Q10 — Consumer Equilibrium (Cardinal Utility Analysis)

Introduction

In microeconomic theory, the central problem of the consumer is how to allocate his limited money income among various commodities in such a way that his total satisfaction (utility) is maximised. The solution to this problem is expressed by the concept of consumer equilibrium. In the cardinal utility analysis (Marshall–Jevons approach), it is assumed that utility can be measured in numerical units, called utils, and that the consumer behaves rationally.

In this framework, consumer equilibrium is derived using the Law of Diminishing Marginal Utility and the Law of Equi-marginal Utility. The discussion below explains (i) the meaning of consumer equilibrium, (ii) conditions of equilibrium under cardinal analysis, (iii) illustration with schedule and diagram, (iv) assumptions, (v) critical evaluation, and (vi) importance of the concept, in a manner consistent with the treatment in T.R. Jain & V.K. Ohri, Microeconomics (B.Com Semester I).

Meaning of Consumer Equilibrium

A consumer is said to be in equilibrium when he has reached such a position that he has no tendency to rearrange his expenditure on the various commodities, given the prices of goods and his money income. In equilibrium:

The consumer is obtaining the maximum possible total satisfaction from the goods he purchases.
He has fully adjusted his budget and has no incentive to shift a rupee of expenditure from one good to another.
Any change in his present pattern of consumption would reduce his total utility.

Basic Concepts: Total Utility, Marginal Utility and Marginal Utility of Money

Before deriving equilibrium, the cardinal approach makes use of the following core concepts:

Total Utility (TU): The total satisfaction a consumer derives from consuming all units of a commodity.
Marginal Utility (MU): The additional satisfaction obtained by consuming one more unit of a commodity: MU_n = TU_n − TU_n−1
Marginal Utility of Money (MU_m): The additional satisfaction obtained from spending one more rupee. In the simple Marshallian model, it is assumed to be constant over the relevant range of income.

Key Idea: For a utility-maximising consumer under cardinal analysis, equilibrium is achieved when the marginal utility of the last rupee spent on each commodity is equal and equals the marginal utility of money.

I. Consumer Equilibrium: Single Commodity Case

To begin with, assume that the consumer spends his income only on one commodity X, whose price is P_x and whose marginal utility schedule is known. He will decide how many units of X to buy.

Condition of Equilibrium (Single Commodity)

Consumer equilibrium in respect of commodity X is reached when:

MU_x = P_x × MU_m

If we take MU in “utils” and assume MU_m = 1 util per rupee (for simplicity), then equilibrium condition reduces to:

MU_x = P_x

A rational consumer will keep buying additional units of X as long as MU_x > P_x. Once MU_x falls to P_x, he stops buying further units because the last unit’s utility is just equal to the sacrifice in terms of money.

Illustrative Schedule (Single Commodity)

Suppose the marginal utility of successive units of X and its price are as follows:

Units of X	MU_x (utils)	Price P_x (₹)	Decision
1	16	10	MU > P: Buy
2	13	10	MU > P: Buy
3	10	10	MU = P: Equilibrium reached
4	7	10	MU < P: Do not buy

The consumer maximises his satisfaction by buying 3 units of X because at that level MU_x = P_x. Buying more (4th unit) would reduce overall satisfaction since the additional utility is less than the price paid.

II. Consumer Equilibrium: Two-Commodity Case

In reality, a consumer buys many goods. For clarity, consider a two-good world: commodities X and Y, with prices P_x and P_y. The consumer has a given money income M. Cardinal analysis states that the consumer reaches equilibrium when his limited income is so allocated between X and Y that no reallocation of expenditure can increase his total utility.

Equilibrium Condition (Two Commodities)

The condition for consumer equilibrium is that the marginal utility per rupee spent on each commodity must be equal:

MU_x / P_x = MU_y / P_y = MU_m

If MU_x/P_x > MU_y/P_y, then 1 rupee spent on X gives more satisfaction than 1 rupee spent on Y. The consumer should shift expenditure from Y to X, thus increasing total utility. This process continues until equality is achieved.

Illustrative Numerical Example

Assume that the prices of X and Y are each ₹2 per unit. The marginal utilities (in utils) are:

Units	MU_x	MU_x/P_x	MU_y	MU_y/P_y
1	20	10	18	9
2	16	8	14	7
3	12	6	10	5
4	8	4	7	3.5
5	6	3	5	2.5

Suppose the consumer has ₹12 to spend. One possible equilibrium combination is 3 units of X and 3 units of Y (total expenditure = 6 units × ₹2 = ₹12). At 3 units of each:

MU_x/P_x = 12 / 2 = 6
MU_y/P_y = 10 / 2 = 5

If the consumer slightly adjusts quantities (e.g., 4X, 2Y or 2X, 4Y) and compares the total utility, he eventually arrives at a combination where MU_x/P_x and MU_y/P_y are approximately equal given his budget. At that point, shifting one rupee from one good to another would not increase total utility; equilibrium is achieved.

III. Consumer Equilibrium with Many Commodities

When the consumer spends his income on many commodities X, Y, Z, … the condition of consumer equilibrium generalises to:

MU_x/P_x = MU_y/P_y = MU_z/P_z = … = MU_m

subject to the budget constraint:

P_xQ_x + P_yQ_y + P_zQ_z + … = M

This condition reflects the Law of Equi-marginal Utility: the last rupee spent on each good yields the same marginal utility. If this were not so, the consumer could rearrange his spending and increase total satisfaction.

Diagrammatic Explanation (Two-Commodity Case)

The equi-marginal condition can also be explained with the help of marginal utility per rupee curves. On the X-axis we measure the quantity of each commodity; on the Y-axis we measure MU per rupee. Equilibrium occurs where the MU/P curves of the two goods intersect, given their prices.

_x/P_x MU_y/P_y

Fig. — Consumer equilibrium where MU_x/P_x = MU_y/P_y. At point E the marginal utility per rupee is equal for both goods; any deviation reduces total satisfaction.

IV. Assumptions of Consumer Equilibrium under Cardinal Analysis

The above derivation is based on several simplifying assumptions:

Cardinal measurability of utility: Utility can be measured and compared in numerical units.
Rational consumer: The consumer behaves rationally and aims at maximum satisfaction.
Diminishing marginal utility: The marginal utility of each good diminishes as its consumption increases.
Constant marginal utility of money: MU of money remains constant over the relevant income range.
Given prices and income: Prices of all goods and the money income of the consumer are given and constant.
Divisibility of goods: Commodities are divisible so that consumption can be adjusted in small units.
Independent utilities: Utility derived from one commodity is independent of the quantity consumed of other goods.
No saving or borrowing: The entire income is spent on consumption in the current period.

V. Critical Evaluation of Cardinal Consumer Equilibrium

While the cardinal analysis of consumer equilibrium is simple and intuitive, modern economists have raised several objections:

Utility is not cardinally measurable: It is unrealistic to assume that consumers can measure satisfaction in absolute units (utils). Hicksian indifference curve analysis treats utility as ordinal, requiring only ranking of bundles.
Marginal utility of money is not constant: As a consumer spends more of his income, his remaining money becomes scarce and more valuable; MU of money should rise, not remain constant.
Independence of utilities is doubtful: Many goods are substitutes or complements. Utility from one good depends on consumption of others (e.g., tea and sugar).
Practical difficulty in marginal calculations: Ordinary consumers do not consciously compute MU_x/P_x for every good. Their behaviour is more rule-of-thumb based.
Neglect of income and substitution effects separation: The cardinal model does not analytically separate substitution and income effects of price changes, which is a strength of indifference curve analysis.
Static framework: The analysis assumes a static world with no changes in tastes, expectations, or prices during the adjustment process.

Balanced Appraisal: Despite these limitations, the cardinal approach to consumer equilibrium provides a clear and straightforward explanation of how a rational consumer would allocate income so that the “last rupee spent” on each good yields the same marginal utility. It is pedagogically very useful at the introductory level and remains part of the B.Com syllabus.

VI. Importance and Applications of the Concept of Consumer Equilibrium

The concept of consumer equilibrium under cardinal analysis is important for several reasons:

1. Foundation of the Law of Demand
Consumer equilibrium, combined with the Law of Diminishing Marginal Utility, leads directly to a downward-sloping demand curve. When price falls, MU per rupee from a commodity rises, disturbing equilibrium. The consumer buys more of that commodity until MU per rupee is restored to equality with other goods. Hence, equilibrium analysis explains why quantity demanded varies inversely with price.

2. Basis of the Equi-marginal Principle
The equi-marginal rule, which guides optimal allocation of any scarce resource among competing uses, is rooted in the concept of consumer equilibrium. This principle is widely used in production, public finance, time allocation and investment decisions.

3. Helpful in Welfare Comparisons
Cardinal utility and consumer equilibrium concepts provide a simple framework to discuss the effect of taxes, subsidies or price controls on consumer welfare, even though modern welfare economics uses more refined tools.

4. Basis for Demand Forecasting and Market Analysis
Understanding consumer equilibrium helps firms judge how changes in price and income will affect the demand for their products and for related goods, thereby supporting pricing and marketing strategies.

5. Pedagogical Importance
For B.Com students, the cardinal approach offers a clear step-by-step logic of how utility, marginal utility, and price interact to determine equilibrium. It provides a conceptual stepping stone for the more advanced indifference curve analysis which follows in the syllabus.

Exam Tip: For a 15-marks answer in Panjab University, structure your answer as: (i) clear meaning of consumer equilibrium, (ii) brief recap of TU, MU and MU of money, (iii) equilibrium condition for one commodity, (iv) equilibrium condition for two/many commodities with MU/P formulae, (v) illustrative schedule and labelled diagram, (vi) assumptions, (vii) critical evaluation, and (viii) importance and applications, followed by a neat conclusion. This format is highly scoring.

Conclusion

To conclude, consumer equilibrium under cardinal utility analysis explains how a rational consumer, having limited income and facing given prices, distributes his expenditure among various goods so as to maximise total satisfaction. The equi-marginal condition MU_x/P_x = MU_y/P_y = … = MU_m summarises this optimisation behaviour. Although the assumptions of cardinal measurability and constant marginal utility of money may not be fully realistic, the framework remains extremely useful for developing economic intuition and is of high examination importance for B.Com Semester I under Panjab University.

This answer forms part of a carefully curated set of important questions that have frequently appeared in past university examinations and therefore hold a high probability of reappearing in future assessments. While prepared with academic accuracy and aligned to the prescribed syllabus, these solutions should be treated as high-quality preparation material rather than a guaranteed prediction of any upcoming exam paper.