Introduction
The Law of Equi-marginal Utility, also known as the Law of Substitution or the Law of Maximum Satisfaction, is one of the most important laws of consumption in cardinal utility analysis. While the Law of Diminishing Marginal Utility explains how the marginal utility of a single commodity declines as its consumption increases, the Law of Equi-marginal Utility explains how a rational consumer distributes his limited income among different commodities so as to attain maximum possible satisfaction.
This law generalises consumer behaviour to the realistic case of many goods and provides the basis of the condition for consumer’s equilibrium in cardinal utility theory. It is frequently asked in Panjab University examinations in the form: “Critically discuss the Law of Equi-marginal Utility along with its importance.”
Meaning and Statement of the Law
A consumer typically has a limited money income and faces many commodities with given market prices. The central question is: how should the consumer allocate his income among different goods so that total satisfaction is maximised? The Law of Equi-marginal Utility provides the answer.
A rational consumer will distribute his given income among various commodities in such a way that the marginal utility of the last rupee spent on each commodity is equal. If this equality does not hold, the consumer can increase his total utility by transferring expenditure from one commodity to another.
In other words, the consumer attains maximum satisfaction when the ratio of the marginal utility of each commodity to its price is the same across all commodities. This is the equimarginal condition.
Condition of Consumer’s Equilibrium (Two-Commodity Case)
Consider a consumer who consumes two goods X and Y. Let MUx and MUy be the marginal utilities of X and Y respectively, and Px, Py their market prices. For maximum satisfaction:
MUx / Px = MUy / Py = MUm
where MUm is the marginal utility of money. The first equality ensures that the last rupee spent on X and Y yields the same satisfaction. If MUx/Px > MUy/Py, the consumer can increase total utility by spending more on X and less on Y until equality is restored.
Extension to Many Commodities
When a consumer buys many commodities X, Y, Z, …, the equilibrium condition generalises to:
MUx/Px = MUy/Py = MUz/Pz = … = MUm
subject to the budget constraint that total expenditure equals money income. This equality of marginal utility per rupee across all goods is the formal statement of the Law of Equi-marginal Utility.
Assumptions of the Law of Equi-Marginal Utility
The law is based on certain assumptions that simplify consumer behaviour and allow precise formulation:
- Cardinal measurability of utility: Utility can be measured in quantitative units (utils) and compared across goods.
- Rational behaviour: The consumer is rational and aims at maximising total satisfaction.
- Limited money income: The consumer has a fixed money income to be allocated among different goods.
- Given prices: Market prices of commodities are known and constant during the decision period.
- Diminishing marginal utility: The marginal utility of each good decreases as more of it is consumed.
- Divisibility of goods: Commodities are divisible, so expenditure can be adjusted in small units.
- Constancy of tastes, fashion and habits: These remain unchanged while the consumer makes choices.
- Marginal utility of money is constant: The satisfaction obtained from each rupee remains unchanged over the relevant range.
Illustrative Schedule (Two-Good Case: X and Y)
The working of the law can be shown with the help of a simple hypothetical schedule. Suppose the consumer has ₹6 to spend on goods X and Y. The price of each unit of X and Y is ₹1. The marginal utility schedules are:
| Units | MUx (Utils) | MUy (Utils) |
|---|---|---|
| 1 | 18 | 16 |
| 2 | 14 | 12 |
| 3 | 10 | 9 |
| 4 | 7 | 7 |
| 5 | 5 | 5 |
| 6 | 3 | 3 |
The consumer must decide how many units of X and Y to buy so that total utility is maximised, given that the total money available is ₹6 and each unit costs ₹1.
One possible equilibrium combination:
Suppose the consumer buys 3 units of X and 3 units of Y.
• MUx of 3rd unit = 10 utils
• MUy of 3rd unit = 9 utils
Since price of each good is ₹1, we have:
• MUx/Px ≈ 10, MUy/Py ≈ 9
This combination is close to equimarginal equality. By trying nearby allocations (like 4X + 2Y or 2X + 4Y) and summing total utilities,
we find that the consumer reaches maximum total satisfaction when the marginal utilities per rupee spent on X and Y are approximately equal.
Diagrammatic Explanation (Two-Good Case)
The law can be diagrammatically illustrated by plotting the marginal utility curves of X and Y against their respective quantities, assuming the same money price for both goods. Consumer equilibrium is reached at that combination of X and Y where the marginal utility per rupee spent is equal.
Working of the Law: Substitution Process
The law operates through a process of substitution:
- If MUx/Px > MUy/Py, the last rupee spent on X yields more satisfaction than the last rupee spent on Y.
- The consumer can increase total utility by transferring some expenditure from Y to X (buying more X and less Y).
- As consumption of X rises, MUx falls (due to diminishing marginal utility); as consumption of Y falls, MUy rises.
- This process continues until MUx/Px and MUy/Py become equal. At that point, any further reallocation would reduce total utility.
Thus, equilibrium is stable because any deviation from equality of marginal utilities per rupee automatically sets in motion substitutions that restore the equimarginal condition.
Critical Evaluation and Limitations
Like the law of diminishing marginal utility, the Law of Equi-marginal Utility has been criticised on several grounds:
- Cardinal Measurement and Additivity: The law assumes that the consumer can measure and add utilities of different goods, which modern ordinal utility theory rejects. In reality, utility is not measurable in absolute units.
- Constant Marginal Utility of Money: The assumption that MU of money remains constant while the consumer spends more or less is unrealistic. Changing money balances may alter the marginal utility of money.
- Rational Calculation Difficulty: The law implicitly assumes that consumers calculate MUx/Px for all goods and adjust expenditure accordingly. Ordinary consumers do not perform such explicit marginal calculations.
- Oversimplified Environment: In real life, prices often change, tastes evolve, credit facilities exist, and information is imperfect. These complications are ignored in the simple version of the law.
- Indifference Curve Alternative: Modern microeconomics uses the indifference curve–budget line framework to derive the condition for consumer equilibrium. In that setting, equilibrium is achieved when the marginal rate of substitution equals the price ratio (MRS = Px/Py), rather than by equating cardinal marginal utilities per rupee.
Importance and Applications of the Law of Equi-Marginal Utility
The importance of the law extends far beyond individual consumption. It can be applied to a wide range of economic and managerial decisions:
In cardinal utility theory, the law provides the formal condition under which a consumer attains equilibrium: equality of MU per rupee across goods. Without the Law of Equi-marginal Utility, we cannot explain how consumers actually divide income among many commodities.
The law generalises to the allocation of any scarce resource—time, effort, capital—across competing uses. Maximum satisfaction or output is achieved when the marginal benefit of the last unit of the resource is equal in all uses. This is the equi-marginal principle in production, finance, and resource management.
Producers distribute limited factors of production (like labour and capital) among different production lines so that the marginal productivity per rupee spent is equalised. This is essentially the same equi-marginal principle applied to factor allocation.
Governments allocate limited budget among various heads such as education, health, defence and infrastructure. Social welfare is maximised when the marginal social benefit of expenditure is equal across all uses. This is again an application of the equi-marginal rule at the macro level.
Firms often have to decide how much to spend on different activities—advertising, R&D, distribution, after-sales service. According to the equi-marginal principle, total profit is maximised when the marginal return per rupee spent is equalised across these alternative uses.
Individuals distribute their limited time among work, leisure, study, and other activities. Maximum satisfaction is achieved when the marginal utility of time spent in each activity is equal. This is a practical interpretation of the equi-marginal rule in daily life.
The law explains why consumers, firms, and governments avoid extreme concentration on a single activity and instead choose a diversified, balanced pattern of consumption, production, and expenditure. Diversification is the natural outcome of equating marginal utilities or marginal returns at the margin.
Conclusion
To sum up, the Law of Equi-marginal Utility is a fundamental principle of rational choice under scarcity. It explains how a consumer, with limited income, allocates expenditure among different goods to achieve maximum satisfaction and provides a general rule for optimal allocation of any scarce resource among competing uses. Although its cardinal utility foundations have been replaced by modern ordinal analysis, the equi-marginal idea continues to play a central role in consumer theory, production theory, public finance and welfare economics, and remains a favourite question in Panjab University examinations.