘A’ is given below. Derive his total
utility schedule. (Assume that total utility of consuming zero units is zero.)
Units Consumed |
Marginal Utility |
1 |
7 |
2 |
10 |
3 |
8 |
4 |
6 |
5 |
3 |
6 |
0 |
Answer:
Units Consumed |
Marginal Utility |
Total Utility |
1 |
7 |
7 |
2 |
10 |
17 |
3 |
8 |
25 |
4 |
6 |
31 |
5 |
3 |
34 |
6 |
0 |
34 |
A
consumer has a given income which he has to spend on various goods he wants.
Now, the question is how he would allocate his money income among various
goods, that is to say, what would be his equilibrium position in respect of the
purchases of the various goods. It may be mentioned here that consumer is
assumed to be ‘rational’, that is, he coldly and carefully calculates and
substitutes goods for one another so as to maximize his utility or
satisfaction.
The
budget line divides the commodity space into two parts which may be termed as:
(i)
Feasibility Area: The area recumbent in the South-West of the budget line is
feasibility area. Any combination of goods X and Y which is represented by a
point in this area (ie.g., point A) or on the boundary line (i.e., budget line)
is a feasible combination, given M, Px and Py.
(ii)
Non-Feasibility Area : The area in the North-East of the budget line is
non-feasibility area because any point falling in this area, e.g.,point B, is
unattainable (given M, Px and Py).
(ii)
Ordinal Analysis : It is a powerful analytical tool of consumer analysis. Ordinal
utility is not a quantity or a numerical value. It is only an expression of the
consumer’s preference for one commodity over another or for one basket of goods
over another.
1. Rationality
2. Limited money income
3. Maximisation of satisfaction
4. Utility is cardinally measurable
5. Diminishing marginal utility
6. Constant utility of money
7. Utility is additive.
These forms are clarified by the given schedule:
1. Cardinal measurability of utility
is unrealistic.
2. Hypothesis of independent utilities
is wrong.
3. Assumption of constant cardinal
utility of money is not valid.
4. Marshallian Law of Demand cannot genuinely
be derived except in a one-commodity case.
5. Cardinal utility analysis does not
split up the price effect into substitution and income effects.
6. Marshall could not explain Giffen
Paradox.
7. Cardinal utility analysis assumes
too much and explains too little.
1.mConsumer’s surplus is fiction,
fantasy and misleading because most consumers cannot pay for more than their
income.
2. It is based upon the invalid concepts that
different units of the goods give different amount of satisfaction to the
consumer.
3. It ignores the interdependence between the
goods, that is the relationships between substitute and complementary goods.
4. It is based upon questionable assumptions of
cardinal measurability of utility and constancy of the marginal utility of
money.
Very Short Answer Type Questions
1. That the two goods are imperfect substitutes for
one another.
2. That the Marginal Rate of Substitution (MRS)
between the two goods decreases as a consumer moves along an indifference
curve.
1.Cardinal utility analysis, 2. Ordinal
utility analysis.
Multiple-Choice Questions
Question 10. Calculation of marginal utility of nth unit is as follows: