4 Demand, Revealed Preference, and Consumer Welfare

Income, prices, and consumer demand

Consumers choose bundles of goods subject to prices and limited income. The budget constraint describes which bundles are affordable, and the consumer chooses an affordable bundle that best fits their preferences.

For two goods, the constraint is

where $p_x$ and $p_y$ are prices, $x$ and $y$ are quantities, and $m$ is income. When prices stay fixed, higher income expands the budget set, while lower income contracts it.

Income and demand

When income rises, demand for a normal good rises, other things equal. Demand for an inferior good falls as income rises. A good can be normal for one consumer or income range and inferior for another.

Price changes and demand

A price change affects both the relative cost of goods and the consumer’s purchasing power. If the price of $x$ falls, the budget line becomes flatter and the consumer can afford more $x$, holding other factors fixed.

The total response has two parts. The substitution effect shifts the consumer toward a good that has become relatively cheaper and away from goods that have become relatively more expensive. For a compensated comparison, purchasing power is adjusted to keep the consumer at the original level of utility. The income effect arises because a price change changes real purchasing power even when money income is unchanged: a price fall increases it, while a price rise reduces it.

For a normal good, both effects of a price fall tend to increase its consumption. For an inferior good, the income effect may work against the substitution effect. In the unusual Giffen-good case, the opposing income effect is strong enough that a price rise increases demand for that good.

A demand curve summarizes how much of a good consumers choose at different prices, holding other determinants constant. A change in the good’s own price produces a movement along its demand curve; a change in income or another determinant can shift the curve.

Inferring preferences from choices

Revealed preference infers a consumer’s preference from observed choices rather than requiring the analyst to measure utility directly. If a consumer chooses bundle $A$ when bundle $B$ was affordable, the choice reveals that $A$ was at least as preferred as $B$ in that choice situation.

For example, suppose a consumer has income of $\$8$ and faces prices $(p_x,p_y)=(2,1)$. They choose $A=(3,2)$, which costs $\$8$. Bundle $B=(2,3)$ costs $\$7$, so it was also affordable. The choice reveals $A$ as weakly preferred to $B$.

The Weak Axiom of Revealed Preference (WARP) says that if a consumer chooses $A$ when $B$ is affordable, they should not later choose $B$ when $A$ is affordable, unless the bundles are the same. Such a reversal is inconsistent with stable, orderly choice under the usual consumer model.

With many observations, economists use related tests, including the Generalized Axiom of Revealed Preference (GARP), to check whether observed choices can be rationalized by utility maximization. A failed test may reflect changing preferences, incomplete information, measurement error, or inconsistent choices; it does not by itself identify the cause.

Revealed preference links theories of preferences to observable data. It can also help assess welfare: if one chosen option was available under another budget, the choice can establish a preference ranking across those situations, subject to the assumptions of the model.

Consumer surplus and welfare

A consumer’s willingness to pay for a unit is the most they would give up to obtain it. In the standard demand-curve interpretation, consumer surplus is the difference between willingness to pay and the amount actually paid. For multiple units, consumer surplus is the sum of these differences; graphically, it is the area below the demand curve and above the market price.

For example, if a consumer values three units at $\$10$, $\$8$, and $\$6$, and pays $\$5$ per unit, their consumer surplus is

A lower price generally raises consumer surplus: buyers pay less on units they already purchase, and some may buy additional units. A higher price generally reduces it. These gains and losses are commonly used to summarize the consumer side of a policy or market change.

Limits of consumer surplus as a welfare measure

Consumer surplus is a convenient welfare measure, but it is not always an exact measure of the change in a person’s well-being. The area under an ordinary demand curve can be an approximation when income effects matter.

Compensating variation and equivalent variation instead express a welfare change as a money amount tied to a specified reference point. Roughly, compensating variation is the income adjustment needed to offset a change in prices, while equivalent variation is the income change at original prices that would have an equivalent effect. The measures can differ when income effects are present; changes in consumer surplus are exact in important special cases, such as with quasilinear preferences.

Adding up consumers’ surplus changes gives a monetary summary, not a complete judgment about fairness. The same dollar gain can matter differently to households with different incomes, and consumer surplus alone does not capture every social cost or benefit.