Consumer Behaviour

Lessons

Senior 4 · Economics

Consumer Behaviour

4 lessons

Lesson 2 of 4

The budget line and how it moves

25 min

Frw 1,535 a day

The National Institute of Statistics of Rwanda measures poverty by asking what it costs to live at a minimum standard. In its Seventh Integrated Household Living Conditions Survey (EICV7, carried out in 2023–24 and published in 2025), the total poverty line is Frw 560,127 per adult equivalent per year, in January 2024 prices: about Frw 1,535 a day. Of this, Frw 356,432 is the food poverty line, the cost of 2,400 kilocalories a day. By this measure 27.4% of Rwandans were poor in 2024.

A family living on such a budget makes hard choices every day: one more kilogram of beans means less of something else. Lesson 1 measured what a consumer wants. This lesson draws what a consumer can afford: the budget line.

Definition

Budget constraint: the limit that income and prices place on what a consumer can buy: spending cannot exceed income.

Budget line (price line, or consumption possibility line): a line showing every combination of two goods that a consumer can buy when all income is spent at given prices.

Budget set (attainable set): every combination on or below the budget line.

Notation: $M$ is money income; $P_{x}$ and $P_{y}$ are the prices of goods X and Y; $X$ and $Y$ are the quantities bought.

1. The equation of the budget line

Mugabo's household has Frw 12,000 a week for two staples: beans (X) at Frw 1,000 per kg and maize flour (Y) at Frw 500 per kg (illustrative prices). Spending on beans plus spending on flour cannot exceed income:

P_x X + P_y Y \le M \qquad\Rightarrow\qquad 1{,}000X + 500Y \le 12{,}000

When all income is spent, this becomes an equality: the budget line. Rearranged for Y:

Y = \frac{M}{P_y} - \frac{P_x}{P_y}X \qquad\Rightarrow\qquad Y = 24 - 2X

Feature	Formula	Mugabo's line	Meaning
Y-intercept	$\frac{M}{P_y}$	$\frac{12{,}000}{500} = 24$ kg	All income spent on flour
X-intercept	$\frac{M}{P_x}$	$\frac{12{,}000}{1{,}000} = 12$ kg	All income spent on beans
Slope	$-\frac{P_x}{P_y}$	$-\frac{1{,}000}{500} = -2$	Each extra kg of beans costs 2 kg of flour

Reading the diagram. The slope is the relative price of the two goods, and it is also an opportunity cost: to buy one more kilogram of beans, Mugabo must give up 2 kg of flour. Every point in the shaded budget set can be bought; points beyond the line cannot, however much they are wanted.

Worked example 1: testing bundles against the budget

With $M = 12,000$ , $P_x = 1{,}000$ and $P_{y} = 500$ , can Mugabo buy (a) 5 kg of beans and 12 kg of flour; (b) 7 kg of beans and 12 kg of flour?

(a) Cost $= 1{,}000(5) + 500(12) = 5{,}000 + 6{,}000 = 11{,}000 \le 12{,}000$ . Affordable, with Frw 1,000 left: the point lies inside the line.

(b) Cost $= 1,000 (7) + 500 (12) = 7,000 + 6,000 = 13,000 > 12,000$ . Not affordable: the point lies outside. Check with the equation: at $X = 7$ the line gives $Y = 24 - 2 (7) = 10$ , so 12 kg of flour is 2 kg too many.

2. How changes in income and prices move the line

Because the intercepts are $\frac{M}{P_x}$ and $\frac{M}{P_y}$ and the slope is $-\frac{P_x}{P_y}$ , each change has its own signature.

A change in income, prices unchanged: both intercepts change in the same proportion and the slope does not. The line shifts parallel: outwards when income rises, inwards when it falls.
A change in the price of one good: only that good's intercept moves. The line pivots about the other intercept: outwards when the price falls, inwards when it rises. The slope changes.
Both prices change in the same proportion: the slope is unchanged and the line shifts parallel, exactly as if income had changed the other way. Doubling both prices has the same effect as halving income.
Income and both prices change in the same proportion: nothing changes. If all three double, $\frac{2M}{2P_x} = \frac{M}{P_x}$ : the consumer's real income is the same.

Reading the diagrams. In (a) the three lines are parallel, all with slope −2: income changed and relative prices did not. In (b) every line starts from 24 kg of flour, because a change in the price of beans does not change how much flour Frw 12,000 can buy.

Worked example 2: a rise in food prices at the poverty line

Use NISR's EICV7 figures: a total poverty line of Frw 560,127 per adult equivalent per year, of which Frw 356,432 is food.

(a) Share of food. $\frac{356{,}432}{560{,}127} \times 100\% \approx 63.6\%$ . Non-food is $560,127 - 356,432 = 203,695$ francs a year.

(b) Food prices rise by 10%, income does not. The same food now costs $356{,}432 \times 1.10 = 392{,}075.2 \approx 392{,}075$ francs, an extra Frw 35,643. To keep eating the same food, the household must cut non-food spending to $203,695 - 35,643 = 168,052$ francs, a fall of $\frac{35{,}643}{203{,}695} \times 100\% \approx 17.5\%$ .

(c) On the diagram. With food on the X-axis, the budget line pivots inwards about the non-food intercept. Because food takes almost two-thirds of the budget, a 10% rise in food prices costs a poor household far more than the same rise costs a rich household whose food share is small.

Warning

Get the slope the right way up. The slope is $-\frac{P_x}{P_y}$ , with the price of the good on the horizontal axis on top. Writing $-\frac{P_y}{P_x}$ is the commonest error in this topic. And remember: income moves the line parallel; one price pivots it.

Tip

"Intercept = income ÷ own price." Find the two intercepts first, join them, and the slope follows. To see what a change does, recompute only the intercepts.

Important

Discuss. To help a poor household, a government could give it Frw 5,000 in cash or a Frw 5,000 voucher that can only be spent on food. Sketch the budget line in each case (food on the X-axis). Which would the household prefer, and does your answer depend on how much it already spends on food?

Ashley Hodgson, "Budget Constraints: Shift, Rotate and Kink". Watch for the parallel shift when income changes and the rotation when one price changes, and compare them with diagrams (a) and (b) above. The final part, on kinked budget lines, goes beyond this lesson.

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Practice

Define the budget line and the budget set, and write the general equation of the budget line.
A student has Frw 9,000 to spend on X at Frw 300 and Y at Frw 450. Find the two intercepts, the slope, and the equation of the budget line in the form $Y = a + b X$ .
With the budget in question 2, can the student buy (a) 15 X and 10 Y; (b) 18 X and 9 Y? Show your working.
Starting from question 2, state and sketch the effect on the budget line of: (a) income rising to Frw 12,000; (b) the price of X rising to Frw 450; (c) income and both prices doubling.
A budget line meets the X-axis at 50 units and the Y-axis at 25 units, and income is Frw 10,000. Find $P_{x}$ , $P_{y}$ and the slope.
Explain why the slope of the budget line is an opportunity cost.
Using the EICV7 poverty line (Frw 560,127 a year, of which Frw 356,432 is food), find the daily food budget and the daily non-food budget, to the nearest franc.
A poor household is offered Frw 5,000 in cash or a Frw 5,000 food voucher that cannot be resold. Using budget lines, explain when it would prefer the cash.

Show answersHide answers

The budget line shows every combination of two goods that can be bought with all income at given prices; the budget set is every combination on or below it. $P_{x} X + P_{y} Y = M$ .
X-intercept $\frac{9{,}000}{300} = 30$ ; Y-intercept $\frac{9{,}000}{450} = 20$ ; slope $-\frac{300}{450} = -\frac{2}{3}$ ; $Y = 20 - \frac{2}{3}X$ .
(a) $300 (15) + 450 (10) = 4,500 + 4,500 = 9,000$ : affordable, on the line. (b) $300 (18) + 450 (9) = 5,400 + 4,050 = 9,450 > 9,000$ : not affordable.
(a) Parallel outward shift: intercepts 40 and $\frac{12{,}000}{450} \approx 26.7$ . (b) Pivot inwards about the Y-intercept: the X-intercept falls to 20, Y stays 20, slope becomes −1. (c) No change.
$P_x = \frac{10{,}000}{50} = 200$ ; $P_y = \frac{10{,}000}{25} = 400$ ; slope $= -\frac{200}{400} = -0.5$ .
The slope $-\frac{P_x}{P_y}$ tells how many units of Y must be given up to buy one more unit of X with the same income: the next best alternative forgone.
Food: $\frac{356{,}432}{365} \approx 977$ francs a day. Non-food: $\frac{203{,}695}{365} \approx 558$ francs a day.
Cash shifts the whole line out in parallel. The voucher shifts it out too, but the top part is flat: the household cannot have more non-food goods than before. If it wants to spend at least Frw 5,000 on food anyway, both give the same choices; if it would rather spend less than that on food, only cash lets it, so it prefers cash.

Quick check

Key points

The budget line $P_{x} X + P_{y} Y = M$ shows what a consumer can afford; its intercepts are $\frac{M}{P_x}$ and $\frac{M}{P_y}$ .
Its slope $-\frac{P_x}{P_y}$ is the relative price, the opportunity cost of X in terms of Y.
A change in income shifts the line parallel; a change in one price pivots it about the other intercept.
Equal proportional changes in income and all prices leave it unchanged.

Sources and credits

Poverty lines and poverty rate: EICV7 Poverty Profile, Thematic Report, National Institute of Statistics of Rwanda (NISR), 2025. Daily figures, shares and the price-rise example calculated by Ganzaa.
Photo: Kigali City Supermarket 2024, Uwasegrace, Wikimedia Commons, CC BY-SA 4.0.
Video: Budget Constraints: Shift, Rotate and Kink, Ashley Hodgson, embedded from YouTube.

Written by Ganzaa: the text, the budget-line diagrams (drawn to scale from the equations), the tables, the worked examples and the practice items. The prices of beans and flour are illustrative.

This lesson adapts CC BY-SA material and is shared under CC BY-SA 4.0.

1Frw 1,535 a day

21. The equation of the budget line

32. How changes in income and prices move the line

Frw 1,535 a day

1. The equation of the budget line

2. How changes in income and prices move the line