Consumer's equilibrium under indifference curve analysis; price, income and substitution effects

1. The ordinal approach

The cardinal approach assumed utility could be measured in numbers. J.R. Hicks and R.G.D. Allen (“A Reconsideration of the Theory of Value”, 1934), building on F.Y. Edgeworth and Vilfredo Pareto, replaced this with the ordinal approach: a consumer cannot say how much utility a combination gives, but can rank combinations, saying whether one is preferred to, or equal to, another. Hicks set the analysis out fully in Value and Capital (1939).

Assumptions: the consumer is rational and has a scale of preferences; preferences are consistent and transitive (if A is preferred to B and B to C, A is preferred to C); more of a good is preferred to less (non-satiety); the marginal rate of substitution diminishes.

2. Indifference schedule, curve and map

An indifference schedule lists combinations of two goods that give the consumer equal satisfaction.

Plotted, these points give an indifference curve: the locus of combinations of two goods yielding the same satisfaction. A set of such curves, each representing a different level of satisfaction, is an indifference map; a curve further from the origin shows a higher level.

The marginal rate of substitution of X for Y (MRS_xy) is the amount of Y the consumer is willing to give up for one more unit of X while remaining equally well off. In the table it falls from 4 to 1: the more apples he has, the fewer oranges he will sacrifice for another. This is the principle of diminishing MRS, and MRS is the slope of the curve.

3. Properties of indifference curves

1. Slope downward from left to right. To get more X the consumer must give up some Y to stay on the same level of satisfaction.
2. Convex to the origin, because MRS diminishes.
3. Two indifference curves never intersect. If they did, the point of intersection would give equal satisfaction on both, which contradicts their being different levels.
4. A higher curve shows higher satisfaction, since it contains more of at least one good.
5. They need not be parallel, as the rate of substitution may differ between levels.
6. They do not normally touch either axis, since the consumer is assumed to want some of both goods.

4. The budget (price) line

The budget line shows all combinations of X and Y the consumer can buy with a given income at given prices. With income Rs. 100, P_x = Rs. 10 and P_y = Rs. 5, he can buy 10 X (and no Y) or 20 Y (and no X). The straight line joining these two points is the budget line; its slope is P_x / P_y = 10 / 5 = 2. Combinations on the line exhaust income; those inside are affordable but leave money unspent; those outside are unaffordable.

A rise in income shifts the line outward parallel to itself; a fall in P_x swings it outward along the X axis, pivoting on the Y intercept.

5. Consumer’s equilibrium

The consumer aims to reach the highest indifference curve his budget allows. Place the budget line on the indifference map. He is in equilibrium at the point where the budget line is tangent to an indifference curve (call it point E on IC₂).

Conditions:

1. Necessary (first-order) condition: the slope of the indifference curve equals the slope of the budget line, that is MRS_xy = P_x / P_y.
2. Sufficient (second-order) condition: the indifference curve must be convex to the origin at the point of tangency (MRS diminishing).

Described diagram: points on the budget line to the left or right of E (say R and S) lie on a lower curve IC₁; the consumer can move along the line towards E and gain. A higher curve IC₃ lies wholly beyond the budget line and is out of reach. Only at E is the highest attainable curve touched. In the example the budget line has slope 2, so the consumer settles where his highest attainable indifference curve also has an MRS_xy of 2: he is willing to give up two oranges for an apple, and the market makes him give up exactly two (Rs. 10 ÷ Rs. 5). If his MRS were 3, an apple would be worth more to him than its market cost in oranges, and he would buy more apples until MRS fell to 2.

6. Income effect

The income effect is the change in the consumer’s purchases caused by a change in money income, prices of X and Y remaining the same. As income rises, the budget line shifts outward in parallel and the consumer reaches new equilibrium points on higher curves. Joining these points gives the income consumption curve (ICC).

• For two normal goods the ICC slopes upward to the right: more of both is bought.
• If X is inferior, the ICC bends back towards the Y axis: the income effect on X is negative.

7. Substitution effect

The substitution effect is the change in purchases caused by a change in relative prices alone, the consumer’s real income held constant. When X becomes cheaper, the consumer substitutes X for Y. To isolate this, Hicks takes away enough money income (the compensating variation) to leave the consumer on his original indifference curve. He then moves along the same curve to a point with more X and less Y. The substitution effect is always negative: a fall in the relative price of X always increases its demand.

8. Price effect

The price effect is the total change in purchases when the price of one good changes, money income and the other price being constant. A fall in P_x swings the budget line outward along the X axis; joining successive equilibrium points gives the price consumption curve (PCC), from which the demand curve for X is derived.

The price effect is the sum of the two effects already explained:

Price effect = Substitution effect + Income effect

(This decomposition is often called the Slutsky equation, after Eugen Slutsky, who reached it in 1915.) For a normal good both effects increase demand for X when its price falls, so the demand curve slopes downward. For an inferior good the income effect is negative but smaller than the substitution effect, so demand still rises. For a Giffen good the negative income effect is larger than the substitution effect, so a fall in price reduces demand: the exception to the law of demand is explained.

Principles of Economics covers the curves and equilibrium in its note on indifference curves.

How this is examined

January 2026 (80-mark) set “Explain consumer’s equilibrium under indifference curve” for 10 marks; the 100-mark paper of the same sitting asked for an 8-mark short note on “Indifference curve”. For the equilibrium answer write sections 1 to 5 with the diagram described and both conditions; for the short note, the definition, schedule, MRS and the six properties. If price, income and substitution effects are asked, draw on sections 6 to 8 and end with the Giffen case.