These slides include the different concepts of cardinal utility analysis and briefly show the assumptions, TU and MU, Law of diminishing utility analysis, and the law of equi-marginal utility, and finally, includes the limitations of cardinal utility analysis.

1. Cardinal Utility Analysis
• Assumptions
• Concept of Total and Marginal Utility
• Consumer’s Equilibrium
• One Commodity Model
• Two Commodity Model
• Derivation of Demand Curve
• Limitations
Indra Pyakurel
Biratnagar-1
ippyakurel@gmail.com

2. What is cardinal utility?
• Initially developed by Hermann Heinrich Gossen
• Popularized by Alfred Marshall

3. Cont…..
• Cardinal utility approach measures utility in terms of numbers like 1,2,3,….

4. Assumptions
1. Rationality: It is assumed that the consumers are rational, and they satisfy their wants in the order of their preference.
This means they will purchase those commodities first which yields the highest utility and then the second highest and
so on.
2. Limited Resources (Money): The consumer has limited money to spend on the purchase of goods and services and
thus this makes the consumer buy those commodities first which is a necessity.
3. Maximize Satisfaction: Every consumer aims at maximizing his/her satisfaction for the amount of money he/she
spends on the goods and services.
4. Utility is cardinally Measurable: It is assumed that the utility is measurable, and the utility derived from one unit of
the commodity is equal to the amount of money, which a consumer is ready to pay for it, i.e. 1 Util = 1 unit of money.
5. Diminishing Marginal Utility: This means, with the increased consumption of a commodity, the utility derived from
each successive unit goes on diminishing. This law holds true for the theory of consumer behavior.
6. Marginal Utility of Money is Constant: It is assumed that the marginal utility of money remains constant
irrespective of the level of a consumer’s income.
7. Utility is Additive: The cardinalists believe that not only the utility is measurable but also the utility derived from the
consumption of different commodities are added up to realize the total utility.

5. Concept of TU and MU
• Total Utility refers to the sum of utility that an individual derives from the consumption of all the
units of a given commodity at a point or over a period of time. Suppose a consumer consumes four
units of commodity X at a point of time and derives utilities from the successive consumption of
units as u1, u2, u3, u4, then the total utility from the consumption of commodity X can be measured
as follows:
Ux = u1+u2+u3+u4
• If the consumer consumes ‘n’ number of commodities, then the utility derived from the
consumption of each commodity, let’s say, X, Y and Z are Ux, Uy, Uz. The total utility is the sum of
utilities of each individual commodity and hence is measured as:
• TUn = Ux + Uy +Uz

6. Contd…
• Marginal Utility refers to the additional benefit (utility) a consumer derives from the consumption
of one additional unit of good or service. It can be measured as the change in the total utility
obtained from the consumption of an additional unit, say X, symbolically it can be represented as:
When ‘n’ number of units are consumed, then the marginal utility can be measured as:
MU of nth unit = TUn – TUn-1

7. Law of Diminishing Marginal Utility
• Law of Diminishing Marginal Utility posits that with the more and more consumption of the
units of the commodity the utility derived from each successive unit goes on diminishing, provided
the consumption of other commodities remain constant.

8. Assumptions of Law of Diminishing Marginal Utility
1. It is assumed that the unit of the consumer good is a standard one, i.e. the rational quantity of the commodity is
consumed. Such as, a cup of tea, a pair of shoes, bottle of cold drink, glass of water, etc.
2. It is assumed that the utility is measurable, and the satisfaction of the consumers can be expressed in the quantitative
terms.
3. The consumer’s tastes and preferences remain same during the period of the consumption.
4. There must be continuity in the consumption. If a break is necessary, then the time interval between the consumption
of two units should be appropriately short.
5. It is assumed that the quality of the commodity remains uniform during the period of consumption.
6. All the commodities consumed by the consumer are said to be independent of each other, such as the marginal utility
of one commodity has no relation with the marginal utility of another commodity.
7. It is assumed that the income of the consumer and the price of goods and services remains unchanged during the
period of consumption.
8. The marginal utility of money remains constant for the consumer.
9. The mental condition of the consumer should remain normal during the consumption period. For example, if a person
drinks any alcoholic drink, then he will derive more pleasure with each additional glass of drink, this is because of a
change in his mental status due to intoxication.

9. The law of diminishing marginal utility can be illustrated through the table given below. Suppose there is a
commodity X, whose utility can be measured in the quantitative terms. Also, the total utility and marginal utility of
the commodity is given in the table.
Units of Commodity X Total Utility (Tux) Marginal Utility (MUx)
1 30 30
2 50 20
3 65 15
4 70 5
5 65 -5
6 45 -20

10. Diagram

11. Relationship between TU and MU
 When MU decreases, TU increases at a decreasing rate.
 When MU is Zero, TU is maximum.
 When MU is negative, TU starts declining.

12. Derivation of Demand Curve in the Case of a Single Commodity (Law of Diminishing Marginal Utility):
• A rational consumer, before, while purchasing a commodity compares the price of the commodity
which he has to pay with the utility of a commodity he receives from it. So long as the marginal
utility of a commodity is higher than its price (MUx > Px), the consumer would demand more and
more units of it till its marginal utility is equal to its price MUx = Px or the equilibrium condition is
established.

13. Diagram

14. Law of Equi-Marginal Utility
• The law of equi-marginal utility states that the consumer will distribute his money income between the goods in such a
way that the utility derived from the last rupee spent on each good is equal. In other words, consumer is in equilibrium
position when marginal utility of money expenditure on each good is the same. Now, the marginal utility of money
expenditure on a good is equal to the marginal utility of a good divided by the price of the good. In symbols,
• MUm = MUx / Px
• The law of equi-marginal utility can therefore be stated thus: the consumer will spend his money income on different
goods in such a way that marginal utility of money expenditure on each good is equal. That is, consumer is in equilibrium
in respect of the purchases of two goods X and V when
• MUx / Px= MUy / Py
• Thus, the consumer will be in equilibrium when the following equation holds good:
• MUx / Px = MUy / Py = MUm
• Where MUm is marginal utility of money expenditure (that is, the utility of the last rupee spent on each good).

15. Schedule
• Let the prices of goods X and Y be Rs. 2 and Rs. 3 respectively. Reconstructing the above table by
dividing marginal utilities (MU) of X by Rs. 2 and marginal utilities (MU) of 7 by Rs. 3 we get the
Table 7.3.

16. Contd…....
• Consumer will be in equilibrium when he is buying 6 units of good X and 4 units of good 7and will
be spending (Rs. 2 x 6 + Rs. 3 x 4 ) = Rs. 24 on them that are equal to consumer’s given income. Thus,
in the equilibrium position where the consumer maximises his utility.
• MUx / Px = MUy / Py = MUm
• 10/2 = 15/3 =5
• Thus, marginal utility of the last rupee spent on each of the two goods he purchases is the same,
that is, 5 utils.

17. Diagram
The consumer is in
equilibrium when he is
buying 6 units of X and 4
units of Y. No other
allocation of money
expenditure will yield him
greater utility than when he
is buying 6 units of
commodity X and 4 units of
commodity Y

18. Derivation of the Demand Curve in the Case of Two or More than Two Commodities (Law of Equi-Marginal
Utility):
• The law of diminishing marginal utility can also be applied in case of two or more than two goods.
When a consumer has to spend a certain given income on a number of goods, he attains maximum
satisfaction when the marginal utilities of the goods are proportional to their prices as stated below.
• MUx / Px = MUy / Py = ……….. MUn / Pn

19. Diagram

20. Criticisms (Limitations) of Cardinal Utility Approach
• Utility cannot be measured cardinally
• Single Commodity Model is Unrealistic
• Money is an Imperfect Measure of Utility
• Marginal Utility of Money is not constant
• Consumer not of Calculating Mind
• Man is not Rational
• Utility Analysis does not study Income Effect, Substitution Effect and Price Effect
• Utility Analysis fails to clarify the Study of Inferior and Giffen Goods

21. Thank You