Total and Marginal Utility: Schedules and Saturation Point

Imagine eating small slices of your favourite cake after lunch. The first is lovely. The second is enjoyable too, but perhaps not quite as exciting. By the next few slices, you might be thinking, “That is enough, thank you.”

Your enjoyment from all the slices together and your enjoyment from the latest slice are two different things. That distinction is the whole starting point of total utility and marginal utility.

It also explains why a falling marginal utility column does not automatically mean that total utility is falling. A smaller addition is still an addition.

What do total utility and marginal utility mean?

Utility means the satisfaction a consumer derives from a good or service. It depends on the person and the situation. A warm drink may be far more welcome on a cold morning than after a long walk in the heat.

Total utility (TU) is the satisfaction from the entire quantity consumed. Marginal utility (MU) is the change in that total when one additional unit is consumed.

In a numerical schedule, satisfaction is expressed in imaginary units called utils. This is the cardinal approach: it assumes that utility can be represented numerically. It is a classroom model, not a claim that a person’s happiness can actually be read from a measuring instrument. These definitions and the numerical approach follow NCERT’s Theory of Consumer Behaviour, Section 2.1.

For example, suppose two slices give 34 utils and three give 45 utils. The third slice contributes 11 utils. It does not contribute 45 utils, because 45 already includes satisfaction from the first two slices.

When reading a question, ask yourself: “Is this number the whole total so far, or the addition made by the latest unit?”

The formulas you actually need

For quantities increasing one unit at a time:

MU of the nth unit = TU from n units - TU from (n - 1) units

The same relationship can be rearranged:

Current TU = Previous TU + Current MU

Previous TU = Current TU - Current MU

If TU at zero consumption is taken as zero, adding the marginal utilities gives the total:

TU from n units = MU of unit 1 + MU of unit 2 + … + MU of unit n

For a change involving more than one unit, calculate:

Change in TU per unit = Change in TU / Change in quantity

This gives an average over the interval. It does not reveal each individual unit’s MU unless the question gives enough extra information. OpenStax: Consumption Choices explains the change-in-utility approach and the distinction between total and additional satisfaction.

A complete utility schedule, read slowly

Here is an original imaginary schedule for equal-sized portions consumed during one sitting. Every number refers to the same consumer.

Portions consumed	TU (utils)	MU of latest portion (utils)
0	0	Not applicable
1	20	20
2	36	16
3	48	12
4	56	8
5	60	4
6	60	0
7	56	-4

Let us check the rows that usually cause trouble.

Third portion: MU = 48 - 36 = 12 utils. TU increases by 12, even though MU has fallen from 16 to 12.

Fifth portion: MU = 60 - 56 = 4 utils. The consumer still gains satisfaction, but the gain is small.

Sixth portion: MU = 60 - 60 = 0 utils. The additional portion changes nothing in the total.

Seventh portion: MU = 56 - 60 = -4 utils. This portion reduces total satisfaction by 4 utils. The consumer may feel overfull.

The negative sign belongs to the change. TU itself is still positive at 56 utils.

Why is MU not shown at zero consumption?

There is no latest portion at quantity zero. The first marginal calculation compares one portion with zero portions. Writing “not applicable” or a dash in the zero-quantity MU cell avoids confusing the starting point with the first addition.

Why does total utility rise more slowly?

Compare the increases: 20, 16, 12, 8 and 4. Each is positive, but each is smaller than the previous increase. TU therefore climbs in progressively smaller steps.

Think of a savings jar. Adding Rs. 20 today and Rs. 10 tomorrow still makes the jar fuller tomorrow. The second addition being smaller does not remove the first one.

How to identify the saturation point

In the usual diminishing-MU illustration, the saturation point is reached when the additional unit gives zero marginal utility and total utility is at its maximum, with further consumption reducing it.

In our schedule, the sixth portion has MU = 0. The standard saturation answer is therefore six portions, with maximum TU of 60 utils.

But notice something useful: TU is 60 at both five and six portions. That is not a printing error. The sixth portion adds zero, so the maximum total appears in two adjacent rows.

A precise written answer would be:

If the question asks for the first quantity at which maximum TU is attained, answer five portions. If it asks for the zero-MU saturation row, answer six. Read the wording before circling a number.

What if there is no zero in the MU column?

Consider this separate schedule:

Quantity	TU (utils)	MU (utils)
0	0	Not applicable
1	13	13
2	22	9
3	27	5
4	28	1
5	25	-3

The highest observed TU is 28 at four units. MU changes from positive to negative without an observed zero.

For indivisible units, four units maximise TU in this table. Do not invent a fifth-unit MU of zero, and do not claim that the table proves an exact fractional saturation quantity. A smooth curve fitted between the observations would require an extra assumption.

Does MU = 0 always prove a maximum?

Zero MU proves that the latest unit caused no change in TU. To call that level a maximum, check the surrounding pattern.

For example, TU values of 10, 10 and 15 contain a zero change followed by a positive change. The flat step at 10 is not the maximum of that schedule.

The familiar saturation rule works with the usual pattern of diminishing MU, where positive additions give way to zero and then negative additions. In a smooth curve, the corresponding peak has MU changing from positive to negative.

The law of diminishing marginal utility

The law describes additional satisfaction becoming smaller as consumption of a commodity increases, other relevant circumstances remaining unchanged.

Use comparable units and a clear consumption period. Comparing one small biscuit today with a whole packet next month changes too many things to illustrate the idea cleanly. Keep the consumer, tastes, quality and context sufficiently stable, and hold consumption of other goods constant.

The law concerns marginal utility. It does not say that the total must fall from the second unit onward. In our first schedule, MU diminishes throughout, while TU rises for five portions, stays level for one portion and then falls.

It also does not require every observed schedule to reach zero. A short table may stop while MU is still positive. You can then say TU is still increasing over the displayed range; you cannot locate an unseen saturation point from that table alone.

How to draw the TU and MU graphs

Use two panels, one above the other, so that the quantity marks line up. This makes it easier to connect a change in the TU graph with the corresponding MU value.

1. Label the horizontal axis Quantity consumed in both panels.
2. Label the upper vertical axis Total utility (utils).
3. Plot the TU points from the first schedule: (0, 0), (1, 20), (2, 36), (3, 48), (4, 56), (5, 60), (6, 60), (7, 56).
4. Label the lower vertical axis Marginal utility (utils), leaving space below zero.
5. Plot the MU observations at quantities 1 to 7: 20, 16, 12, 8, 4, 0 and -4.
6. Mark the zero-MU observation and the maximum TU level clearly.

For this discrete schedule, join observations with straight segments if appropriate for the question. The TU segment between five and six is flat. The MU value of the sixth unit is the change over that segment, recorded at quantity six.

A smooth textbook curve expresses the same broad idea: TU rises, flattens at its peak and then falls; MU slopes downward and passes through zero at the peak. Do not force a smooth curve to match every detail of a table of indivisible units.

For readers comfortable with calculus, MU is the slope of a smooth TU curve. For schedule questions, ordinary subtraction is enough.

Solved example: fill the missing values

Suppose a question provides the following information:

Quantity	TU (utils)	MU (utils)
0	0	Not applicable
1	18	A
2	B	14
3	42	C
4	D	6
5	50	E
6	F	0
7	46	G

Start from a known total and move through the table.

• A = 18 - 0 = 18.
• B = 18 + 14 = 32.
• C = 42 - 32 = 10.
• D = 42 + 6 = 48.
• E = 50 - 48 = 2.
• F = 50 + 0 = 50.
• G = 46 - 50 = -4.

The completed MU sequence is 18, 14, 10, 6, 2, 0, -4. Its sum is 46, matching TU at seven units.

The zero-MU row is quantity six. Maximum TU is 50, shared by quantities five and six.

Working backwards from a negative MU

Suppose instead you are only told that TU at six units is 44 and MU of the sixth unit is -3.

TU at five units = 44 - (-3) = 47 utils.

This answer makes sense: the sixth unit reduces a previous total of 47 to 44. Writing 41 would mistakenly reduce the total a second time.

Solved example: a quantity jump of two units

A table shows TU of 30 at two units and TU of 46 at four units.

The change in TU is 46 - 30 = 16 utils. The change in quantity is 4 - 2 = 2 units.

Average additional utility per unit over the interval = 16 / 2 = 8 utils.

This does not prove that the fourth unit has MU of 8. The third and fourth units could have marginal utilities of 10 and 6, or 9 and 7. Both pairs add to 16.

If the question specifically asks for MU of the fourth unit, you need TU at three units or some other information that determines the split.

Saturation is different from the quantity worth buying

A utility schedule describes satisfaction. A purchasing decision must also consider the sacrifice involved in paying for the good.

Imagine that the marginal benefits of four units, expressed in money, are Rs. 30, Rs. 22, Rs. 14 and Rs. 6. Each unit costs Rs. 10, and the consumer can afford all four. Under this simple diminishing-benefit model, the first three are worth buying. The fourth costs more than its additional benefit.

The consumer stops while marginal benefit is still positive. There is no need to keep buying until it reaches zero. This opportunity-cost reasoning is explained in OpenStax’s lesson on choices and budget constraints.

Be careful with units. If MU is measured in utils and price is in rupees, they cannot be equated directly. In the simple cardinal model, MU divided by the marginal utility of money expresses the benefit in money terms. For divisible goods, an interior purchasing optimum equates marginal benefit in money to price, under the model’s assumptions.

For a TU-MU table asking only about saturation, you normally do not need to introduce price at all.

Five mistakes to catch before submitting

Dividing TU by quantity to find MU. That gives average utility. MU requires the change between quantities.

Subtracting in the wrong order. Use current TU minus previous TU. Reverse subtraction turns a gain into a loss.

Calling every fall in MU a fall in TU. A change from MU of 12 to MU of 8 still means TU rises by 8.

Calling negative MU negative TU. A total of 60 falling to 56 has negative MU but positive TU.

Selecting the largest MU as saturation. The largest MU is often the first unit. Saturation concerns no further addition to an already maximum total in the usual schedule.

A useful answer has three parts: the quantity, the relevant figures, and the interpretation. “At six units, MU is zero and TU is at its maximum of 60 utils” is stronger than an unexplained “six”.

Try these six quick questions

Attempt these before reading the answers.

1. TU at two units is 29 and TU at three units is 40. Find MU of the third unit.
2. The first four marginal utilities are 17, 12, 7 and 2. Find TU at four units, taking starting TU as zero.
3. TU at three units is 35. MU of the fourth unit is -5. Find TU at four units.
4. TU for quantities zero to five is 0, 15, 25, 30, 30 and 27. Identify the zero-MU saturation row and all quantities with maximum TU.
5. TU at two units is 24 and TU at five units is 45. Find the average additional utility per unit over the interval. Can you identify MU of the fifth unit?
6. MU falls from 9 to 5. A student says total utility must now be falling. Correct the statement.

Answers and reasons

1. 11 utils, because 40 - 29 = 11.
2. 38 utils, because 17 + 12 + 7 + 2 = 38.
3. 30 utils, because 35 + (-5) = 30.
4. Quantity four has MU = 0. Maximum TU of 30 utils occurs at both three and four units.
5. 7 utils per unit, because (45 - 24) / (5 - 2) = 21 / 3. The fifth unit’s individual MU cannot be found from these two totals alone.
6. TU is still rising, because MU remains positive. It rises by 5 rather than by the previous 9 utils.

When you can explain each answer in a sentence, you are ready for a mixed schedule with blanks, a graph question or a short reasoning answer.

Frequently asked questions

What is the difference between total utility and marginal utility?

Total utility is satisfaction from the whole quantity consumed. Marginal utility is the change in that total caused by an additional unit.

What is the formula for marginal utility?

For a one-unit increase, subtract the previous total utility from the current total utility. For a larger interval, change in TU divided by change in quantity gives the average change per unit over that interval.

Can total utility increase while marginal utility decreases?

Yes. If MU remains positive, each additional unit increases TU. Smaller positive MU means TU rises by smaller amounts.

What happens when marginal utility becomes zero?

The additional unit leaves TU unchanged. In the usual diminishing-MU schedule, this is the saturation row at maximum TU. Check the surrounding values before treating any zero change as a maximum.

Why can maximum total utility appear in two rows?

A zero-MU unit adds nothing to the previous total. The quantity before it and the quantity including it therefore have the same TU, which is the maximum if subsequent MU is negative.

Does negative marginal utility mean total utility is negative?

No. It means TU falls. If TU falls from 50 to 46, MU is -4 while total utility remains positive at 46.

What if the schedule has no exact zero marginal utility?

Choose the largest observed TU when asked for the quantity that maximises satisfaction among the listed options. If MU jumps from positive to negative, state that no exact zero-MU row is shown.

Is marginal utility the same as average utility?

No. Average utility is TU divided by quantity. Marginal utility is the additional utility from a change in quantity. They answer different questions.

Must a consumer buy up to the saturation point?

No. Prices and alternative uses of money matter. A consumer can stop buying while MU is positive because the next unit is not worth its cost.

What is the fastest way to check a completed utility schedule?

Subtract consecutive TU entries to check each MU. Then add the MU values to the starting TU and confirm that you recover the final total. Finally, check that positive, zero and negative MU match rising, unchanged and falling TU.