Budget Line
What is Budget Line?
A budget line shows every combination of two goods a consumer can buy by spending all income, with slope equal to minus the price ratio, -Px/Py.
A budget line plots the bundles of two goods that exactly exhaust a consumer's income at given prices. Its equation is Px·X + Py·Y = I, so the horizontal intercept is I/Px, the vertical intercept is I/Py, and the slope is negative Px/Py, the rate at which the market lets you trade one good for the other. A change in income shifts the line parallel to itself, outward if income rises and inward if it falls, because both intercepts scale but the price ratio does not change. A change in one price rotates the line around the intercept of the other good, since only that good's intercept moves. The budget line is the constraint, not the preference; indifference curves carry the preferences, and the best affordable bundle sits where an indifference curve is tangent to the budget line.
Budget Line: a worked example
Suppose Maya has $60 a week, pizza costs $6, and a soda costs $2. All $60 on pizza buys 10 pizzas ($60/$6); all $60 on soda buys 30 sodas ($60/$2), so the slope is -3 and each pizza costs her 3 sodas. If her income rises to $90, the intercepts become 15 pizzas and 45 sodas while the slope stays -3, so the line shifts out parallel. If instead income stays at $60 and pizza falls to $3, the pizza intercept moves to 20, the soda intercept stays at 30, and the line rotates outward with a flatter slope of -1.5.
The mistake students make with budget line
Students often say a price cut shifts the whole budget line outward. It does not: only the intercept of the good whose price fell moves, so the line rotates and its slope changes. A parallel shift comes only from a change in income (or from all prices changing in the same proportion). Watch the direction too; a price increase rotates the line inward around the other good's intercept.
Budget Line questions
What is the slope of a budget line?
The slope of a budget line is negative Px/Py, the price of the good on the horizontal axis divided by the price of the good on the vertical axis, made negative. It tells you how many units of the vertical good you must give up to buy one more unit of the horizontal good. Because prices are fixed for the consumer, the line is straight.
Does a budget line shift or rotate when income changes?
A change in income shifts the budget line parallel to the original; it does not rotate the line. Both intercepts move by the same percentage, so the price ratio and therefore the slope stay the same. Higher income shifts it outward; lower income shifts it inward.
What is the difference between a budget line and an indifference curve?
A budget line shows what a consumer can afford, while an indifference curve shows what a consumer equally likes. The budget line comes from prices and income; the indifference curve comes from preferences. The optimal bundle is where the highest reachable indifference curve just touches the budget line.
Formula / Example
Related terms
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