A household budget constraint is the limit on spending set by income and prices. Anything the household can afford lies on or within it. This lesson shows how to read one, calculate its end points, and describe what changes when income or a price changes, inside money, banking and households.
How do income and prices set the limit?
Suppose a household spends all of its income on two goods, X and Y. If it spends everything on X, it buys income ÷ price of X. If it spends everything on Y, it buys income ÷ price of Y. Those two quantities are the end points of the budget line.
Every affordable mix lies between them.
The budget line also shows opportunity cost. Choosing more X means giving up some Y, because the same income cannot be spent twice.
Worked example: the Tan household
The Tan household in a fictional town has RM240 to spend this week on notebooks (X) at RM8 each and snacks (Y) at RM6 each.
Step 1, end points. All on notebooks: 240 ÷ 8 = 30. All on snacks: 240 ÷ 6 = 40.
Step 2, one affordable mix. Buy 15 notebooks: 15 × 8 = RM120. The remaining RM120 buys 120 ÷ 6 = 20 snacks. Check: 120 + 120 = RM240, so the income is used exactly.
Step 3, opportunity cost. Giving up RM8 for one notebook means 8 ÷ 6 = 1.33 fewer snacks. In exact terms, 3 more notebooks cost RM24, which is 4 snacks.
Step 4, income rises. Income rises to RM300 with the same prices. End points become 300 ÷ 8 = 37.5 notebooks and 300 ÷ 6 = 50 snacks. Both end points rise, so the line moves outward.
Step 5, a price falls. Back at RM240, suppose the notebook price falls to RM6. All on notebooks becomes 240 ÷ 6 = 40. All on snacks is still 40, because the snack price and income have not changed.
| Case | Notebooks if all spent | Snacks if all spent |
|---|---|---|
| Start (RM240, RM8, RM6) | 30 | 40 |
| Income RM300 | 37.5 | 50 |
| Notebook price RM6 | 40 | 40 |
In the last case only one end point changes, so the line pivots rather than shifting in parallel.
The mistake to watch for
Mistaken answer: “When the notebook price falls, the whole budget line shifts outward.”
Only the notebook end point changes. The snack end point stays at 40.
The correction is to calculate both end points every time. If income changes, both end points change by the same proportion, so the line shifts. If one price changes, only that good’s end point changes, so the line pivots. Quote the figures to prove it.
A second slip is to forget that the line is a limit. A point beyond the line is unaffordable at the stated income, even if it looks attractive.
Check yourself
1. A student has RM90 to spend on drinks at RM3 and sandwiches at RM5. Find both end points.
Show answer
All on drinks: 90 ÷ 3 = 30. All on sandwiches: 90 ÷ 5 = 18.
2. She buys 10 drinks. How many sandwiches can she afford with the remaining money?
Show answer
Drinks cost 10 × 3 = RM30. Remaining = 90 − 30 = RM60. Sandwiches = 60 ÷ 5 = 12.
3. Her income falls to RM60 with the same prices. State the new end points and whether the line shifts or pivots.
Show answer
Drinks: 60 ÷ 3 = 20. Sandwiches: 60 ÷ 5 = 12. Both end points fall, so the line shifts inward.
Where this leads next
The final lesson applies this thinking to borrowing: a change in borrowing incentives from stated facts. For arithmetic support, the percentage-base explorer helps with income changes expressed as percentages. The module’s mixed practice set revisits budget lines.
Seeing why a line shifts or pivots is easier with someone asking you questions, which is how online one-to-one Economics tuition can help.