How to Calculate a Budget Constraint
A budget constraint is every bundle whose cost equals income: PxQx + PyQy = Income, and its slope is −Px ÷ Py.
The Budget Constraint formula
Calculator
Enter income and both prices to get the two intercepts, the slope, and whether a bundle sits on the line.
Everything available to spend. The worked example uses $60.
Books at $12 in the worked example. X goes on the horizontal axis.
Coffee at $4 in the worked example. Y goes on the vertical axis.
A bundle you want to check against the line.
The other half of that bundle.
The line falls at 3 units of Y per unit of X, so one more X costs 3 units of Y.
- Most of good X the income buys
- 5
- Most of good Y the income buys
- 15
- Cost of the bundle
- $60
- Where the bundle sits
- On the budget line
Income ÷ Px puts the horizontal intercept at 5 units of X, with nothing left for Y.
Income ÷ Py puts the vertical intercept at 15 units of Y.
The bundle costs $60 against an income of $60.
The bundle spends income exactly, which is where the optimal choice always sits.
How to calculate Budget Constraint, step by step
- 1Write the budget equation. PxQx + PyQy = Income, covering every combination that spends exactly all the money available.
- 2Find the two intercepts. Income ÷ Px is the most x the consumer can buy, and Income ÷ Py is the most y.
- 3Compute the slope. Slope = −Px ÷ Py, the units of y that must be given up to buy one more unit of x.
- 4Plot or test a bundle. Connect the intercepts with a straight line; any bundle costing exactly the income sits on it, and cheaper bundles sit inside it.
Worked example: Budget Constraint
With $60 of income, books at $12 and coffee at $4, the intercepts are 60 ÷ 12 = 5 books or 60 ÷ 4 = 15 coffees. The slope is −12 ÷ 4 = −3, so each extra book costs 3 coffees. The bundle of 3 books and 6 coffees costs (3 × $12) + (6 × $4) = $36 + $24 = $60, so it sits exactly on the constraint.
Budget Constraint questions
What happens to the budget line when income rises?
The line shifts outward parallel to the original, because both intercepts grow by the same proportion while the price ratio and the slope stay unchanged.
What happens when only one price changes?
The line pivots: the intercept for that good moves while the other intercept stays fixed, so the slope changes. A lower Px swings the x intercept outward.
What do points inside and outside the line mean?
Points inside the line are affordable but leave income unspent, and points outside cost more than income, so they are unattainable. The optimal bundle always sits on the line itself.
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