Cardinal Utility Theory: Concept, Assumptions, Equilibrium & Drawbacks

2 years ago

Atiqur Rahman

16 minutes

Introduction

Demand for a good refers to the quantity which the consumers can buy at different prices and at different levels of money income. Here it is important to differentiate between the desires/wants for a commodity with the ability to buy it.

The desire of a person to buy is something which he wants to buy, but whether he can buy that or not depends on the money income which he has. Hence demand is not a want or desire to buy something; it is the ability of a person to buy different things at different prices given his money income.

Demand depends on various factors like the price of the good, the price of the other related good, income of the consumers, taste and preferences of the consumers, government policies etc., but the main problem for a consumer is to determine how much quantity of each good to buy and at what price in their current income? The answer lies in the Theory of consumer behaviour.

According to the theory of consumer behaviour/ demand, a consumer always consumes and demands that much quantity of a good, which maximizes his utility. Here, by utility, we mean the satisfaction derived from a commodity, which is even there before consuming that commodity, but it can only be felt after consuming the commodity; in fact, utility is the only thing which induces a person to consume a good.

Hence the level of satisfaction comes only after consuming the good. But the next question is how to measure the utility. For this, there are two schools of thought. One was given by the neoclassical economists as the Cardinal utility theory, and the other was given by the modern economists as the ordinal utility theory.

Cardinal Utility Theory

The Cardinal utility approach was originally given by Marshall. According to him, utility can be measured in utils, where utils is a scale like 1,2,3,… where one can measure his level of satisfaction or utility. (utils were originally derived by Walrus)

Whereas the ordinal utility approach was given by Hicks, where the utility cannot be measured in the cardinal approach; rather, it could be measured in terms of ranks or orders. For instance, the highest satisfaction/utility level would be given the highest rank, and the lesser satisfaction/utility could be given a lesser rank in terms of measurement of utility and so on.

The theory of consumer behaviour attempts to seek the consumption of goods which maximize the consumer’s utility. It also helps a consumer in his decision-making about how to allocate his consumption expenditure on different goods so that his total utility could be maximized. But before moving ahead in the theory of consumer behaviour based on the cardinal approach, it is important to know the assumption of this approach.

Assumptions of Cardinal Utility Theory

● Rationality: A consumer is always rational, i.e. he always prefers more goods and services to derive maximum utility. Thus he always buys the commodity which gives him maximum utility first, and then he buys the least utility-giving commodity at the end.

● Finite Money Income: The consumers have limited money income, which they spend on the purchase of all the goods and services for their living. Thus they allocate this income as their consumption expenditure on all goods and services.

● Cardinal Utility: The utility derived from the consumption of each good is measurable in terms of utils which is, in turn, equal to the money a consumer is willing to pay for it, i.e. 1 util= utility of 1 unit of money.

● Constant Marginal Utility of Money: The utility of each unit of money spent on buying the good remains the same, i.e. one.

● Diminishing Marginal Utility: According to this, the utility derived from the consumption of each successive unit of the good diminishes. As we consume more of a good, the utility derived from each successive unit of it decreases (although the total utility from the consumption of the total quantity of good increases). This is also known as ‘Gossen’s first law’. Note that here each successive unit of the good is homogeneous in nature.

● Additive Utility: According to this, the utility derived from the consumption of all goods and services is additive in nature. Therefore, the utility function of a basket ‘n’, comprising various goods and services, is represented as follows:

U = f (x₁, x₂, x₃, ….. , x_n)

Here, x₁, x₂, x₃, ….., x_n are the quantity of different goods and services consumed by the consumer with his limited money income.

Now based on this, the total utility function of n items is addictive and can be written as:

TU = U₁ (x₁) + U₂ (x₂) + U₃ (x₃) + ……. + U_n (x₄)

Concept of Total Utility and Marginal Utility

Total utility refers to the sum of utility derived from the consumption of each unit of a good. Since, as per the cardinal approach, the utility can be measured. Hence Total utility can also be measured in utils and in monetary terms.

Algebraically:

TU = U₁ + U₂ + U₃ + ……………… + U_n = U_N

Marginal utility is defined as the utility derived from the last unit consumed. It is also defined as the utility derived from the consumption of each successive unit of the same good. More precisely, Marginal utility is the change in the total utility due to an additional unit consumed.

Algebraically:

MU = ∆TU/∆Q

Or,

MU = TU_n – TU_n-1

Where TU_n is the total utility derived from the consumption of n units of a good and TU_n-1 is the total utility derived from the n-1 unit of the same good.

This can be explained with the help of the following table:

Quantity (in units)	Total Utility (in utils)	Marginal Utility (utils)
0	0	–
1	40	40
2	70	30
3	90	20
4	100	10
5	100	0
6	90	-10

Table: 1

The above table and the above figure clearly show that initially, the total utility increases as we consume a good, but as we consume more of a good, it increases but at a diminishing rate, as in we can see from the table and from the figure that initially the total utility increases to 40 and then to 70 to 90 to 100 but the marginal utility first increases by 40 and then by 30 (TU_n – TU_n-1; 70-40=30) then by 20 and then by just 10.

However, when the total utility reaches its maximum, i.e. at 100, then it starts falling as the consumer increases his consumption; correspondingly, the marginal utility becomes zero and then negative.

Note that the point where the total utility reaches its maximum is the point where the marginal utility becomes zero. Thereafter when the consumer increases his consumption of the goods again, then total utility decreases, and marginal utility goes negative.

Thus we can conclude that there exists the following relationship between total utility and marginal utility:

Total utility increases initially at an increasing rate first, and marginal utility also increases.
Thereafter total utility increases at a diminishing rate, and marginal utility diminishes.
When total utility reaches its maximum, marginal utility becomes zero.
When more of the units of the good is consumed even after achieving the highest level of total utility, then the total utility decreases and correspondingly, marginal utility becomes negative.

Consumer Equilibrium Under Cardinal Utility Approach

After talking about the assumptions and the total utility and marginal utility concepts, we can now evaluate the consumer equilibrium according to the cardinal approach. As a general rule, a consumer is always in equilibrium at a point where he maximizes his Total Utility. This can be explained with the help of the following two cases.

Case I: Consumer Equilibrium Under Single Commodity Case

Suppose that the consumer is having his money income and can consume only one commodity, ‘X’. In this case, he has only two choices; either spend his money income on the commodity or can retain his money income with himself, where both his money income and the commodity ‘X’ has a certain utility for him.

If he retains all of his income and purchases no commodity, then the Marginal Utility of money would be lower than the marginal utility of the commodity because MU_m=1 (as per assumption).

Thus the consumer can increase his total utility by exchanging his money income with the consumption of the commodity (as the marginal utility of the commodity is greater) as far as MU_x > MU_m.

Moreover, as it has been stated in the assumptions above that, X has a diminishing marginal utility, and money has a constant marginal utility. Therefore, the utility-maximizing consumer will exchange his money income for commodity X as long as MU_x > MU_m and will reach his equilibrium level of consumption when MU_x = MU_m.

However, the prices of the commodities are generally greater than Rs.1. Therefore, in this case, the consumer equilibrium can be expressed as: MU_x = P_x (MU_m), where MU_m = 1

Hence, consumer equilibrium in the case of a single commodity occurs at a point where the consumer’s MU_x = P_x. This can be represented graphically as follows:

Consumer Equilibrium in Single Commodity Case

Hence, the condition for the equilibrium is:

MU_x = P_x

If MU_x > P_x, the consumer can increase welfare by purchasing more of x commodities.

If MU_x < P_x, the consumer can increase his total satisfaction by cutting down his purchase of x commodities.

If MU_x = P_x, the consumer will be in equilibrium.

Case II: Consumer Equilibrium Under Multiple Commodity Case

In the real world, the consumer just does not spend on purchasing only one commodity. In order to make a living and fulfil his demand, a consumer always demands many commodities. We have earlier seen how he determines his equilibrium level of consumption when he just demands only one commodity.

Let’s now check out how the equilibrium of a utility-maximizing consumer is determined when he purchases several commodities.

As we know that different commodities are different, so the utility derived from them would also be different. Some commodities would give the consumer the highest level of satisfaction or maximum utility, whereas some would give him the second highest or even lesser utility.

In such a condition, the consumer keeps on switching his allocation of money income on different commodities as per their MU. He keeps on switching his consumption expenditure from one commodity to another till the MU of all the commodities becomes equal to each other. This is also known as the concept of equi marginal utility.

Let us now explain the law of equi marginal utility with the help of two commodities cases. In such a situation, suppose the consumer consumes only two commodities, ‘X’ and ‘Y’, by spending his finite money income. The prices of the commodity ‘X’ is given as “P_x” and that of commodity ‘Y’ is given as “P_y”.

If we just apply the same concept which we have applied in CASE I above, then as per that MU_x = P_x (MU_m) and MU_y = P_y (MU_m).

Now, MU_x = P_x (MU_m)

Or, MU_x/ P_x (MU_m) = 1 ………. (1)

Similarly, MU_y = P_y (MU_m)

Or, MU_y/ P_y (MU_m) = 1 ………. (2)

Therefore, from equation (1) and (2), we get:

MU_x/ P_x (MU_m) = MU_y/ P_y (MU_m) = 1

Or, MU_x/ MU_y = P_x (MU_m)/ P_y (MU_m)

Or, MU_x/ MU_y = P_x/ P_y ………. (3)

Or, MU_x/ P_x = MU_y / P_y ………. (4)

Thus, according to the above discussion, a utility-maximizing consumer is in equilibrium under two commodity cases at the consumption level where his MU_x/ MU_y = P_x/ P_y or MU_x/ P_x = MU_y / P_y.

Hence, accordingly, a consumer consuming multiple commodities (in his given money income ) would maximize his utility at a point where his MU_x/ P_x = MU_y / P_y = MU_z / P_z = …… MU_n / P_n.

In other words, a utility-maximizing consumer would be in equilibrium where the MU derived from each commodity is equal to each other, i.e. where he equalizes the MU of each unit of his money expenditure on various goods and services.

Derivation of Demand Curve

The main purpose of studying the theory of consumer behaviour is to derive the demand curve of consumers. In order to derive the demand curve by the cardinal approach, we have to consider the single commodity case, where the consumer reaches his equilibrium at the point where MU_x = P_x.

The left-hand panel shows the equilibrium of the consumer under the cardinal approach. It shows that if the price of the commodity changes, then the equilibrium quantity where the consumer maximizes his utility (MUx = Px) also changes.

Suppose that the consumer is in equilibrium at point E0, where given the price of X at P0, MU_x = P0. Here, the equilibrium quantity is OQ0. Now, if the price of the commodity falls to P1 the equilibrium condition will be disturbed, making MU_x > P0.

Since MU_m is constant, the only way to attain equilibrium again is to reduce MU_x. This can be done only by buying more of commodity X. Thus, by consuming Q0Q1 additional units of X, he reduces his MU_x to E1Q1 and, thereby, restores the equilibrium condition, i.e., MU_x = P1. Similarly, if the price falls further, he buys and consumes more to maximize his satisfaction.

As we can see from the left panel that as the price of the commodity falls from P0 to P3, the equilibrium quantity where the consumer maximizes his utility increases (as each price line intersects with the MU_x curve at different equilibrium points, which in turn gives the corresponding increasing equilibrium quantities).

However, when we stretch the equilibrium points derived from the left panel to the right, then we can see from the right panel that as the price is decreasing, the quantity of the commodity consumed is increasing, which is depicting the law of demand.

Hence joining all the equilibrium points, we get the demand curve at the right panel, which is downward sloping, i.e. showing a negative relationship between the price and the quantity of the commodity.

Drawbacks of Cardinal Utility Approach

Although the cardinal utility approach analyzes consumer behaviour in an easy and simple way but economists have still drawn some of the drawbacks of this approach. Following are some of those drawbacks of the cardinal utility theory which were pointed out by the economists:

● First, the assumption of the cardinal utility approach that utility is measurable in utils and in monetary terms is very dissatisfying. The utility is a subjective concept which cannot be measured quantifiably. It can always be measured by giving preferences for each level of utility.

● Secondly, the cardinal utility approach assumes that the marginal utility of money remains constant, and it also serves as a measure of utility. This assumption is also unrealistic because the marginal utility of money can also change, like all other goods; thus, it cannot serve as a measure of utility derived from goods and services.

● Thirdly, the psychological law of diminishing MU has been established from introspection. This law is accepted as an axiom/ proverb without any practical confirmation.

● Fourthly, the cardinal utility approach and derivation of the demand curve on the basis of this approach are based on the ceteris paribus assumption, which is unrealistic. It is for this reason that this theory ignores the substitution and income effects which might operate simultaneously.

● Finally, the cardinal approach considers that the effect of price changes on the demand curve is exclusively the price effect. This assumption is also unrealistic because the price effect may include income and substitution effects also.

Cardinal Utility Theory: Concept, Assumptions, Equilibrium & Drawbacks

Introduction

Cardinal Utility Theory

Assumptions of Cardinal Utility Theory

Concept of Total Utility and Marginal Utility

Consumer Equilibrium Under Cardinal Utility Approach

Case I: Consumer Equilibrium Under Single Commodity Case

Case II: Consumer Equilibrium Under Multiple Commodity Case

Derivation of Demand Curve

Drawbacks of Cardinal Utility Approach

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Introduction

Cardinal Utility Theory

Assumptions of Cardinal Utility Theory

Concept of Total Utility and Marginal Utility

Consumer Equilibrium Under Cardinal Utility Approach

Case I: Consumer Equilibrium Under Single Commodity Case

Case II: Consumer Equilibrium Under Multiple Commodity Case

Derivation of Demand Curve

Drawbacks of Cardinal Utility Approach

Read More- Microeconomics

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