Income and price changes: ICC, PCC and the income and substitution effects
A price change has two parts: the substitution effect from changed relative prices and the income effect from changed real income. Together they shape demand.
Two curves traced by the consumer
Worked example 1: income change (ICC)
Using MRSxy = Y ÷ X, Px = Rs. 100 and Py = Rs. 50, the consumer's equilibrium at income Rs. 2,000 is X = 10, Y = 20. Find the new equilibrium if income rises to Rs. 3,000.
- Tangency still needs Y ÷ X = 100 ÷ 50 = 2, so Y = 2X.
- Budget: 100X + 50(2X) = 3,000 → 200X = 3,000 → X = 15.
- Y = 2 × 15 = 30. Check: 1,500 + 1,500 = Rs. 3,000. ✓
The equilibrium moves from (10, 20) to (15, 30). Both goods rise with income, so both are normal goods and the ICC slopes upwards.
Worked example 2: price change (PCC and the demand curve)
Income stays at Rs. 2,000 and Py at Rs. 50, but Px falls from Rs. 100 to Rs. 50. Find the new equilibrium and two points on the demand curve for X.
- Tangency now needs Y ÷ X = 50 ÷ 50 = 1, so Y = X.
- Budget: 50X + 50X = 2,000 → 100X = 2,000 → X = 20, and Y = 20.
- Check: 50 × 20 + 50 × 20 = Rs. 2,000. ✓
- Demand points for X: at Rs. 100, X = 10; at Rs. 50, X = 20.
The PCC runs from (10, 20) to (20, 20). The demand curve for X passes through (Rs. 100, 10) and (Rs. 50, 20): it slopes downwards.
Deriving the demand curve from the PCC
Splitting the price effect
When the price of X falls, the total price effect has two parts. The substitution effect is the change in X caused only by X becoming relatively cheaper, holding real income constant; it always increases purchases of the cheaper good. The income effect is the change in X caused by the rise in real income (purchasing power). In the Hicks method, income is taken away until the consumer is back on the original indifference curve; the move along that curve is the substitution effect. In the Slutsky method, income is adjusted so the consumer can just afford the original bundle. The rest of the change is the income effect.
Worked example 3: substitution and income effects (Slutsky method)
Px falls from Rs. 100 to Rs. 50 (income Rs. 2,000, Py = Rs. 50). X rose from 10 to 20. Split this into substitution and income effects using the Slutsky method.
- Compensated income = cost of the old bundle (10 X, 20 Y) at new prices = 50 × 10 + 50 × 20 = 500 + 1,000 = Rs. 1,500.
- At the new price ratio (Y = X) with Rs. 1,500: 50X + 50X = 1,500 → X = 15.
- Substitution effect = 15 − 10 = +5 units.
- Income effect = 20 − 15 = +5 units (the real income gain is given back).
- Total effect = 5 + 5 = +10 units, matching 10 → 20. ✓
Substitution effect +5, income effect +5, total +10. Both push in the same direction, so X is a normal good.
Normal, inferior and Giffen goods (price of the good falls)
| Type of good | Substitution effect | Income effect | Total effect on quantity |
|---|---|---|---|
| Normal | Increase | Increase | Increase (demand curve slopes down) |
| Inferior | Increase | Decrease, but smaller | Increase, though smaller |
| Giffen (a strongly inferior good) | Increase | Decrease, and larger | Decrease (demand curve slopes up) |
When a supermarket chain such as Keells cuts the price of a branded product, part of the sales gain is substitution (buyers switch from rival brands) and part is income (shoppers feel better off). For basic staples bought by poor households, the income effect can work the other way.
Short answer: “What is the price consumption curve?” The line joining the consumer's equilibrium points as the price of one good changes, with income and the other price fixed.
Structured question: “Px falls from Rs. 100 to Rs. 50 and X rises from 10 to 20. With compensated income Rs. 1,500 the consumer would buy 15. Find the substitution and income effects.” Substitution effect = 15 − 10 = +5; income effect = 20 − 15 = +5; total = +10, so X is a normal good.
Essay: “Explain the income and substitution effects of a fall in price and distinguish between normal, inferior and Giffen goods.” Define both effects, show the Hicks decomposition on an IC diagram, work a numerical case, then a table of signs for normal, inferior and Giffen goods.
Price effect = Substitution effect + Income effect. Substitution always favours the cheaper good. Only the income effect can change sign: normal +, inferior −, Giffen −− (bigger).