Page 1
Theory of Demand Cardinal Utility Analysis
Institute of Lifelong Learning, University of Delhi
Subject : Microeconomics
Lesson : Theory of Demand Cardinal Utility Analysis
Lesson Developer : Kajleen Kaur
College/Department : SGGSCC, University of Delhi
Page 2
Theory of Demand Cardinal Utility Analysis
Institute of Lifelong Learning, University of Delhi
Subject : Microeconomics
Lesson : Theory of Demand Cardinal Utility Analysis
Lesson Developer : Kajleen Kaur
College/Department : SGGSCC, University of Delhi
Theory of Demand Cardinal Utility Analysis
Institute of Lifelong Learning, University of Delhi
Index
1. Introduction ......................................................................................... 3
2. Utility .................................................................................................. 3
2.1 Meaning and Characteristics ............................................................. 3
2.2 Utility Function ............................................................................... 4
2.3 Cardinal Measurement of Utility ........................................................ 4
2.4 Law of Diminishing Marginal Utility (DMU) .......................................... 6
2.5 Assumptions of the Utility Analysis .................................................... 8
3. Consumer’s Equilibrium ......................................................................... 8
3.1 Single Commodity Case .................................................................. 8
3.2 Many Commodities Case – The Law of Equi-Marginal Utility .................. 9
4. Derivation of Demand Curve ................................................................ 11
5. Diamond Water Paradox ...................................................................... 12
6. Summary .......................................................................................... 14
Page 3
Theory of Demand Cardinal Utility Analysis
Institute of Lifelong Learning, University of Delhi
Subject : Microeconomics
Lesson : Theory of Demand Cardinal Utility Analysis
Lesson Developer : Kajleen Kaur
College/Department : SGGSCC, University of Delhi
Theory of Demand Cardinal Utility Analysis
Institute of Lifelong Learning, University of Delhi
Index
1. Introduction ......................................................................................... 3
2. Utility .................................................................................................. 3
2.1 Meaning and Characteristics ............................................................. 3
2.2 Utility Function ............................................................................... 4
2.3 Cardinal Measurement of Utility ........................................................ 4
2.4 Law of Diminishing Marginal Utility (DMU) .......................................... 6
2.5 Assumptions of the Utility Analysis .................................................... 8
3. Consumer’s Equilibrium ......................................................................... 8
3.1 Single Commodity Case .................................................................. 8
3.2 Many Commodities Case – The Law of Equi-Marginal Utility .................. 9
4. Derivation of Demand Curve ................................................................ 11
5. Diamond Water Paradox ...................................................................... 12
6. Summary .......................................................................................... 14
Theory of Demand Cardinal Utility Analysis
Institute of Lifelong Learning, University of Delhi
Learning Outcomes
After going through this chapter you will able to:
? Explain the concepts of utility, marginal utility and total utility.
? Compare total utility with marginal utility.
? Describe the law of diminishing marginal utility and its implications.
? Derive the law of demand using the law of diminishing marginal utility and the
logic behind the marginal utility-to-price ratio equalization rule.
? Grasp the concept of consumer surplus.
? Understand the water-diamond paradox.
1. Introduction
Theory of demand seeks to analyse the behaviour of households in the market place with
regards to maximisation of satisfaction/utility from the spending of his available money
income. Every household faces a common problem of allocation of income among
different ends so as to get maximum possible satisfaction out of its expenditure.
Once the household reaches such combination, it is said to be in equilibrium. Consumer’s
equilibrium may be defined as a situation when a household allocated his resources
among the various uses in such a way that he has no incentive for change in between
these uses. Many theories have been propounded from time to time by economists to
explain consumer equilibrium. One of them is cardinal utility theory, the subject matter of
the present chapter.
The marginal utility analysis is the traditional theory of demand or consumer behaviour.
This theory uses the concept of utility to explain the law of demand. The marginal utility
approach of consumer behaviour was published by Gossen (1854), W.S. Jevons (1871),
Leon Walras (1874) and Carl Menger. Alfred Marshall (1890) made important contribution
to this theory therefore, the theory is popularly known as Marshallian Utility Theory.
Did you know?
Marshal’s contribution to the theory of demand ranges from the very basic use of demand
and supply functions of price determination to explaining the situation of consumer’s
equilibrium. In fact, price as a function of quantity demanded in the form of inverse
demand function has been one of his works. The equilibrium of consumption (shown
later in this chapter), wherein the consumer adjusts his consumption until marginal utility
equals the price was also among one of his main theories. He further used the concept
price elasticity of demand. As a part of measuring economic welfare, Marshal also
developed the concepts of consumer surplus and producer surplus which are together
often called ‘Marshallian Surplus’. He used the concept of surplus to assess the effect of
taxes and subsidies on the market. The credit of developing the concept of quasi-rent is
also goes to Prof. A. Marshal.
2. Utility
2.1 Meaning and Characteristics
Utility is a property common to all commodities consumed by a person. It has no physical
or material existence. According to Lipsey and Crystal, “The satisfaction a consumer
receives from consuming a product is called utility.” Utility has nothing to do with
Page 4
Theory of Demand Cardinal Utility Analysis
Institute of Lifelong Learning, University of Delhi
Subject : Microeconomics
Lesson : Theory of Demand Cardinal Utility Analysis
Lesson Developer : Kajleen Kaur
College/Department : SGGSCC, University of Delhi
Theory of Demand Cardinal Utility Analysis
Institute of Lifelong Learning, University of Delhi
Index
1. Introduction ......................................................................................... 3
2. Utility .................................................................................................. 3
2.1 Meaning and Characteristics ............................................................. 3
2.2 Utility Function ............................................................................... 4
2.3 Cardinal Measurement of Utility ........................................................ 4
2.4 Law of Diminishing Marginal Utility (DMU) .......................................... 6
2.5 Assumptions of the Utility Analysis .................................................... 8
3. Consumer’s Equilibrium ......................................................................... 8
3.1 Single Commodity Case .................................................................. 8
3.2 Many Commodities Case – The Law of Equi-Marginal Utility .................. 9
4. Derivation of Demand Curve ................................................................ 11
5. Diamond Water Paradox ...................................................................... 12
6. Summary .......................................................................................... 14
Theory of Demand Cardinal Utility Analysis
Institute of Lifelong Learning, University of Delhi
Learning Outcomes
After going through this chapter you will able to:
? Explain the concepts of utility, marginal utility and total utility.
? Compare total utility with marginal utility.
? Describe the law of diminishing marginal utility and its implications.
? Derive the law of demand using the law of diminishing marginal utility and the
logic behind the marginal utility-to-price ratio equalization rule.
? Grasp the concept of consumer surplus.
? Understand the water-diamond paradox.
1. Introduction
Theory of demand seeks to analyse the behaviour of households in the market place with
regards to maximisation of satisfaction/utility from the spending of his available money
income. Every household faces a common problem of allocation of income among
different ends so as to get maximum possible satisfaction out of its expenditure.
Once the household reaches such combination, it is said to be in equilibrium. Consumer’s
equilibrium may be defined as a situation when a household allocated his resources
among the various uses in such a way that he has no incentive for change in between
these uses. Many theories have been propounded from time to time by economists to
explain consumer equilibrium. One of them is cardinal utility theory, the subject matter of
the present chapter.
The marginal utility analysis is the traditional theory of demand or consumer behaviour.
This theory uses the concept of utility to explain the law of demand. The marginal utility
approach of consumer behaviour was published by Gossen (1854), W.S. Jevons (1871),
Leon Walras (1874) and Carl Menger. Alfred Marshall (1890) made important contribution
to this theory therefore, the theory is popularly known as Marshallian Utility Theory.
Did you know?
Marshal’s contribution to the theory of demand ranges from the very basic use of demand
and supply functions of price determination to explaining the situation of consumer’s
equilibrium. In fact, price as a function of quantity demanded in the form of inverse
demand function has been one of his works. The equilibrium of consumption (shown
later in this chapter), wherein the consumer adjusts his consumption until marginal utility
equals the price was also among one of his main theories. He further used the concept
price elasticity of demand. As a part of measuring economic welfare, Marshal also
developed the concepts of consumer surplus and producer surplus which are together
often called ‘Marshallian Surplus’. He used the concept of surplus to assess the effect of
taxes and subsidies on the market. The credit of developing the concept of quasi-rent is
also goes to Prof. A. Marshal.
2. Utility
2.1 Meaning and Characteristics
Utility is a property common to all commodities consumed by a person. It has no physical
or material existence. According to Lipsey and Crystal, “The satisfaction a consumer
receives from consuming a product is called utility.” Utility has nothing to do with
Theory of Demand Cardinal Utility Analysis
Institute of Lifelong Learning, University of Delhi
usefulness. Alcohol may be harmful for health, but, it is paid for and is consumed since
it possesses utility. Utility in economics is devoid of legal, social or ethical implications. It
depends upon intensity of want, and is a relative concept.
Utility is not to be confused with satisfaction. Utility is what consumer thinks,
whereas satisfaction is what consumer gets. Therefore, utility is expected satisfaction
and satisfaction is realised utility. The decision of buying a commodity by a consumer
depends upon its utility and not satisfaction because satisfaction is derived only after
consumption.
2.2 Utility Function
Utility function explains the relationship between utility derived from the consumption of
various commodities and the units of commodity consumed. It can be stated as:
U = f (X
1
, X
2
,...,X
n
)
Where,
U denotes total utility and, X
1
, X
2
,...., X
n
denotes commodities consumed be the
consumer
2.3 Cardinal Measurement of Utility
Several economists including Marshall suggested the measurement of utility in cardinal
terms. Under cardinal measure of utility, it is possible to measure the utility in terms of
some quantifiable unit which a person derives from consumption of various units of a
commodity or combination of commodities. According to Bentham, the utility of an action
is the difference between pleasure enjoyed and the pain suffered. He and some other
economists used a psychological unit of measurement of utility called utils.
2.3.1 Marginal Utility
Marginal utility is the utility derived from the additional unit of a commodity consumed by
a consumer. It is the change in total utility results from a unit change in consumption.
Symbolically,
MU
n
= TU
n
- TU
n-1
Where,
MU
n
is the marginal utility of the nth unit,
TU
n
is the total utility of the nth unit, and
TU
n-1
is the total utility of the (n-1)
th
unit.
2.3.2 Total Utility
Total utility is the sum of the utilities derived from all units of a commodity consumed by
a consumer. In other words, it is the sum of the marginal utilities derived from the
consumption of the successive units of a commodity by the consumer. Symbolically,
TU
n
= MU
1
+ MU
2
+ ... + MU
n
2.3.3 Relationship between Total Utility and Marginal Utility
The following table 1 shows the relationship between Total Utility and Marginal Utility
Table 1
No. Of Units Total Utility (TU) Marginal Utility (MU)
1 10 10
Page 5
Theory of Demand Cardinal Utility Analysis
Institute of Lifelong Learning, University of Delhi
Subject : Microeconomics
Lesson : Theory of Demand Cardinal Utility Analysis
Lesson Developer : Kajleen Kaur
College/Department : SGGSCC, University of Delhi
Theory of Demand Cardinal Utility Analysis
Institute of Lifelong Learning, University of Delhi
Index
1. Introduction ......................................................................................... 3
2. Utility .................................................................................................. 3
2.1 Meaning and Characteristics ............................................................. 3
2.2 Utility Function ............................................................................... 4
2.3 Cardinal Measurement of Utility ........................................................ 4
2.4 Law of Diminishing Marginal Utility (DMU) .......................................... 6
2.5 Assumptions of the Utility Analysis .................................................... 8
3. Consumer’s Equilibrium ......................................................................... 8
3.1 Single Commodity Case .................................................................. 8
3.2 Many Commodities Case – The Law of Equi-Marginal Utility .................. 9
4. Derivation of Demand Curve ................................................................ 11
5. Diamond Water Paradox ...................................................................... 12
6. Summary .......................................................................................... 14
Theory of Demand Cardinal Utility Analysis
Institute of Lifelong Learning, University of Delhi
Learning Outcomes
After going through this chapter you will able to:
? Explain the concepts of utility, marginal utility and total utility.
? Compare total utility with marginal utility.
? Describe the law of diminishing marginal utility and its implications.
? Derive the law of demand using the law of diminishing marginal utility and the
logic behind the marginal utility-to-price ratio equalization rule.
? Grasp the concept of consumer surplus.
? Understand the water-diamond paradox.
1. Introduction
Theory of demand seeks to analyse the behaviour of households in the market place with
regards to maximisation of satisfaction/utility from the spending of his available money
income. Every household faces a common problem of allocation of income among
different ends so as to get maximum possible satisfaction out of its expenditure.
Once the household reaches such combination, it is said to be in equilibrium. Consumer’s
equilibrium may be defined as a situation when a household allocated his resources
among the various uses in such a way that he has no incentive for change in between
these uses. Many theories have been propounded from time to time by economists to
explain consumer equilibrium. One of them is cardinal utility theory, the subject matter of
the present chapter.
The marginal utility analysis is the traditional theory of demand or consumer behaviour.
This theory uses the concept of utility to explain the law of demand. The marginal utility
approach of consumer behaviour was published by Gossen (1854), W.S. Jevons (1871),
Leon Walras (1874) and Carl Menger. Alfred Marshall (1890) made important contribution
to this theory therefore, the theory is popularly known as Marshallian Utility Theory.
Did you know?
Marshal’s contribution to the theory of demand ranges from the very basic use of demand
and supply functions of price determination to explaining the situation of consumer’s
equilibrium. In fact, price as a function of quantity demanded in the form of inverse
demand function has been one of his works. The equilibrium of consumption (shown
later in this chapter), wherein the consumer adjusts his consumption until marginal utility
equals the price was also among one of his main theories. He further used the concept
price elasticity of demand. As a part of measuring economic welfare, Marshal also
developed the concepts of consumer surplus and producer surplus which are together
often called ‘Marshallian Surplus’. He used the concept of surplus to assess the effect of
taxes and subsidies on the market. The credit of developing the concept of quasi-rent is
also goes to Prof. A. Marshal.
2. Utility
2.1 Meaning and Characteristics
Utility is a property common to all commodities consumed by a person. It has no physical
or material existence. According to Lipsey and Crystal, “The satisfaction a consumer
receives from consuming a product is called utility.” Utility has nothing to do with
Theory of Demand Cardinal Utility Analysis
Institute of Lifelong Learning, University of Delhi
usefulness. Alcohol may be harmful for health, but, it is paid for and is consumed since
it possesses utility. Utility in economics is devoid of legal, social or ethical implications. It
depends upon intensity of want, and is a relative concept.
Utility is not to be confused with satisfaction. Utility is what consumer thinks,
whereas satisfaction is what consumer gets. Therefore, utility is expected satisfaction
and satisfaction is realised utility. The decision of buying a commodity by a consumer
depends upon its utility and not satisfaction because satisfaction is derived only after
consumption.
2.2 Utility Function
Utility function explains the relationship between utility derived from the consumption of
various commodities and the units of commodity consumed. It can be stated as:
U = f (X
1
, X
2
,...,X
n
)
Where,
U denotes total utility and, X
1
, X
2
,...., X
n
denotes commodities consumed be the
consumer
2.3 Cardinal Measurement of Utility
Several economists including Marshall suggested the measurement of utility in cardinal
terms. Under cardinal measure of utility, it is possible to measure the utility in terms of
some quantifiable unit which a person derives from consumption of various units of a
commodity or combination of commodities. According to Bentham, the utility of an action
is the difference between pleasure enjoyed and the pain suffered. He and some other
economists used a psychological unit of measurement of utility called utils.
2.3.1 Marginal Utility
Marginal utility is the utility derived from the additional unit of a commodity consumed by
a consumer. It is the change in total utility results from a unit change in consumption.
Symbolically,
MU
n
= TU
n
- TU
n-1
Where,
MU
n
is the marginal utility of the nth unit,
TU
n
is the total utility of the nth unit, and
TU
n-1
is the total utility of the (n-1)
th
unit.
2.3.2 Total Utility
Total utility is the sum of the utilities derived from all units of a commodity consumed by
a consumer. In other words, it is the sum of the marginal utilities derived from the
consumption of the successive units of a commodity by the consumer. Symbolically,
TU
n
= MU
1
+ MU
2
+ ... + MU
n
2.3.3 Relationship between Total Utility and Marginal Utility
The following table 1 shows the relationship between Total Utility and Marginal Utility
Table 1
No. Of Units Total Utility (TU) Marginal Utility (MU)
1 10 10
Theory of Demand Cardinal Utility Analysis
Institute of Lifelong Learning, University of Delhi
The information provided in the above table reveals the following relationship between
TU and MU:
1. As the consumer consumes more and more of the good, the TU increases but less
than in proportion and the MU gradually decline.
2. When TU is maximum, MU is zero. Here the consumer reaches the saturation point of
consumption.
3. A rational consumer will stop consumption at 6 units where TU is the maximum and
MU is zero. Because, beyond this point of consumptionTU declines and MU becomes
negative.
This relationship between TU and MU is shown in the following figure:
2 18 8
3 24 6
4 28 4
5 30 2
6 30 0
7 28 -2
8 24 -4
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