The Consumer's Budget

The Consumer’s Budget

A consumer does not have unlimited resources. She has a fixed amount of money — her income — to spend on the goods she wants. In the market, the prices of those goods are given; she cannot change them. This means she cannot simply buy any combination of goods she might wish for. The bundles of goods she can actually afford depend on two things: her income and the market prices of the goods.

For simplicity, we consider a consumer who spends her entire income on only two goods. Let those goods be called Good 1 and Good 2. Let the price of Good 1 be $p_1$ per unit, and the price of Good 2 be $p_2$ per unit. Let the consumer’s income be $M$ (measured in rupees, say). Then, if she buys $x_1$ units of Good 1 and $x_2$ units of Good 2, her total expenditure is:

She can afford a bundle $(x_1, x_2)$ only if this total expenditure does not exceed her income. That is, the bundle must satisfy:

This inequality is called the budget constraint. It defines the set of all bundles that are affordable for the consumer, given her income and the prices.

The consumer can choose any bundle that lies on or inside the budget line. The entire set of such bundles — all points satisfying $p_1 x_1 + p_2 x_2 \leq M$ — is called the budget set.

The Budget Line

If the consumer spends all her income on Good 2 (so $x_1 = 0$), then $p_2 x_2 = M$, which gives $x_2 = M / p_2$. This is the vertical intercept of the budget line — the maximum amount of Good 2 she can buy if she buys none of Good 1.

Similarly, if she spends all her income on Good 1 (so $x_2 = 0$), then $p_1 x_1 = M$, giving $x_1 = M / p_1$. This is the horizontal intercept — the maximum amount of Good 1 she can buy if she buys none of Good 2.

The budget line is a straight line connecting these two intercepts. Its slope is given by the ratio of the prices, with a negative sign:

Why negative? Because to buy more of Good 1, the consumer must give up some of Good 2, given her fixed income. The slope tells us the rate at which the market allows her to trade Good 2 for Good 1. Specifically, if she wants one extra unit of Good 1, she must reduce her consumption of Good 2 by $p_1 / p_2$ units.

Changes in the Budget Line

The budget line shifts or rotates when either income or a price changes.

Change in income. If the consumer’s income increases from $M$ to $M'$ (with prices unchanged), both intercepts increase: the new vertical intercept is $M'/p_2$ and the new horizontal intercept is $M'/p_1$. The budget line shifts outward, parallel to the original line. The slope remains $-p_1/p_2$ because prices haven’t changed. A decrease in income shifts the budget line inward, also parallel.

Change in price of one good. Suppose the price of Good 1 falls from $p_1$ to $p_1'$ (with income $M$ and $p_2$ unchanged). The vertical intercept $M/p_2$ stays the same — the consumer can still buy the same maximum amount of Good 2. But the horizontal intercept increases to $M/p_1'$ because she can now buy more of Good 1 with her income. The budget line rotates outward around the vertical intercept. Its slope becomes steeper (in absolute value) because $p_1'/p_2$ is smaller than $p_1/p_2$ — the trade-off has become cheaper. A rise in the price of Good 1 rotates the budget line inward around the vertical intercept.

Similarly, a change in the price of Good 2 rotates the budget line around the horizontal intercept.

The Budget Set: A Numerical Example

Let the consumer have an income of ₹20. Let the price of Good 1 be ₹4 per unit and the price of Good 2 be ₹5 per unit. Then the budget constraint is:

$4x_1 + 5x_2 \leq 20$ …