Utility and Indifference Curves: Consumer Behaviour Notes

Microeconomics begins with a single question: how does a buyer with limited money decide what to buy? The answer is the theory of consumer behaviour, and it is taught in two versions. The older cardinal version, associated with Alfred Marshall, assumes that satisfaction can be measured in numbers, while the modern ordinal version, given by J. R. Hicks and R. G. D. Allen, assumes only that a buyer can rank combinations as better, worse or equally good. Papers set by SSC, Railway, Banking and State commissions ask this chapter as a set of definitions, formulas and properties, and every question has a one-line answer if the two approaches are kept apart in the mind.

Utility and the two ways of measuring it

Utility is the want-satisfying power of a commodity. It is subjective, so the same glass of water has a different utility for a thirsty traveller and for a man sitting beside a river. In the cardinal approach utility is treated as measurable in imaginary units called utils, so a consumer can say that a cup of tea gives him ten utils and a samosa six. In the ordinal approach no such measurement is claimed; the consumer merely says that he prefers one basket to another or is indifferent between them. The ordinal approach rests on four assumptions, namely completeness of preferences, transitivity, more of a good being preferred to less, and a diminishing marginal rate of substitution, and because it demands less of the consumer it is regarded as the better theory.

Total utility and marginal utility

Total utility is the sum of the satisfaction from all the units consumed, and marginal utility is the addition made to total utility by one more unit, that is MU equals the change in total utility divided by the change in quantity. The relationship between the two is fixed and is asked again and again.

While marginal utility is positive, total utility rises; when marginal utility becomes zero, total utility is at its maximum and the consumer has reached the point of satiety; when marginal utility turns negative, total utility falls. This is the whole of the law of diminishing marginal utility, also called Gossen's first law, which explains why a demand curve slopes downward: a buyer will pay less for a later unit because it gives him less satisfaction.

The law of equi-marginal utility and cardinal equilibrium

A consumer spending on several goods arranges his expenditure so that the last rupee spent on each good yields the same satisfaction. This is the law of equi-marginal utility, Gossen's second law, also called the law of substitution or the law of maximum satisfaction. The condition of consumer equilibrium in the cardinal approach is therefore that the marginal utility of a good divided by its price is equal for all goods and equal to the marginal utility of money, that is MU of X upon price of X equals MU of Y upon price of Y equals the marginal utility of money. If the ratio for one good is higher, the consumer shifts expenditure to it until the ratios are equal again.

Indifference curves and their properties

An indifference curve is the locus of all combinations of two goods that give the consumer the same level of satisfaction, so that he is indifferent between them; a family of such curves is an indifference map. The concept was first drawn by F. Y. Edgeworth, developed by Vilfredo Pareto and completed as a theory by Hicks and Allen.

• It slopes downward from left to right, because more of one good must be given up to take more of the other.
• It is convex to the origin, because the marginal rate of substitution diminishes.
• A higher indifference curve represents a higher level of satisfaction.
• Two indifference curves can never intersect or be tangent to each other, since that would mean one combination giving two different levels of satisfaction.
• An indifference curve does not touch either axis, because the consumer wants some quantity of both goods.

The slope of an indifference curve is the marginal rate of substitution, the quantity of the second good a consumer is willing to give up for one more unit of the first; it equals the ratio of the two marginal utilities. Two special cases are worth remembering: for perfect substitutes the indifference curve is a straight line with a constant marginal rate of substitution, and for perfect complements it is L-shaped, a right angle.

The budget line and consumer equilibrium

The budget line, also called the price line, shows all the combinations a consumer can buy by spending his whole income, so its equation is the price of X multiplied by the quantity of X plus the price of Y multiplied by the quantity of Y equal to income. Its slope is the ratio of the two prices, that is the price of X divided by the price of Y. A change in income shifts the budget line parallel to itself, outward for a rise and inward for a fall, while a change in the price of one good swings or pivots the line on the intercept of the other good. The consumer is in equilibrium at the point where the budget line is tangent to the highest attainable indifference curve, where the marginal rate of substitution equals the ratio of the prices and the indifference curve is convex at that point.

Price effect, income effect and consumer surplus

When the price of a good falls, the whole price effect can be split into a substitution effect, by which the consumer buys more of the cheaper good in place of the other, and an income effect, by which his real income has risen. For a normal good both work in the same direction. For an inferior good the income effect works against the substitution effect, and in the rare case where it is strong enough to overwhelm it, the good is a Giffen good and its demand curve slopes upward, the chief exception to the law of demand. Consumer surplus, a concept of Marshall's, is the difference between what a consumer is willing to pay and what he actually pays. Adam Smith's paradox of value, that water is essential yet cheap while diamonds are useless yet dear, is explained by the same marginal reasoning: price follows marginal utility, not total utility.