ECON1101 Chap.4 Budget Constraints and the Best Bundle
Budget Constraints and the Best Bundle
Budget Constraints and the Best Bundle extends consumer choice to two goods. The budget line’s intercepts come from income divided by each price and its slope is the price ratio, the opportunity cost of one good in units of the other. The best affordable bundle spends all income and equalises marginal utility per dollar across goods.
The chapter then traces how a price change pivots the line and splits into substitution and income effects, and how an income change shifts it and reveals normal and inferior goods. Every result is checked against the consumer equilibrium condition, which the course states as a theorem and uses in tutorials and multiple-choice items alike.
What this chapter covers
- 01
Bundles and the budget constraint
- 02
Intercepts, slope and opportunity cost
- 03
Feasible, optimal and unaffordable bundles
- 04
Equal marginal utility per dollar
- 05
Substitution and income effects
- 06
Normal and inferior goods from an income change
Worked example · free
Pat’s budget line before and after a book price rise
- 1Movie intercept = 96/8 = 12 tickets in both cases, since the ticket price is unchanged.
- 1Book intercept = 96/12 = 8 at $12 and 96/16 = 6 at $16; slopes −12/8 = −1.5 and −16/8 = −2.
- 1The line pivots inward around the movie intercept, so (4, 6), which cost exactly $96, is now out of reach.
- 1At the new price (4, 6) costs 4 × 16 + 6 × 8 = $112, so Pat needs $16 more.
Key terms
- Budget constraint
- The budget constraint is the set of bundles that cost exactly the consumer’s income at current prices.
- Consumer equilibrium condition
- The consumer equilibrium condition requires equal marginal utility per dollar across goods and full spending of income.
- Substitution effect
- The substitution effect is the shift in purchases away from a good that has become relatively more expensive.
- Income effect
- The income effect is the change in purchases caused by the change in real income that follows a price change.
- Feasible set
- The feasible set is every bundle the consumer can afford, on or inside the budget line.
Budget Constraints and the Best Bundle FAQ
What does the slope of the budget line mean?
It is the price ratio with a minus sign, and it tells you how many units of the vertical-axis good must be given up to buy one more unit of the horizontal-axis good: the opportunity cost set by market prices.
Why is equal marginal utility per dollar the rule rather than equal marginal utility?
Goods cost different amounts. A dollar moved from a good with a low ratio to one with a high ratio buys more utility, so the best bundle is reached only when the last dollar spent on each good brings the same return.
How do the income and substitution effects differ for normal and inferior goods?
For a normal good both effects reduce purchases after a price rise, so they reinforce each other. For an inferior good the income effect pushes purchases up while the substitution effect pushes them down, so they work against each other.
What happens to the budget line when income changes?
Both intercepts move in proportion to income and the slope stays the same, because relative prices have not changed. More income shifts the line outward in parallel; less income shifts it inward.
Why is a bundle inside the budget line never the best choice?
The course assumes wants are unlimited, so leaving money unspent always forgoes some extra utility. Any bundle inside the line can be improved by buying more of at least one good, which means the best affordable bundle must lie on the line itself.
How do I spot the substitution and income effects in a numerical answer?
Check whether the old bundle is still affordable at the new prices; if not, real income has fallen, the income effect. Then compare marginal utility per dollar at the old bundle using the new prices; the good with the lower ratio is substituted away from, the substitution effect.
Exam move
Practise the full table method once a day for a week: intercepts, affordable whole bundles, total utilities, the best bundle and the two-part check. Then redo the same consumer after a price rise and after an income rise, and write one sentence naming the substitution effect and one naming the income effect.
Multiple-choice reallocation items are quick wins: compare marginal utility per dollar and move spending toward the higher ratio. When a table is given, cross out bundles that do not spend the full budget before adding any utilities, which halves the arithmetic and removes the commonest wrong answers.
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