7.2 Indifference curves and budget lines

An indifference curve contains combinations of two goods that give the consumer the same satisfaction. A budget line contains combinations that exhaust income at given prices.

For standard preferences, indifference curves are downward sloping and convex because the marginal rate of substitution usually falls. The budget line’s slope reflects the relative prices; its intercepts reflect income divided by each price.

If income is $60 and prices are$10 for X and $5 for Y, the intercepts are 6 units of X and 12 of Y. Any point inside is affordable but leaves income unspent.

An indifference curve is not a demand curve, and points on a higher curve are preferred only if the curves represent the same preferences and are reachable.

A rise in income shifts the budget line outward in parallel; a fall shifts it inward. A change in one good’s price rotates the line because one intercept changes while the other stays fixed.

The slope changes with relative prices, not with income. The new best affordable bundle depends on preferences, so the same budget-line movement can produce different quantities for different consumers.

If income rises from $60 to$80 with prices unchanged, both intercepts increase by one-third. If X’s price falls while Y’s price stays fixed, the X-intercept moves outward and the Y-intercept is unchanged.

A parallel shift is not caused by a single price change, and a budget-line change alone does not tell you whether demand for a good rises or falls.

When the price of a good changes, the consumer’s choice changes for two reasons. The substitution effect replaces relatively expensive goods with the now relatively cheaper good; the income effect changes real purchasing power.

For a normal good, a price fall usually raises demand through both effects. For an inferior good the income effect works in the opposite direction; for a Giffen case it could be so strong that demand falls when price falls, although this is unusual.

A cheaper bus ticket makes bus travel cheaper relative to taxis and also leaves the household with more real purchasing power. Both channels can raise bus journeys, but a normal-good assumption is doing work.

The income effect is not simply a cash-income change, and the substitution effect is not “switching because preferences changed”.

The standard indifference-curve model assumes coherent preferences, complete information, divisible goods, a fixed income and prices, and curves that are ordered and usually convex.

Real choices may involve uncertainty, habits, status, discrete purchases, changing preferences, imperfect information or behavioural biases. Perfectly straight or kinked curves can represent special cases such as perfect substitutes or complements.

A commuter cannot buy 0.3 of a bus journey, and a loyalty habit may keep them with a familiar provider even after the relative price changes; the smooth-curve prediction is then only an approximation.

The model’s elegance is not evidence that people literally calculate utility; it is a conditional tool for analysing trade-offs.