Difficulty: Introductory | Prerequisites: Basic algebra (solving for x, plotting straight lines on a graph). Familiarity with the concept of scarcity and trade-offs is helpful but not required.
Budget lines are one of the first tools in consumer theory. They show every combination of two goods a consumer can afford at given prices and income. Understanding how budget lines shift when prices or income change is the foundation for predicting how people adjust their spending. If you can draw and interpret a budget line, you can layer on indifference curves later to find the consumer's optimal choice, and that pairing drives most of the analysis in introductory microeconomics.
A budget line plots all the bundles of two goods a consumer can buy with a fixed income. Its slope equals the negative ratio of the goods' prices. When income falls or a price rises, the line shifts inward, shrinking what the consumer can afford; when income rises or a price falls, it shifts outward.
Budget line (budget constraint)
The set of all bundles of two goods that exactly exhaust a consumer's income at current prices. Graphically, it is a straight line whose intercepts are income divided by each good's price.
In simple terms, it is the boundary of what you can afford. Anything on or below the line is within reach; anything above it is not.
Slope of the budget line
The negative of the price ratio: –(Px / Py), where good X is on the horizontal axis and good Y on the vertical axis. It tells you how many units of Y you must give up to get one more unit of X.
Think of it as the market's exchange rate between the two goods.
Absolute price
The price of a good stated in money terms (e.g. £10 per unit of shelter). This is the number on the price tag.
Relative price
The price of one good expressed in units of another good, i.e. the ratio Px / Py. It determines the slope of the budget line, regardless of the actual pound figures.
In simple terms, it answers: "How many units of Y does one unit of X cost me?"
Budget set (feasible set)
All bundles on or below the budget line. These are the combinations the consumer can actually purchase.
Indifference curve
A curve showing all bundles of two goods that give the consumer the same level of satisfaction (utility). The consumer is indifferent among every point on the same curve.
Think of it as a contour line on a satisfaction map.
Optimal bundle (optimal market basket)
The bundle the consumer chooses: the point where the highest attainable indifference curve is tangent to the budget line. At that point the marginal rate of substitution equals the price ratio.
Income effect (of a recession)
The change in consumption that results purely from a change in real purchasing power, with the price ratio held constant. A recession shrinks income, shifting the budget line inward and, for normal goods, reducing quantities consumed.
Start with the budget equation: I = Px · X + Py · Y, where I is income, Px is the price of food (horizontal axis), Py is the price of shelter (vertical axis).
Find the intercepts:
Vertical intercept (all income spent on shelter): I / Py
Horizontal intercept (all income spent on food): I / Px
Connect the intercepts with a straight line. Every point on that line exhausts the budget exactly.
Worked example from the assignment (scenario a):
Income = $500, price of shelter Py = $10, slope = –5
Slope = –(Px / Py), so –5 = –(Px / 10), giving Px = $50
Vertical intercept = 500 / 10 = 50 units of shelter
Horizontal intercept = 500 / 50 = 10 units of food
The budget line runs from (0, 50) to (10, 0)
Scenario (b): Both prices double (Px → $100, Py → $20), income unchanged at $500
New vertical intercept: 500 / 20 = 25
New horizontal intercept: 500 / 100 = 5
The budget line shifts inward (parallel). The slope stays at –5 because the price ratio Px / Py is unchanged. The consumer can afford less of everything, but the trade-off rate between the two goods is the same.
Key insight: doubling all prices with income fixed is identical in effect to halving income with prices fixed.
Scenario (c): Absolute price of food unchanged ($50), but its relative price doubles
Relative price doubling means Px / Py doubles: from 5 to 10. Since Px stays at $50, Py must fall to $5.
New vertical intercept: 500 / 5 = 100
Horizontal intercept: 500 / 50 = 10 (unchanged)
The budget line pivots outward on the food axis. The consumer can now buy far more shelter, but the same amount of food. The slope steepens to –10.
Key insight: a change in relative price pivots the budget line around the intercept of the good whose absolute price has not changed.
Scenario (d): Absolute price of food halved ($50 → $25), shelter price unchanged ($10)
New horizontal intercept: 500 / 25 = 20
Vertical intercept: 500 / 10 = 50 (unchanged)
The budget line pivots outward on the food axis, fanning out from (0, 50) to (20, 0). Slope changes from –5 to –(25/10) = –2.5.
Key insight: a fall in one good's price rotates the line outward around the other good's intercept, expanding the feasible set.
During a recession consumers typically lose income (job losses, reduced hours, falling asset values). In the budget-line framework:
The budget line shifts inward in a parallel fashion when income drops and prices remain roughly constant. The slope stays the same because the price ratio has not changed, but both intercepts shrink.
The consumer's previous optimal bundle now lies outside the new, smaller budget set. They can no longer afford it.
The new optimum sits on a lower indifference curve, meaning less utility (satisfaction). For normal goods, the consumer buys less of most things.
If some prices also fall during the recession (deflation), the line may pivot rather than shift purely in parallel, but the dominant effect of a large income drop is still a contraction of the feasible set.
This is the theory behind the observation that recessions cause consumers to cut back broadly: the budget line has moved inward, and the best attainable indifference curve has dropped.
I = P_X \cdot X + P_Y \cdot YRearranged for Y (the vertical axis):
Y = \frac{I}{P_Y} - \frac{P_X}{P_Y} \cdot XVertical intercept = I / Py
Horizontal intercept = I / Px
Slope = –(Px / Py)
Diagram checklist for exam answers:
Label both axes with the good names.
Mark the intercepts with their numerical values.
Write the slope on or near the line.
When drawing multiple budget lines on the same graph, label each clearly (a, b, c, d) and note which parameter changed.
Budget lines describe the same trade-off people face every day: a fixed pay cheque and a choice between rent, groceries, transport, and everything else. When petrol prices spike, the budget line pivots inward on the petrol axis, and drivers either cut mileage or spend less elsewhere. During the 2008 – 09 recession, falling household incomes shifted budget lines inward across the board, which is exactly why retail spending, restaurant visits, and discretionary purchases all dropped at the same time.
Students often confuse a parallel shift with a pivot. A parallel shift happens when income changes (or all prices change proportionally). A pivot happens when only one good's price changes, rotating the line around the intercept of the good whose price stayed the same.
Students sometimes think doubling all prices makes the consumer worse off in a different way than halving income. The two are mathematically identical: both halve the intercepts and leave the slope unchanged.
A steeper budget line does not always mean the consumer is worse off. It means food is relatively more expensive, but if income or the other price changed favourably at the same time, the budget set could still be larger.
Students mix up absolute and relative price. A good's absolute price can stay fixed while its relative price changes, if the other good's price moves. Scenario (c) in the assignment is a direct test of this distinction.
⚠️ You will almost certainly be asked to draw a budget line from given prices and income, then show how it changes when one parameter shifts. Practise until you can do it quickly.
⚠️ The distinction between a parallel shift and a pivot is a classic exam question. Know which parameter change produces which.
⚠️ Explaining a recession in terms of budget lines and indifference curves is a common short-answer or essay prompt. Be ready to connect "income falls" to "budget line shifts inward" to "lower indifference curve" to "less consumption."
⚠️ Scenario (c), where absolute price stays constant but relative price changes, is a conceptual trap. Make sure you can explain how Py must change to double the relative price of food while Px stays fixed.
True or False: Doubling both prices while holding income constant shifts the budget line inward but does not change its slope.
True or False: If only the price of the good on the horizontal axis falls, the budget line pivots outward around the vertical intercept.
Fill in the blank: The slope of the budget line equals –(_____ / _____).
True or False: A consumer whose income drops but faces unchanged prices will move to a higher indifference curve.
Fill in the blank: The horizontal intercept of a budget line equals _____ / _____.
Q: A consumer has income of $500, the price of food is $50, and the price of shelter is $10. What are the intercepts and slope of the budget line?
A: Horizontal intercept = 500/50 = 10 units of food. Vertical intercept = 500/10 = 50 units of shelter. Slope = –(50/10) = –5.
Q: Starting from the budget line above, both prices double. Describe what happens to the line.
A: Both intercepts halve (food intercept becomes 5, shelter intercept becomes 25). The line shifts inward in parallel. The slope remains –5 because the price ratio is unchanged.
Q: If the absolute price of food stays at $50 but its relative price doubles, what must have happened to the price of shelter?
A: Relative price = Px/Py. Originally 50/10 = 5. Doubling it to 10 with Px fixed at 50 means Py must have fallen to $5.
Q: During a recession, a consumer's income falls while prices stay constant. Using a budget-line and indifference-curve diagram, explain why the consumer buys less of most goods.
A: The budget line shifts inward in parallel (same slope, both intercepts smaller). The consumer's old optimal bundle is now outside the feasible set. The new tangency with the highest attainable indifference curve sits on a lower curve, so the consumer reaches less utility and, for normal goods, buys smaller quantities of both.
Q: What is the difference between a parallel shift and a pivot of the budget line?
A: A parallel shift occurs when income changes (or all prices change by the same proportion), moving both intercepts by the same factor without changing the slope. A pivot occurs when one good's price changes while the other's stays fixed, rotating the line around the intercept of the unchanged good.
This material connects directly to indifference curve analysis and the theory of consumer choice, where the budget line meets preferences to determine the optimal bundle. It also sets up the income and substitution effects you will study when decomposing a price change (Slutsky decomposition). The recession discussion links to macroeconomic concepts of aggregate demand: when millions of budget lines shift inward simultaneously, total spending in the economy falls.
Budget constraint, budget line equation, price ratio, feasible set, consumption bundle, income change budget line, price change budget line, parallel shift vs pivot, indifference curve tangency, optimal consumption bundle, recession consumer behaviour, real income, purchasing power, slope of budget constraint, intercepts of budget line, Intro to Microeconomics NYU, consumer theory basics