Analysis of Consumer Behaviour
Consumer behaviour theory explains how a rational consumer maximises utility subject to a budget constraint. This unit covers the cardinal (utility) and ordinal (indifference curve) approaches, the law of diminishing marginal utility, consumer equilibrium under both approaches, the properties of indifference curves, and the price, income, and substitution effects.
In this chapter
Concept of Utility
Utility is the want-satisfying power of a commodity. The concept was introduced to social thought by English philosopher Jeremy Bentham in 1789, and to economic thought by William Stanley Jevons (1871), Walras (1874), and Carl Menger (1871). There are two approaches to analysing utility: the cardinal approach (utility can be measured numerically, e.g. in 'utils') and the ordinal approach (utility can only be ranked — more or less — but not measured).
Cardinal vs Ordinal Approaches
Comparison of Cardinal and Ordinal Utility Approaches
| Basis | Cardinal Approach | Ordinal Approach |
|---|---|---|
| Measurement | Numerical (utils) | Ranking only |
| Developed by | Marshall, Jevons | Hicks, Allen |
| Tools used | Utility curves | Indifference curves |
| Marginal utility | Cardinal, measurable | Not measurable, only MRS |
| Assumption of money | Constant MU of money | No need for constant MU of money |
| Realism | Less realistic | More realistic |
Cardinal Utility Approach (Marshall)
- rational consumers,
- cardinal measurement of utility,
- constant marginal utility of money,
- diminishing marginal utility, and
- additivity of utility
Assumptions of Cardinal Utility
Key Assumptions
- Rationality — consumers aim to maximise total utility given their income.
- Cardinal measurability — utility can be measured in cardinal numbers (utils) or in money.
- Constant marginal utility of money — the MU of the measuring rod (money) does not change.
- Diminishing marginal utility — as more units are consumed, MU falls.
- Additivity of utility — total utility is the sum of utilities from different goods: TU = TU_x + TU_y.
- Continuity — consumption is a continuous variable, not discrete.
Total Utility and Marginal Utility
Total utility (TU) is the sum of the utility derived from the consumption of all units of a commodity: TU = MU₁ + MU₂ + … + MUₙ = ΣMU. It can also be obtained by multiplying average utility by the number of units: TU = AU × n. Marginal utility (MU) is the additional utility gained from consuming one more unit of the commodity: MU = ΔTU / ΔQ. The relationship between TU and MU is central to consumer theory.
Total utility and marginal utility
Law of Diminishing Marginal Utility
The law of diminishing marginal utility states that as a consumer consumes more and more units of a commodity, the marginal utility derived from each successive unit goes on diminishing, other things remaining the same. This is one of the most fundamental laws of economics. It explains the downward-sloping demand curve — since each additional unit gives less satisfaction, the consumer is willing to pay less for it.
TU and MU Schedule (illustrating diminishing MU)
| Units Consumed | MU (utils) | TU (utils) |
|---|---|---|
| 1 | 10 | 10 |
| 2 | 8 | 18 |
| 3 | 6 | 24 |
| 4 | 4 | 28 |
| 5 | 2 | 30 |
| 6 | 0 | 30 |
| 7 | −2 | 28 |
Key Relationship
When MU is positive and diminishing, TU increases at a decreasing rate. When MU = 0, TU is at its maximum (satiation point). When MU becomes negative, TU starts to fall — the consumer is worse off from consuming more.
Law of Equi-Marginal Utility
The law of equi-marginal utility (also called the law of maximum satisfaction) states that a rational consumer allocates income across goods so that the marginal utility per rupee spent on each good is equal. If MU_x / P_x > MU_y / P_y, the consumer should buy more of X and less of Y; as they do so, MU_x falls and MU_y rises (by diminishing MU), until the two ratios are equal. This is the principle of consumer equilibrium in the multi-good cardinal model.
Law of equi-marginal utility
Illustration — Allocating Rs 10 Between Goods X and Y
| Units | MU_x (P_x=Rs 2) | MU_x/P_x | MU_y (P_y=Rs 1) | MU_y/P_y |
|---|---|---|---|---|
| 1 | 20 | 10 | 10 | 10 |
| 2 | 18 | 9 | 8 | 8 |
| 3 | 16 | 8 | 6 | 6 |
| 4 | 14 | 7 | 4 | 4 |
| 5 | 12 | 6 | 2 | 2 |
Nepal Example: Allocating a Student Budget
A BBS student in Kathmandu has Rs 1,000 per month for textbooks (P_x = Rs 200) and tiffin (P_y = Rs 50 per meal). She allocates spending so that the marginal utility per rupee is equal: the last textbook gives 100 utils (0.5 utils/rupee) and the last tiffin gives 25 utils (0.5 utils/rupee). At this point she cannot increase total utility by shifting a rupee from one good to another — she is in equilibrium. This equi-marginal logic applies to every household budget decision in Nepal.
Consumer's Equilibrium: Cardinal Approach
A consumer is in equilibrium when they derive maximum satisfaction from their expenditure. In the one-commodity model, equilibrium occurs when MU of the good equals its price (in terms of money): MU_x / P_x = MU_m, where MU_m is the marginal utility of money. In the two-commodity model, the consumer allocates income between goods X and Y to reach equilibrium when the equi-marginal principle holds: MU_x / P_x = MU_y / P_y = MU_m.
Consumer equilibrium — two commodities (cardinal)
Consumer Surplus under Cardinal Approach
Alfred Marshall defined consumer surplus as the excess of what a consumer is willing to pay over what they actually pay. Under the cardinal approach, the consumer's willingness to pay for each unit equals its marginal utility in money terms. Because of diminishing marginal utility, the consumer is willing to pay a high price for the first unit but a lower price for later units. Yet the market charges a single uniform price for all units — equal to the marginal utility of the last unit purchased. Therefore, the consumer enjoys a surplus on every unit except the last.
Marshallian consumer surplus
Ordinal Utility: The Indifference Curve
The ordinal utility approach uses the indifference curve — a curve showing all combinations of two goods that give the consumer equal satisfaction. A higher indifference curve represents greater satisfaction. The consumer reaches equilibrium at the point where the indifference curve is tangent to the budget line. This approach was developed by J.R. Hicks and R.G.D. Allen as an improvement over the cardinal approach — it does not require measuring utility numerically.
Properties of Indifference Curves
- Indifference curves slope downward from left to right — to keep satisfaction constant, more of one good means less of the other.
- Higher indifference curves represent higher satisfaction — more is preferred to less.
- Two indifference curves never intersect — intersection would violate transitivity of preferences.
- Indifference curves are convex to the origin — due to diminishing marginal rate of substitution (MRS).
- The MRS is the slope of the indifference curve: how much of Y the consumer gives up for one more unit of X while staying on the same curve.
Marginal rate of substitution and consumer equilibrium (ordinal)
Budget Line and Its Properties
The budget line (also called the budget constraint) shows all combinations of two goods that a consumer can afford given their income and the prices of the two goods. If income is M, the prices are P_x and P_y, the budget line is: P_x · X + P_y · Y = M. The slope of the budget line is −P_x / P_y, which is the rate at which the market allows the consumer to substitute Y for X.
Budget constraint — linear form
Properties of the Budget Line
- Linear and downward-sloping — straight line because prices are constant; slope = −P_x / P_y.
- Intercepts — vertical intercept = M / P_y (max Y affordable); horizontal intercept = M / P_x (max X affordable).
- Income changes shift the line — parallel outward for income rise, inward for income fall.
- Price changes pivot the line — if P_x falls, the line rotates outward on the X-axis (Y-intercept unchanged).
- Slope = relative price ratio — the rate at which the market allows the consumer to trade Y for X.
- Affordable set — all bundles on or below the budget line are affordable; bundles above are not.
Derivation of Demand Curve from Indifference Curve
- start at the initial equilibrium where IC₁ is tangent to the budget line at point A — record (P_x1, X1)
- let P_x fall — the budget line pivots outward on the X-axis, giving a new tangency at B on IC₂ — record (P_x2, X2)
- let P_x fall again — get C on IC₃ — record (P_x3, X3). Plotting these (P_x, X) pairs in a separate diagram gives the downward-sloping demand curve
Why Indifference Curves Never Intersect
If two indifference curves intersected, the same bundle (at the intersection point) would yield two different satisfaction levels. But this violates transitivity — if bundle A ~ B (on IC₁) and A ~ C (on IC₂), then B ~ C must also hold, which is impossible if IC₂ represents higher satisfaction than IC₁.
Price Effect: Income and Substitution Effects
- the substitution effect — the consumer substitutes toward the good that has become relatively cheaper (always negative for price increase, i.e. demand falls)
- the income effect — the price change alters the consumer's real purchasing power. For normal goods, the income effect reinforces the substitution effect. For inferior goods, the income effect works against it. For Giffen goods, the income effect is so strong it outweighs the substitution effect, giving an upward-sloping demand curve
Effect of a Price Fall on Different Types of Goods
| Type of Good | Substitution Effect | Income Effect | Total Price Effect | Demand Curve Slope |
|---|---|---|---|---|
| Normal good | Buy more (+) | Buy more (+) | Strongly positive | Downward |
| Inferior good | Buy more (+) | Buy less (−) | Positive but weak | Downward |
| Giffen good | Buy more (+) | Buy much less (−) | Negative | Upward |
Key Terms and Definitions / मुख्य शब्द र परिभाषा
- Utility: Want-satisfying power of a commodity — उपयोगिता: वस्तुको आवश्यकता-सन्तुष्टि गर्ने शक्ति।
- Cardinal utility: Utility measured numerically — कार्डिनल उपयोगिता: संख्यात्मक रूपमा नापिने उपयोगिता।
- Ordinal utility: Utility ranked but not measured — अर्डिनल उपयोगिता: क्रमबद्ध मात्र गरिने, नाप्न नसकिने।
- Total utility (TU): Sum of utility from all units — कुल उपयोगिता: सबै एकाइबाट उपयोगिताको योग।
- Marginal utility (MU): Extra utility from one more unit — सीमान्त उपयोगिता: एक थप एकाइबाट थप उपयोगिता।
- Law of diminishing MU: MU falls as consumption rises — घट्दो MU को नियम: उपभोग बढ्दा MU घट्छ।
- Equi-marginal principle: MU_x/P_x = MU_y/P_y = MU_m — समान-सीमान्त सिद्धान्त।
- Indifference curve: Combinations giving equal satisfaction — अन्तर वक्र: बराबर सन्तुष्टि दिने संयोजन।
- Marginal rate of substitution (MRS): Slope of indifference curve — सीमान्त प्रतिस्थापन दर: अन्तर वक्रको ढलान।
- Budget line: Combinations affordable given income and prices — बजेट रेखा: आय र मूल्य दिइएकोमा किन्न सकिने संयोजन।
- Consumer surplus: Willingness to pay minus price paid — उपभोक्ता अधिशेष: तिर्न तयार रकम माइनस तिरेको मूल्य।
- Price effect = Substitution effect + Income effect — मूल्य प्रभाव = प्रतिस्थापन प्रभाव + आय प्रभाव।
Practice Problem
A consumer consumes two goods X and Y. The marginal utilities and prices are: MU_x = 40, P_x = Rs 5; MU_y = 30, P_y = Rs 3. The marginal utility of money is 6 utils/rupee. Is the consumer in equilibrium? If not, how should they reallocate spending to reach equilibrium?
Practice Problem
A consumer's utility function is U(x, y) = x · y. The consumer's income is Rs 200, and the prices are P_x = Rs 4 and P_y = Rs 5. (a) Write the budget constraint. (b) At the optimal bundle, the MRS_xy equals the price ratio. With U = x·y, the MRS is y/x. Find the optimal x and y. (c) What is the maximum utility?