Consumer Equilibrium and Utility Explained for SHS 2 Economics (Sem. 1 – Week 5)
Every consumer faces a simple economic problem: how can limited income be used to obtain the greatest possible satisfaction?
The economic concept of utility provides a way of analysing that question.
Utility: Measuring Satisfaction
Utility refers to the satisfaction, pleasure or benefit obtained from consuming goods and services. Because satisfaction is difficult to observe directly, Economics uses the theoretical unit util to express it.
Suppose someone consumes several slices of yam. The first slice may provide a high level of satisfaction because the consumer is hungry. Another slice may still provide satisfaction, but perhaps not as much as the first.
This leads to three useful measures: Total Utility, Marginal Utility and Average Utility.
Total Utility: The Whole Amount of Satisfaction
Total Utility (TU) is the combined satisfaction from all units consumed.
If the successive utilities from four slices of yam are 10, 8, 5 and 2 utils:
TU = 10 + 8 + 5 + 2 = 25 utils.
The calculation shows why TU is cumulative. Each new unit adds its own utility to what has already been obtained.
| Units consumed | Utility from latest unit | Total Utility |
|---|---|---|
| 1 | 10 | 10 |
| 2 | 8 | 18 |
| 3 | 5 | 23 |
| 4 | 2 | 25 |
Marginal Utility: What Does One More Unit Add?
Marginal Utility (MU) measures the additional satisfaction resulting from an additional unit of consumption.
The formula is:
MU = ΔTU / ΔQ
Suppose total utility rises from 18 to 23 when consumption rises from two units to three:
MU = (23 − 18) / (3 − 2)
= 5 utils.
The consumer therefore gains five additional utils from the third unit.
Why Marginal Utility Usually Falls
The law of diminishing marginal utility states that as consumption of a good increases, the additional satisfaction obtained from successive units tends to decline.
The yam example demonstrates this pattern: marginal utility falls from 8 for the second slice to 5 for the third and 2 for the fourth.
Average Utility: Satisfaction Per Unit
Average Utility (AU) shows the average satisfaction obtained per unit.
Its formula is:
AU = TU / Q
After three slices of yam:
AU = 23 / 3 ≈ 7.67 utils.
So, although total utility is 23 utils, the average utility per slice is approximately 7.67 utils.
Putting the Three Measures Together
| Measure | Meaning | Formula |
|---|---|---|
| TU | Total satisfaction from all units. | Sum of utilities |
| MU | Additional satisfaction from an extra unit. | ΔTU / ΔQ |
| AU | Average satisfaction per unit. | TU / Q |
From Satisfaction to Consumer Equilibrium
Utility becomes particularly important when consumers have to decide how to allocate limited income.
For a single commodity, the equilibrium condition is:
MUx = Px
This means the marginal utility of the commodity is equal to its price.
For multiple commodities, the condition becomes:
MUx/Px = MUy/Py
The consumer is therefore comparing the additional utility gained from each cedi spent.
A Numerical Example
Suppose a commodity has a price of 5 and its marginal utilities are:
| Quantity | Marginal Utility | Price |
|---|---|---|
| 1 | 10 | 5 |
| 2 | 8 | 5 |
| 3 | 7 | 5 |
| 4 | 6 | 5 |
| 5 | 5 | 5 |
| 6 | 4 | 5 |
At the fifth unit:
MU = 5
P = 5
Therefore:
MU = P
The consumer reaches equilibrium at 5 units.
Reading a Utility Schedule
A utility table can reveal several things at once. Consider the sequence:
10, 18, 25, 31, 36, 40, 43, 45, 46, 46
These are the total utilities associated with quantities from one to ten units in the given schedule.
The marginal utilities are obtained from the successive differences:
10, 8, 7, 6, 5, 4, 3, 2, 1, 0.
For quantity 8:
TU = 45
MU = 45 − 43 = 2
AU = 45 / 8 = 5.625 ≈ 5.63
For quantity 10:
TU = 46
MU = 46 − 46 = 0
AU = 46 / 10 = 4.6
Why the Calculations Matter
The three measures provide different information.
TU tells us how much satisfaction has accumulated.
MU tells us what the next unit adds.
AU tells us the average satisfaction obtained from each unit.
Consumer equilibrium then uses marginal utility to determine the point at which the consumer’s allocation is balanced.
Quick Check
1. If TU rises from 30 to 36 as quantity rises from 4 to 5:
MU = (36 − 30) / (5 − 4) = 6.
2. If TU = 40 for 8 units:
AU = 40 / 8 = 5.
3. If price = 4 and MU = 4:
MU = P, so the single-commodity equilibrium condition is satisfied.
Final Takeaway
Consumer choice can be understood by following the movement from total satisfaction to additional satisfaction and then to consumer equilibrium.
TU = total satisfaction.
MU = additional satisfaction.
AU = satisfaction per unit.
MU = P identifies equilibrium for a single commodity.
For multiple commodities, equilibrium requires equal marginal utility per cedi spent.
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