Introduction
The general concept of elasticity of demand measures the degree of responsiveness of quantity demanded to a change in any of its determinants. While price elasticity of demand considers changes in own price, income elasticity and cross elasticity extend this analysis to other crucial determinants—namely, consumer income and prices of related goods. T.R. Jain and V.K. Ohri treat these elasticities as essential tools for understanding how demand behaves in a realistic, multi-variable economic environment.
In this note, we explain in detail the meaning, types and significance of (a) Income Elasticity of Demand, and (b) Cross Elasticity of Demand, along with their importance in theory and policy. This structured discussion is exactly in line with the expectations of Panjab University for a 15-marks long answer.
I. Income Elasticity of Demand
1. Meaning and Definition
Income Elasticity of Demand (usually denoted by Ey) measures the degree of responsiveness of quantity demanded of a commodity to a change in the income of the consumer, other factors such as price and tastes remaining constant.
Income elasticity of demand is the percentage change in quantity demanded of a commodity divided by the percentage change in the income of the consumer, ceteris paribus.
Ey = (% change in Q) ÷ (% change in Y)
2. Measurement (Basic Formula)
For finite changes, income elasticity of demand can be measured as:
Ey = (ΔQ / Q) ÷ (ΔY / Y) = (ΔQ / ΔY) × (Y / Q)
Where ΔQ = change in quantity demanded, ΔY = change in income, Q = initial quantity demanded and Y = initial income. In certain contexts, an arc formula using averages of Q and Y may be used to measure income elasticity over a range.
3. Types of Income Elasticity of Demand
Depending on the sign and magnitude of Ey, we classify income elasticity into several types:
-
Positive Income Elasticity (Ey > 0):
Quantity demanded increases when income increases. Such goods are called normal goods.
Within this category:
- 0 < Ey < 1: Necessities; demand rises less than proportionately with income.
- Ey = 1: Unit income elasticity; demand rises in the same proportion as income.
- Ey > 1: Luxuries or superior goods; demand rises more than proportionately with income.
- Negative Income Elasticity (Ey < 0): Quantity demanded decreases when income increases. Such goods are inferior goods in the Hicksian sense. As people become richer, they substitute these goods with better-quality alternatives.
- Zero Income Elasticity (Ey = 0): Quantity demanded remains unchanged when income changes. Demand for such goods is completely independent of income (e.g. life-saving drugs within a certain range).
• Rice or wheat for low-income consumers typically shows positive but less than unit income elasticity (necessity).
• High-end imported chocolates and premium cars may show income elasticity greater than one (luxury goods).
• Coarse grains or very low-quality clothing may exhibit negative income elasticity for higher income groups (inferior goods).
4. Importance of Income Elasticity of Demand
Income elasticity of demand plays an important role in several areas of economic analysis and policy:
Firms use income elasticity to forecast how sales of their products will change with economic growth. A product with high positive income elasticity will experience rapid growth in demand in periods of rising national income. This helps firms plan capacity expansion, investment and long-term strategy.
Income elasticity provides an analytical basis for classifying goods. Necessities typically have low but positive income elasticity, luxuries have income elasticity greater than one, and inferior goods have negative income elasticity. This classification is important for welfare analysis and tax policy.
Governments closely study the income elasticity of different goods while designing tax structures and subsidy policies. Highly income-elastic luxury goods can be taxed more heavily, whereas necessities consumed by low-income groups may be given concessions or subsidies.
In developing economies, as per capita income rises, demand shifts away from basic necessities towards manufactured goods and services with higher income elasticity. Understanding these patterns (Engel’s law) helps planners anticipate structural changes in the economy.
Countries exporting goods with high income elasticity benefit more from global income growth. Knowledge of income elasticity structure thus influences trade and export promotion policies.
II. Cross Elasticity of Demand
1. Meaning and Definition
While income elasticity deals with responsiveness to changes in income, cross elasticity of demand (denoted by Exy) measures the responsiveness of demand for one good to changes in the price of another related good. It is therefore primarily concerned with the relationship between substitute goods and complementary goods.
Cross elasticity of demand is the percentage change in quantity demanded of one commodity (X) divided by the percentage change in the price of another related commodity (Y), ceteris paribus.
Exy = (% change in Qx) ÷ (% change in Py)
2. Measurement (Basic Formula)
For measurable changes, cross elasticity can be written as:
Exy = (ΔQx / Qx) ÷ (ΔPy / Py) = (ΔQx / ΔPy) × (Py / Qx)
Here, Qx is quantity demanded of commodity X and Py is the price of related commodity Y. The sign and magnitude of Exy provide crucial information on the nature and strength of the relationship between the two goods.
3. Types of Cross Elasticity of Demand
According to whether two goods are substitutes, complements or unrelated, cross elasticity may be:
- Positive Cross Elasticity (Exy > 0) — Substitutes: When the price of good Y rises, demand for good X increases (and vice versa). This indicates that X and Y are substitute goods, such as tea and coffee, Coke and Pepsi, or butter and margarine.
- Negative Cross Elasticity (Exy < 0) — Complements: When the price of good Y rises, demand for good X falls (and vice versa). This indicates that X and Y are complementary goods, such as car and petrol, printer and ink, mobile handset and data packs.
- Zero (or Almost Zero) Cross Elasticity (Exy ≈ 0) — Unrelated Goods: When a change in the price of Y has practically no effect on the demand for X, the goods are unrelated (e.g. bread and diesel).
• If price of coffee increases and demand for tea rises, cross elasticity of tea with respect to coffee is positive (substitutes).
• If price of petrol increases and demand for cars falls, cross elasticity of cars with respect to petrol is negative (complements).
• If price of pencils changes and demand for refrigerators is unaffected, cross elasticity is zero (unrelated goods).
4. Importance of Cross Elasticity of Demand
Cross elasticity plays a vital role in several analytical and practical contexts:
Cross elasticity provides a quantitative measure of the nature and strength of the relationship between two goods. A positive coefficient confirms substitutability; a negative coefficient confirms complementarity. The higher the absolute value, the stronger the relationship.
In industrial economics and competition law, markets are defined in terms of groups of commodities that are close substitutes for each other. High positive cross elasticity among products indicates that they belong to the same competitive market or industry. This is essential for assessing monopoly power, mergers and anti-competitive practices.
When cross elasticity between the products of different firms is high, a price change by one firm has a significant effect on the sales of rival firms. In such cases, firms must anticipate competitors’ reactions and adopt strategic pricing and advertising policies.
For complementary goods (like cameras and memory cards), producers often design joint marketing and pricing strategies. Knowledge of cross elasticity helps in determining optimal pricing combinations, bundle offers and tie-in sales.
Government policies affecting the price of one good may have unintended consequences on related goods through cross elasticity channel. For instance, raising fuel prices affects car demand, and taxing cigarettes may change demand for substitute tobacco products. Policymakers must consider such cross effects for coherent policy design.
III. Distinction Between Income and Cross Elasticity of Demand
Though both are forms of elasticity of demand, income elasticity and cross elasticity differ fundamentally in the variable whose change is being considered and in their economic interpretation. A clear distinction is often required in exams.
| Basis | Income Elasticity of Demand | Cross Elasticity of Demand |
|---|---|---|
| Definition | Measures responsiveness of demand for a good to a change in consumer income, other things remaining constant. | Measures responsiveness of demand for a good to a change in the price of another related good, other things remaining constant. |
| Notation | Usually denoted by Ey. | Usually denoted by Exy. |
| Sign | Positive for normal goods; negative for inferior goods; zero for income-neutral goods. | Positive for substitutes; negative for complements; approximately zero for unrelated goods. |
| Classification of Goods | Classifies goods as necessities, luxuries and inferior goods. | Classifies goods as substitutes, complements or unrelated goods. |
| Main Use | Forecasting demand under changing income, studying economic development, tax policy on luxuries and necessities. | Defining market boundaries, studying interdependence of firms, designing pricing for related goods and competition policy. |
Conclusion
To conclude, income elasticity and cross elasticity of demand are powerful extensions of the basic elasticity concept. Income elasticity relates demand to changes in consumer income and enables us to distinguish between necessities, luxuries and inferior goods, while cross elasticity relates demand to price changes of related commodities and helps us identify substitutes and complements and delineate market boundaries. A well-prepared answer should state precise definitions, give formulae, classify types on the basis of sign and magnitude, and highlight the practical importance of each elasticity in business decisions and public policy. Such a structured treatment fully matches the standard expected by Panjab University examiners.