7.2 Indifference curves and budget lines
- Syllabus
- 9708–2026–2027
- Topic
- 7.2
- Level
- A2
Learning objectives
7.2.1Indifference curves and budget lines• Meaning of an indifference curve and a budget line7.2.2Budget line shifts• Causes of a shift in the budget line7.2.3Income, substitution and price effects• Income, substitution and price effects for normal, inferior and Giffen goods7.2.4Limits of indifference curve model• Limitations of the model of indifference curves
Preferences meet affordability at consumer equilibrium
| Representation | What it shows | Key geometry |
|---|---|---|
| Indifference curve (IC) | Bundles of X and Y giving equal total satisfaction | Usually downward sloping and convex; slope is the marginal rate of substitution (MRS); higher non-crossing curves represent greater satisfaction |
| Budget line | Bundles exhausting money income at given prices | PxX+PyY=M; intercepts are M/Px and M/Py; slope magnitude is Px/Py |
Points on or inside the budget line are affordable; points outside are unattainable. A point inside leaves income unspent. For a consumer who prefers more to less, the best affordable bundle lies on the budget line.
Consumer equilibrium is the highest attainable indifference curve. For a smooth interior solution, its tangency with the budget line satisfies MRSxy = Px/Py: the consumer's willingness to trade X for Y equals the market trade-off.
Convexity reflects diminishing MRS: as a consumer has more X and less Y, they normally surrender progressively less Y for another unit of X. Perfect substitutes can produce straight ICs and perfect complements right-angled ICs.
An IC is not a demand curve, and a budget line does not show what the consumer wants. Preference and affordability must be combined; tangency is not required at a corner solution.
Income shifts a budget line; one price rotates it
Use PxX+PyY=M. Recalculate the X-intercept M/Px, Y-intercept M/Py and slope −Px/Py; the intercept that changes identifies the movement.
| Change | Budget-line effect |
|---|---|
| Money income rises/falls; prices fixed | Parallel outward/inward shift; slope unchanged |
| Price of X falls/rises; M and Py fixed | X-intercept rotates outward/inward around unchanged Y-intercept |
| Price of Y falls/rises; M and Px fixed | Y-intercept rotates outward/inward around unchanged X-intercept |
| Both prices rise by same percentage; M fixed | Parallel inward shift |
| M and both prices change by same percentage | Real purchasing power and budget line unchanged |
With 60,Px=10 and Py = 5,interceptsare6Xand12Y.IfPxrisesto15, the X-intercept falls to 4 while the Y-intercept remains 12: the line rotates inward and becomes steeper in absolute value when X is horizontal.
Income tax or wages can change disposable income and shift the line. Product taxes change prices. Preferences, advertising or product quality can change the chosen point or IC map, but not the budget line itself.
A new budget line alone does not determine the final bundle; preferences are still needed. Always name the axes before calling a line steeper or flatter.
Split a price effect into substitution and income effects
The price effect is the total change in quantity demanded after an own-price change. The substitution effect is the change caused by altered relative prices at constant satisfaction; the income effect is the remaining change caused by altered real purchasing power, not money income.
For a fall in Px: (1) mark initial equilibrium A; (2) rotate the budget line outward on the X-axis and mark final equilibrium C; (3) draw a compensated line parallel to the new line but tangent to the original IC at B. A→B is substitution; B→C is income; A→C is the price effect.
| Good when Px falls | Substitution effect on X | Income effect on X | Price effect on X | Demand implication |
|---|---|---|---|---|
| Normal | More X | More X | More X | Downward sloping |
| Inferior, non-Giffen | More X | Less X, smaller | More X overall | Downward sloping, often steeper |
| Giffen | More X | Less X, larger | Less X overall | Upward sloping over the relevant range |
For a price rise, reverse every direction. The substitution effect always moves away from the relatively dearer good. The income effect is positive for a normal good and negative for an inferior good; only when the opposing inferior income effect outweighs substitution is the good Giffen.
Repeat the final equilibrium for several prices to form a price-consumption path, then plot each own-price/quantity pair to derive individual demand. A price change cannot by itself reveal whether downward-demand X is normal or inferior because both can buy more after a fall.
Every Giffen good is inferior, but most inferior goods are not Giffen. Do not call an ordinary negative income effect Giffen unless it is larger than the substitution effect.
Indifference curves are a conditional model of rational choice
Indifference-curve analysis ranks bundles ordinally, so it does not require measurable utils. It separates preferences from a real budget constraint and can explain ordinary, inferior and Giffen responses—but only under restrictive assumptions.
| Assumption | Predictive limitation |
|---|---|
| Rational satisfaction maximisation with perfect information | Habit, loyalty, advertising, uncertainty and bounded rationality can move choice away from the calculated optimum |
| Complete preferences: every bundle can be ranked | Consumers may be unable to compare complex or unfamiliar bundles |
| Transitive, stable preferences | Cycles or changing tastes make a consistent non-crossing IC map impossible or temporary |
| More is preferred to less and MRS diminishes | Bads, satiation, addiction, perfect substitutes/complements can give different curve shapes |
| Divisible, substitutable goods in a two-good world | Houses, journeys, complements and many simultaneous goods do not fit smooth two-good trade-offs |
| Income and relevant prices known; other influences fixed | Real markets change several conditions at once, so static ceteris-paribus predictions may fail |
A limited income is realistic, but that does not validate rationality or stable preferences. Loyalty-card evidence, for example, can reflect price discounts, targeted information, habit or emotional involvement, so observed choice may have several explanations.
The model is strongest as a benchmark for consistent trade-offs and for separating substitution from income effects. It is less reliable for discrete, infrequent, uncertain or behaviourally influenced purchases. Evaluate by linking a violated assumption to the direction or certainty of its prediction.
Consumers need not literally draw curves or calculate MRS. The model represents choices; its elegance is not evidence that every consumer behaves as assumed.