Law of diminishing marginal utility

Also called: Diminishing marginal utility · Topic: Consumer Behaviour, Demand and Elasticity · NCERT: Class 9, Ch 9 "The Price Puzzle: What Drives the Market"; Class 12, Ch 2 "Theory of Consumer Behaviour"

Meaning

The law of diminishing marginal utility (DMU) says that as a person consumes more units of a good, the extra satisfaction from each new unit keeps falling, while her consumption of other goods stays the same.

It matters because it explains, in utility analysis, why the demand curve slopes downward. It also supports ideas like progressive taxation and tiered pricing of water.

• Formula: MUₙ = TUₙ − TUₙ₋₁, and TUₙ = MU₁ + MU₂ + … + MUₙ

Explanation

How it works: TU, MU and the three stages

• Utility is the satisfaction a person gets from consuming a good or service.
• Cardinal utility analysis assumes this satisfaction can be measured as a number. The imaginary unit is called a "util".
• Total utility (TU) is the total satisfaction from a given number of units.
• Marginal utility (MU) is the change in TU when she consumes one more unit.

• Example: 4 bananas give TU = 28 and 5 bananas give TU = 30. So MU₅ = 30 − 28 = 2 utils.

• MU is the slope of the TU curve:

• MU > 0 → TU rises
• MU = 0 → TU is at its peak
• MU < 0 → TU falls

Worked example (Table 2.1, Class 12 NCERT):

Units	TU	MU
1	12	12
2	18	6
3	22	4
4	24	2
5	24	0
6	22	−2

• Check the sum rule: 12 + 6 + 4 + 2 + 0 + (−2) = 22 = TU₆.
• Stage I (units 1–4): TU rises at a falling rate.
• MU falls: 12 → 6 → 4 → 2.

• Each unit still adds satisfaction, but less than the one before.

• Stage II (unit 5): MU = 0 and TU is at its maximum (24).

• This point is called satiety (she is fully satisfied with the good).

• Stage III (unit 6): MU = −2 and TU falls to 22.

• The extra unit now causes disutility (discomfort), like being forced to eat a 6th sweet.

• Shape of the curves: the TU curve rises, flattens and then falls, like a hill. The MU curve slopes downward and cuts the x-axis at the 5th unit.

Why MU falls, and the conditions the law needs

• Reason: once she has some of the good, her wish for more of it grows weaker.
• Class 9 example: the first mango tastes delicious, the second is good, and by the third she is barely interested.
• Other name: Gossen's first law, after the German economist Hermann Heinrich Gossen. His work, published in 1854, stated that the extra satisfaction from one more unit of a good falls as more units are consumed [2].
• Conditions (all come from "other things constant"):
• All units are the same size and quality. One small mango and one big mango do not count.
• Units are consumed one after another, without a long gap. A mango tomorrow may taste delicious again.
• Her tastes, her income and the prices of other goods do not change.
• Her consumption of other goods stays fixed.

From DMU to the downward-sloping demand curve

• Chain of logic:
• Each extra unit is worth less to her (DMU).
• So she will pay less for each extra unit.
• So she buys more units only when the price falls.

• Result: a downward-sloping demand curve (lower price → larger quantity bought).

• Class 12 example: at ₹40 per unit she buys 5 units. The 6th unit is worth less to her than the 5th, so she buys it only if the price falls below ₹40.

• Hidden assumption: the marginal utility of money (the satisfaction from one more rupee) stays constant. Only then can MU in utils be turned into a rupee price. Marshall relied on this assumption [4].

Where DMU leads: three linked ideas

• Law of equi-marginal utility (Gossen's second law): a consumer gets the most satisfaction when MUx/Px = MUy/Py = MU of money [5].
• Example: Px = ₹10, MUx = 40 → 4 utils per rupee. Py = ₹5, MUy = 10 → 2 utils per rupee.
• She buys more x and less y.

• Because of DMU, MUx falls and MUy rises. She stops when the two ratios are equal (for example, both at 3).

• Consumer surplus (Alfred Marshall, Principles of Economics, 1890): what she is willing to pay minus what she actually pays [4][8].

• DMU is the reason she would pay more for early units.

• Example: she would pay ₹60 for the 1st unit and ₹50 for the 2nd. The market price is ₹40. Surplus = (60 − 40) + (50 − 40) = ₹30.

• Diamond-water paradox (Adam Smith, Wealth of Nations, 1776): water is essential but cheap, while diamonds are not essential but costly. Smith could not solve this puzzle [3].

• Solution: price follows marginal, not total, utility.
• Water is plentiful, so the MU of one more litre is tiny, but its TU is huge [3].
• Diamonds are scarce, so their MU stays high [3].
• The puzzle was solved by the marginalists: Jevons and Menger (1871) and Walras (1874) [6][7].

In India

DMU is a theory concept, so there is no Indian body that measures it. Its logic, however, appears in Indian policy:

• Progressive income tax:
• Money itself has diminishing MU.
• ₹1,000 taken from a rich person costs them little satisfaction.

• So higher income slabs carry higher tax rates.

• Direct Benefit Transfer (DBT):

• ₹1,000 given to a poor household adds a lot of satisfaction.

• So targeted cash transfers to poor households raise total welfare more than equal handouts to everyone.

• Tiered (slab-wise) water and electricity tariffs in Indian cities and states:

• The first units are essential for life and have high MU, so a free or low-cost "lifeline" block protects them.
• Extra units have lower MU and are often wasted, so higher slab prices discourage over-use.

• This matches the IMF view that water can be free where supply is plentiful, but should carry a positive price where growing use meets limited supply [9] (IMF First Deputy MD speech, 2015).

• Everyday example: at a wedding feast, the first sweet is a delight, the second is fine, and by the fourth the guest refuses. That is DMU, and then satiety.

Don't confuse with

• Diminishing returns (law of variable proportions): this is about production. Extra output from one more worker falls. DMU is about consumption. Extra satisfaction from one more unit falls.
• Law of equi-marginal utility: DMU looks at one good at a time. Equi-marginal utility (Gossen's second law) looks at many goods and gives the equilibrium rule MUx/Px = MUy/Py [5].
• Falling total utility: when MU falls but is still positive, TU still rises, only at a slower rate. TU falls only when MU becomes negative.
• Ordinal utility / diminishing MRS: ordinal utility only ranks bundles using indifference curves. DMU belongs to the cardinal approach, which measures utility in utils.

Prelims Hooks

• MUₙ = TUₙ − TUₙ₋₁; TUₙ = ΣMU; MU is the slope of the TU curve.
• TU is maximum when MU = 0 (satiety). Trap: "TU is maximum when MU is maximum" is wrong.
• The law of DMU is Gossen's first law (1854) [2]. The law of equi-marginal utility is Gossen's second law.
• DMU holds only when consumption of other goods, tastes and income stay constant, and units are the same and consumed without a time gap.
• In utility analysis, DMU explains the downward-sloping demand curve. It assumes the MU of money is constant (Marshall) [4].
• Diamond-water paradox: posed by Adam Smith (1776) and solved through marginal, not total, utility [3]. Marginalists: Jevons and Menger (1871), Walras (1874) [6][7].

Mains Points

• Ethical case for redistribution (GS-III, taxation; GS-II, welfare schemes):
• Money has diminishing MU, so shifting ₹1,000 from rich to poor raises total welfare.
• This supports progressive income tax and DBT.

• Limit: it needs interpersonal comparison of utility (comparing one person's satisfaction with another's), which the ordinal approach rejects.

• Pricing scarce essentials (water, farm power):

• Very low marginal prices lead to over-use, because the last units have low MU.
• Scarce water needs a positive price [9].

• Tiered tariffs balance equity and efficiency: a cheap lifeline block for the high-MU first units, and higher prices for extra use.

• Limits of the theory:

• Utility cannot really be measured in numbers.
• The MU of money is not constant: one more rupee means more to a poor person than to a rich one.
• Behavioural economics shows that habits, addiction and limited attention can break the neat DMU pattern. This matters when designing "nudge" policies, such as for tobacco or alcohol.

Related concepts

• Cardinal utility analysis
• Total utility
• Marginal utility
• Law of equi-marginal utility
• Consumer surplus
• Diamond-water paradox

Read more

• Cardinal utility: total utility, marginal utility and the law of diminishing marginal utility