Theory of Consumer Behaviour

Written and reviewed by Devendra Dubey, Mathematics & Commerce faculty at UniDrill (M.Sc. Mathematics, Osmania University · 10 years teaching). Based on NCERT Economics Class XII (Introductory Microeconomics), Chapter 2.

How do you decide what to buy?

You walk into a fruit shop with ₹120. Bananas are ₹10 each and mangoes ₹20 each. You could buy 12 bananas, or 6 mangoes, or anything in between. What you actually pick depends on two things: what the shop and your wallet allow (prices and income), and what you like (your preferences). This chapter turns that everyday choice into a precise model. Wallet gives the budget line. Likes give the indifference curves. Where they touch is your optimum. Change a price and you trace out your demand curve.

For simplicity, the chapter uses only two goods, bananas and mangoes. A consumption bundle $(x_1, x_2)$ means $x_1$ bananas and $x_2$ mangoes. The bundle $(5, 10)$ is 5 bananas and 10 mangoes, which is not the same as $(10, 5)$. The word "goods" includes services.

Utility: the satisfaction behind demand

Utility is the want-satisfying capacity of a commodity. The stronger the desire for it, the greater its utility. Utility is subjective: a chocolate lover gets far more from a chocolate than someone who dislikes them. It also changes with place and time, since a room heater is worth more in Ladakh than in Chennai, and more in winter than in summer.

There are two ways to analyse choice.

Cardinal analysis: total and marginal utility

Total utility (TU) is the total satisfaction from consuming a given quantity. Marginal utility (MU) is the change in total utility from one more unit.

$$MU_n = TU_n - TU_{n-1}, \qquad TU_n = MU_1 + MU_2 + \dots + MU_n$$

The textbook schedule shows how both behave.

The curves in words. Total utility rises with each unit, but at a decreasing rate, flattens out at the fifth unit, and then falls. Marginal utility starts high and falls with each unit, touches zero where total utility stops rising, and turns negative after that. Total utility is at its maximum exactly where marginal utility is zero.

Why does marginal utility fall? Having had some of a commodity, your desire for still more weakens. This is the Law of Diminishing Marginal Utility: marginal utility from each additional unit declines as consumption rises, keeping the consumption of other commodities constant.

Worked example: marginal utility from total utility. A student's total utility from chocolates is 10, 18, 24, 28, 30, 30, 28 for 1 to 7 chocolates. Find the marginal utility of each, say where total utility peaks, and build her demand schedule if each unit of utility is worth ₹1.

Common wrong step. Computing marginal utility as $TU \div \text{units}$. For the 5th chocolate that gives $30 \div 5 = 6$, but the true MU is $30 - 28 = 2$. Dividing gives average utility, not marginal.

Deriving the demand curve from diminishing MU. Demand is the quantity a consumer is willing to buy and able to afford at given prices of goods, with income and tastes fixed. The demand curve shows quantity demanded at different prices of the same good, holding prices of related goods and income constant. The link between the two is simple. Each successive unit gives lower marginal utility, so the consumer will not pay as much for it. If a consumer buys 5 units at ₹40, the 6th is worth less than the 5th, so she will buy it only if the price falls below ₹40. This negative relation between price and quantity demanded is the Law of Demand.

Ordinal analysis: indifference curves

Because we never really quantify utility, the second approach only needs us to rank bundles. Bundles that give the same satisfaction can be joined into an indifference curve. The consumer is indifferent between all bundles on it.

Look at this schedule. When the consumer gets another banana, she must give up some mangoes to stay equally satisfied.

The amount of mangoes the consumer is willing to give up for one extra banana, with utility unchanged, is the marginal rate of substitution (MRS).

$$\text{MRS} = \left\lvert \dfrac{\Delta x_2}{\Delta x_1} \right\rvert$$

Why MRS diminishes. As the consumer has more bananas, the marginal utility of each extra banana falls. As she has fewer mangoes, the marginal utility of each mango rises. So she is willing to sacrifice smaller and smaller quantities of mangoes for each additional banana. This is the Law of Diminishing Marginal Rate of Substitution, and it makes the indifference curve convex to the origin: it slopes down from left to right and gets flatter as bananas increase.

Perfect substitutes. When two goods are perfect substitutes, MRS does not diminish. For a consumer who treats a five rupee note and a five rupee coin as the same, she always gives up exactly one coin for one note, so the MRS is constantly 1. The indifference curve is a straight line.

Monotonic preferences. Preferences are monotonic if, between two bundles, the consumer prefers the one with more of at least one good and no less of the other. An indifference map is a family of indifference curves, and with monotonic preferences bundles on higher curves are preferred.

Why curves cannot cross. Suppose curves IC1 and IC2 intersect at A, with B on IC1 and C on IC2. B is as good as A, and C is as good as A, so B should be as good as C. But if B has more mangoes than C with the same bananas, B is clearly better. The contradiction shows the curves cannot meet.

Pause and predict: a consumer is indifferent between bundles (5, 6) and (6, 6). Are her preferences monotonic?

Check your answer: no. The second bundle has more of one good and no less of the other, so a consumer with monotonic preferences must strictly prefer it. Being indifferent breaks monotonicity.

The consumer's budget

What the consumer can afford depends on prices and income. If income is $M$ and prices are $p_1$ and $p_2$, a bundle $(x_1, x_2)$ is affordable if its cost does not exceed income.

$$p_1 x_1 + p_2 x_2 \le M$$

This inequality is the budget constraint, and the set of all affordable bundles is the budget set. For example, with ₹20 and both goods at ₹5 in whole units, 15 bundles are affordable. Five of them, (0, 4), (1, 3), (2, 2), (3, 1) and (4, 0), cost exactly ₹20, and the rest cost less. (3, 3) costs ₹30 and is not affordable.

For divisible goods, the bundles that cost exactly $M$ form the budget line:

$$p_1 x_1 + p_2 x_2 = M \quad \Longleftrightarrow \quad x_2 = \dfrac{M}{p_2} - \dfrac{p_1}{p_2}\,x_1$$

The curve described in words: a straight line sloping down from the vertical axis to the horizontal axis. It meets the horizontal axis at $\dfrac{M}{p_1}$ (all income on bananas) and the vertical axis at $\dfrac{M}{p_2}$ (all income on mangoes). The budget set is the triangle on or below the line.

Why the slope is $-\dfrac{p_1}{p_2}$. Take two points on the line. Both cost $M$, so the cost of the extra bananas must equal the savings on mangoes: $p_1 \Delta x_1 + p_2 \Delta x_2 = 0$, so $\dfrac{\Delta x_2}{\Delta x_1} = -\dfrac{p_1}{p_2}$. One more banana costs $p_1$ rupees, and that money buys $\dfrac{p_1}{p_2}$ mangoes. The line is downward sloping because to buy more of one good you must give up some of the other. The absolute slope is the rate at which the market lets her swap bananas for mangoes.

Worked example: drawing and shifting the budget line. Income is ₹120, bananas cost ₹10 and mangoes ₹20. Find the intercepts and slope. Then find the new line if (a) the banana price rises to ₹15, (b) income rises to ₹240, (c) both prices and income double.

Common wrong step. Showing a price rise as a parallel shift. A price change alters the slope, so the line pivots about the intercept of the good whose price did not change. Only a change in income shifts the line in parallel. A fall in the banana price makes the line flatter, pivoting outward.

The consumer's optimum

A rational consumer knows what is good for her and always tries to reach the best bundle she can afford. Her problem is to move to the highest possible indifference curve within her budget set.

Where is the optimum? First, on the budget line. Under monotonic preferences, a bundle below the line is always beaten by some bundle on the line with more of at least one good. Second, at the point where the budget line is tangent to an indifference curve. Any other point on the line lies on a lower curve, while higher curves are out of reach.

At the tangency, the slopes are equal:

$$\text{MRS} = \dfrac{p_1}{p_2}$$

The MRS is the rate at which she is willing to swap. The price ratio is the rate at which she is able to swap in the market. At the optimum the two are equal.

Worked example: why MRS must equal the price ratio. Bananas cost ₹10 and mangoes ₹20. At her current bundle, the consumer's MRS is 2. Should she buy more bananas or fewer?

Common wrong step. Using $\dfrac{p_2}{p_1} = 2$ and concluding she is already at the optimum. The slope of the budget line in the (bananas, mangoes) diagram is $\dfrac{p_1}{p_2}$, the price of the good on the horizontal axis divided by the price of the good on the vertical axis. If MRS is below the price ratio, the argument runs the other way and she should buy fewer bananas.

There are also situations where the optimum is at a corner, where the consumer spends her entire income on one good.

Demand from indifference curves

The demand function and the curve. If prices of other goods, income and tastes stay fixed, the quantity a consumer chooses depends only on the good's own price. This relation is the demand function, written $X = f(P)$. Its graph is the demand curve, with price on the vertical axis and quantity on the horizontal axis. In general, it slopes downward.

Deriving it from the optimum. Start at an equilibrium with the banana price at $P'_1$ and plot that price against the quantity chosen. Now let the banana price fall, keeping the mango price and income unchanged. The budget line pivots outward and the new optimum is on a higher indifference curve with more bananas. Plot the new price and quantity, and repeat. The points trace out a downward sloping demand curve.

Two effects of a price fall. The substitution effect: bananas are cheaper relative to mangoes, so the consumer substitutes bananas for mangoes. The income effect: lower price raises purchasing power, so she can buy more of everything.

Beyond the textbook. For the exam: a Giffen good is an inferior good whose income effect is stronger than its substitution effect, so demand moves in the same direction as price. In reality: well-documented cases are extremely rare, which is why the downward sloping demand curve remains the general rule. Why it matters: a statement saying "all demand curves slope downward" is wrong in theory, but a statement calling Giffen goods common is wrong in practice.

Linear demand. A linear demand curve is $d(p) = a - bp$ for $0 \le p \le \dfrac{a}{b}$ and zero for higher prices. Here $a$ is demand at price zero and $b$ is the fall in demand for each rupee rise in price. The curve cuts the price axis at $\dfrac{a}{b}$.

Normal and inferior goods, substitutes and complements

Demand also depends on income and on the prices of related goods.

A good can be normal at low incomes and inferior at higher ones. A very poor consumer's demand for low quality cereals may rise with income, but beyond some income she switches to better cereals and buys less of them.

Movement along the curve versus shift of the curve

A change in the good's own price causes a movement along the demand curve. A change in anything else, such as income, other prices or tastes, causes a shift of the whole curve.

Pause and predict: the price of tea rises. What happens to the demand curve for coffee, and to the demand curve for sugar?

Check your answer: coffee is a substitute for tea, so its demand curve shifts right as consumers switch. Sugar is a complement of tea, so its demand curve shifts left, because people who buy less tea also buy less sugar.

Market demand

The market demand at a price is the total demand of all consumers at that price. Graphically it is the horizontal summation of individual demand curves: add quantities at each price, not prices at each quantity.

Worked example: adding two demand curves. Two consumers have $d_1(p) = 10 - p$ (zero above ₹10) and $d_2(p) = 15 - p$ (zero above ₹15). Find the market demand and its value at ₹4 and at ₹12.

Common wrong step. Using $25 - 2p$ at every price. Above ₹10 consumer 1's demand is zero, not negative, so the market curve has a kink at ₹10.

Price elasticity of demand

Some goods respond strongly to price changes, others hardly at all. Price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price.

$$e_D = \dfrac{\%\ \text{change in quantity}}{\%\ \text{change in price}} = \dfrac{\Delta Q / Q}{\Delta P / P} = \dfrac{\Delta Q}{\Delta P} \times \dfrac{P}{Q}$$

Elasticity is negative because demand and price move in opposite directions, but we usually quote the absolute value. It is a pure number, free of units.

Worked example: elasticity and expenditure. (a) A consumer buys 15 bananas at ₹5 and reduces to 12 when the price rises to ₹7. (b) Another buys 100 units at ₹50 and 115 units when the price falls to ₹45. Find the elasticity and the change in expenditure in each.

Common wrong step. Dividing the percentage change in price by the percentage change in quantity, which gives 2 for case (a) and flips the classification. Quantity goes in the numerator.

Elasticity and expenditure. Expenditure is price times quantity. Whether it rises or falls with a price change depends on elasticity.

The expenditure moves in the opposite direction to price only if demand is elastic, and in the same direction only if demand is inelastic. For small changes the change in expenditure is about $\Delta E \approx \Delta p \cdot q\,(1 + e_D)$, with $e_D$ negative. If $e_D < -1$ the bracket is negative, so $\Delta E$ has the opposite sign to $\Delta p$. If $e_D > -1$ it has the same sign, and at $e_D = -1$ expenditure is unchanged.

Elasticity along a linear demand curve. For $q = a - bp$, the slope is constant at $-b$, yet the elasticity changes from point to point.

$$e_D = -\dfrac{bp}{a - bp}$$

Elasticity is 0 where the line meets the quantity axis (price zero), rises along the curve, equals 1 at the midpoint $p = \dfrac{a}{2b}$, and approaches infinity where it meets the price axis. Geometrically, the elasticity at any point equals the ratio of the lower segment to the upper segment of the line at that point.

Worked example: elasticity down a demand line. Demand is $q = 100 - 5p$. Find the quantity, expenditure and elasticity at ₹4, ₹6, ₹10, ₹14 and ₹16.

The midpoint is at $p = \dfrac{100}{2 \times 5} = 10$. Expenditure peaks there at ₹500. To the left (low prices) a price rise raises spending, and to the right it lowers spending.

Common wrong step. Saying elasticity is the same everywhere on a straight line because the slope is constant. Slope is $\dfrac{\Delta q}{\Delta p}$, but elasticity multiplies it by $\dfrac{p}{q}$, which changes at every point.

Special demand curves with constant elasticity.

What decides elasticity. Demand for necessities is likely to be inelastic and for luxuries elastic. The availability of close substitutes matters too: demand for a specific variety of pulses is more elastic than demand for food in general, because consumers can shift to another variety.

Beyond the textbook. For the exam: elasticity depends on the nature of the good and the availability of substitutes. In reality: time matters as well. Over a short period, buyers cannot change habits or find alternatives, so demand is less elastic. Over years, they adjust, and the same good becomes more elastic. Why it matters: the elasticity figure in a question always belongs to a particular price and time horizon.

Pause and predict: the price of a good with $\lvert e_D \rvert = 0.2$ rises by 10%. What happens to quantity and to total spending on the good?

Check your answer: quantity falls by about $0.2 \times 10 = 2\%$. Because the fall in quantity is much smaller than the rise in price, spending on the good rises.

Exam traps

Formula sheet

60-second revision

Where this chapter connects

• Previous: Introduction sets up scarcity, choice and opportunity cost, which the budget line makes concrete.
• Next: Production and Costs turns to the producer side of the market.
• Then: Market Equilibrium combines the market demand built here with supply to find price and quantity.