Law of Equi-Marginal Utility – Consumer Equilibrium
Everyday Situation 💰
You have ₹100 to spend and two choices:
- Coffee ☕ – ₹20 per cup
- Momos 🥟 – ₹10 per plate
How will you divide ₹100 between coffee and momos to get maximum satisfaction?
The Law of Equi-Marginal Utility explains this allocation.
Statement of the Law
A consumer allocates his limited income among different goods in such a way that the marginal utility per rupee spent on each good is equal. This maximizes total utility.
In formula form (for two goods X and Y):
MUx / Px = MUy / Py = Maximum
Where:
- MUx = Marginal Utility of good X
- Px = Price of good X
This is called consumer equilibrium under cardinal utility analysis.
Illustration with Numbers
Suppose a student consumes tea (T) and samosa (S):
- Price of tea, Pt = ₹10
- Price of samosa, Ps = ₹5
| Units | MU of Tea (utils) | MU of Samosa (utils) |
|---|---|---|
| 1 | 30 | 20 |
| 2 | 25 | 16 |
| 3 | 20 | 12 |
| 4 | 15 | 8 |
| 5 | 10 | 4 |
MU per rupee:
- MU/₹ for Tea = MUt / 10
- MU/₹ for Samosa = MUs / 5
The consumer should allocate income so that MU/₹ is equal for both goods.
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Conditions for Consumer Equilibrium
For two goods X and Y:
- MUx / Px = MUy / Py (Equal marginal utility per rupee).
- Entire income is spent.
- MU falls as more is consumed (diminishing MU).
If MUx / Px > MUy / Py → Spend more on X, less on Y.
If MUx / Px < MUy / Py → Spend more on Y, less on X.
Equilibrium is reached when no reallocation of income can increase total utility.
Assumptions
- Rational consumer – wants to maximize satisfaction.
- Limited income.
- Prices of goods are given and constant.
- Utility is measurable and diminishes with more consumption.
- Preferences are consistent.
Importance of the Law
- Explains how consumers distribute income among many goods.
- Basis for demand of a combination of goods.
- Helps firms understand consumer behaviour and pricing strategies.
Quiz Time 🧠
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Key Takeaway: The Law of Equi-Marginal Utility shows how a rational consumer spreads limited income across different goods so that each rupee spent gives equal marginal utility, leading to maximum total satisfaction.