Budget Constraints and Feasible Choices

Preferences describe what a consumer wants. A budget constraint describes what the consumer can afford. Choice occurs where these two parts meet.

Suppose income is $I$, good X costs $P_x$, and good Y costs $P_y$. A basket $(X,Y)$ is feasible when

The budget line contains baskets that use all income:

Baskets below or inside the line leave some income unspent. Baskets beyond it are unattainable at current prices and income.

Intercepts and slope

If all income is spent on X, the consumer can buy $I/P_x$ units. If all is spent on Y, the intercept is $I/P_y$. Solving for Y gives

With X on the horizontal axis, the slope is $-P_x/P_y$. Its absolute value is the market opportunity cost of one more X: the number of Y units that must be given up.

For example, a learner has 60 to divide between 12-unit meals and 6-unit metro rides. The line is $12M+6R=60$, with intercepts 5 meals and 10 rides. One extra meal costs the same as two rides, so the slope is $-2$ when meals are horizontal.

How income and prices move the line

If income rises while prices stay fixed, both intercepts increase proportionally. The line shifts outward in parallel; relative prices and slope do not change.

If only the price of X falls, the X intercept moves outward while the Y intercept stays fixed. The line rotates around the Y intercept and becomes flatter in absolute value. Some previously unaffordable baskets become feasible. A price change therefore alters both purchasing power and the relative tradeoff between goods.

Several complications matter in real budgets. Bulk discounts create kinks, transit passes create fixed fees, borrowing can extend today's choices while restricting future choices, and time can be a second constraint. The straight line is a useful baseline, not a claim that every opportunity set is perfectly linear.

Choosing on the budget line

If both goods are desirable and can be freely purchased, an optimum usually uses the full budget. But the budget alone cannot identify the chosen point: many baskets are affordable. Preferences determine which feasible basket ranks highest. The next lessons build the marginal reasoning needed to find it.

Test a basket instead of guessing

With income 60, meals costing 12, and rides costing 6, test basket $(M,R)=(2,6)$ by substitution:

It lies exactly on the budget line. Basket $(3,5)$ costs 66 and is unattainable. Basket $(1,6)$ costs 48 and is feasible but leaves 12 unspent. This direct substitution is often safer than judging a point by eye.

Read the slope as an exchange rate

One meal costs the same as two rides. Moving right by one meal along the budget line therefore requires moving down by two rides. The slope $-2$ is not a preference: it is the tradeoff offered by the market. Preferences tell us whether the consumer wants to make that trade.

When ride price falls from 6 to 4, the ride intercept rises from 10 to 15 while the meal intercept remains 5. The line pivots outward. By contrast, an income increase raises both intercepts and shifts the line outward in parallel.

Budget lines answer only “can”

An affordable basket is not automatically chosen. The consumer still compares feasible baskets using preferences. A basket inside the line can be optimal when saving is valuable or goods become undesirable after satiation; the common “spend everything” conclusion needs the assumption that more of at least one available good is preferred.