Lecture 5 - Theory of Demand Cardinal Utility Analysis | Microeconomics- Interaction between individual buyer-seller PDF Download

 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