Income, cross and supply elasticity
Income elasticity sorts goods into normal, luxury and inferior; cross elasticity spots substitutes and complements; supply elasticity shows how quickly producers can respond.
Income elasticity of demand
| Value of YED | Type of good | Example |
|---|---|---|
| Greater than 1 | Normal good, luxury (income-elastic) | Restaurant meals, foreign travel, cars |
| Between 0 and 1 | Normal good, necessity | Rice, bread, electricity |
| Less than 0 (negative) | Inferior good | Cheaper staples that people leave as incomes rise |
Worked example 1: income elasticity
A household's monthly income rises from Rs. 80,000 to Rs. 100,000. Its restaurant meals rise from 4 to 6 a month. Find YED and classify the good.
- %Δincome = (100,000 − 80,000) ÷ 80,000 × 100 = 20,000 ÷ 80,000 × 100 = 25%.
- %ΔQd = (6 − 4) ÷ 4 × 100 = 2 ÷ 4 × 100 = 50%.
- YED = 50% ÷ 25% = +2.
YED = +2: restaurant meals are a normal, luxury good. Demand grows faster than income.
Worked example 2: cross elasticity
(a) The price of coffee rises from Rs. 500 to Rs. 600 and demand for tea rises from 1,000 to 1,060 packets. (b) Petrol prices rise by 25% and demand for motorcycles falls by 10%. Find XED in each case.
- (a) %ΔP of coffee = 100 ÷ 500 × 100 = 20%. %ΔQd of tea = 60 ÷ 1,000 × 100 = 6%.
- XED = 6% ÷ 20% = +0.3. Positive, so tea and coffee are substitutes (weak ones, since 0.3 is small).
- (b) XED = −10% ÷ 25% = −0.4. Negative, so petrol and motorcycles are complements.
(a) XED = +0.3: substitutes. (b) XED = −0.4: complements.
Worked example 3: price elasticity of supply
When the price of a garment rises from Rs. 1,000 to Rs. 1,200 per unit, a factory raises supply from 500 to 650 units a day. Find PES.
- %ΔP = 200 ÷ 1,000 × 100 = 20%.
- %ΔQs = 150 ÷ 500 × 100 = 30%.
- PES = 30% ÷ 20% = +1.5.
PES = 1.5: supply is elastic. The factory has spare capacity and can raise output quickly.
Determinants of elasticity of supply
- Time period: supply is very inelastic in the momentary period, more elastic in the short run, and most elastic in the long run when new capacity can be built.
- Spare capacity: idle machines and workers make supply elastic.
- Stocks and storability: goods that can be stored (canned fish, rice) have more elastic supply than perishables (fresh fish, flowers).
- Production time lag: tea bushes, rubber and coconut trees take years to mature, so their supply is inelastic in the short run.
- Mobility of factors: if workers and machines can switch easily between products, supply is elastic.
- Cost of raising output: if costs rise sharply with output, supply is inelastic.
Business uses
Hotels and tour operators serve demand with a high income elasticity, so they feel economic booms and downturns sharply. Coconut and tea growers face inelastic supply in the short run because new trees and bushes take years to bear, so prices swing when demand changes.
Short answer: “What is an inferior good?” A good with negative income elasticity: demand falls as income rises.
Structured question: “Calculate cross elasticity when coffee rises from Rs. 500 to Rs. 600 and tea demand rises from 1,000 to 1,060. Interpret.” XED = 6% ÷ 20% = +0.3. Positive, so they are substitutes, but only weak ones.
Essay: “Explain income elasticity, cross elasticity and elasticity of supply, and their uses in business decisions.” Define each with formula and sign, give a worked example for each, list determinants of supply elasticity, then forecasting, competitor and product-bundling uses.
YED sorts goods (luxury > 1, necessity 0-1, inferior < 0). XED sorts pairs (+ substitutes, − complements). PES rises with time.