Total, Marginal and Average Utility Curves

Utility can be studied not only through calculations but also through graphs. Total Utility (TU), Marginal Utility (MU) and Average Utility (AU) curves show how consumer satisfaction changes as consumption increases.

1. Total Utility Curve

Total Utility is the total satisfaction obtained from consuming a given quantity of a good or service.

The total utility curve shows how total satisfaction changes as the quantity consumed increases.

At zero consumption, total utility is zero, so the curve begins at the origin. As consumption increases, total utility initially rises. It may rise at an increasing rate and later at a decreasing rate. Eventually, it reaches a maximum and may fall if additional consumption produces dissatisfaction.

2. Marginal Utility Curve

Marginal Utility is the additional satisfaction obtained from consuming one more unit.

The marginal utility curve normally slopes downward because of the law of diminishing marginal utility: as more units are consumed, the additional satisfaction from successive units tends to decrease.

When marginal utility is positive, another unit adds to total utility. When marginal utility becomes zero, total utility is at its maximum. When marginal utility becomes negative, additional consumption reduces total utility.

3. Average Utility Curve

Average Utility is the total utility obtained per unit consumed.

The formula is:

AU = TU / Q

The AU curve may initially rise as average satisfaction increases. It eventually reaches a maximum and then declines as diminishing marginal utility affects additional consumption.

4. The Three Curves Together

Curve	What it shows	General behaviour
TU	Total satisfaction	Rises, becomes flatter, reaches a maximum and may decline
MU	Additional satisfaction	Generally declines as consumption increases
AU	Satisfaction per unit	May rise initially and later decline

5. Relationship Between TU and MU

The marginal utility curve helps explain the movement of the total utility curve.

• When MU is positive, TU increases.
• When MU is falling but remains positive, TU continues to increase, but at a decreasing rate.
• When MU = 0, TU reaches its maximum.
• When MU is negative, TU falls.

This relationship is one of the most important ideas in the graphical analysis of utility.

6. Relationship Between MU and AU

Marginal utility also helps explain the movement of average utility.

• When MU is above AU, AU tends to rise.
• When MU is below AU, AU tends to fall.
• MU and AU are equal at the point where AU reaches its maximum.

This relationship can be understood using an everyday average. If a new value added to a set is above its current average, the average rises. If the new value is below the current average, the average falls.

7. How to Sketch the Curves

Step 1: Draw the axes

Put quantity consumed on the horizontal axis. Put the relevant utility measure on the vertical axis.

Step 2: Sketch TU

Start TU at the origin. Draw it rising as consumption increases. Make the curve progressively flatter. It reaches a maximum when MU becomes zero and may decline if MU becomes negative.

Step 3: Sketch MU

Draw a generally downward-sloping curve. It can cross the horizontal axis when marginal utility becomes zero and continue below the axis when marginal utility becomes negative.

Step 4: Sketch AU

Draw AU rising initially, reaching a maximum, then declining.

Step 5: Show the relationships

Mark the point where MU = 0 and connect it to the maximum point of TU. Also identify the point where MU = AU, which corresponds to the maximum of AU.

8. Worked Example

Consider a consumer whose marginal utility from successive units is:

Quantity	MU	TU
1	10	10
2	8	18
3	5	23
4	2	25
5	0	25

At quantity 5:

MU = 0.

Total utility is:

TU = 10 + 8 + 5 + 2 + 0 = 25 utils.

Because MU has reached zero, TU is at its maximum at this point.

9. Apply the Relationships

Question 1: What happens to TU when MU is positive?

Answer: TU increases.

Question 2: What happens to TU when MU becomes zero?

Answer: TU reaches its maximum.

Question 3: What happens to TU when MU becomes negative?

Answer: TU decreases.

Question 4: When does AU reach its maximum?

Answer: At the point where MU and AU are equal.

Question 5: Why does the MU curve generally slope downward?

Answer: Because of the law of diminishing marginal utility.

10. Final Synthesis

The three curves tell one connected story about consumption.

TU shows the total satisfaction obtained.

MU shows the additional satisfaction from another unit.

AU shows satisfaction per unit on average.

The most important graphical relationships are:

MU > 0 → TU rises.

MU = 0 → TU is maximum.

MU < 0 → TU falls.

MU = AU → AU is maximum.

Once these relationships are understood, the three utility curves become much easier to sketch and interpret.