Elasticity of Demand and Supply
Elasticity measures how responsive quantity is to changes in price, income, or other factors. This unit covers price, income, cross, and advertisement elasticity of demand — their formulas, degrees, and uses — as well as point elasticity, the total expenditure method, and the elasticity of supply.
In this chapter
Concept of Elasticity
The law of demand tells us that price and quantity demanded are inversely related, but it does not tell us how much quantity changes for a given price change. Elasticity of demand fills this gap — it measures the responsiveness (or sensitivity) of demand to a change in any of its determinants. The concept was first introduced by classical economists A.A. Cournot and J.S. Mill, and later developed scientifically by Alfred Marshall in his book Principles of Economics.
Types of Elasticity of Demand
Four Types of Demand Elasticity
- Price elasticity of demand (E_p) — responsiveness to a change in the good's own price.
- Income elasticity of demand (E_y) — responsiveness to a change in consumer income.
- Cross elasticity of demand (E_xy) — responsiveness of one good's demand to a change in another good's price.
- Advertisement elasticity of demand (E_a) — responsiveness to a change in advertising expenditure.
Price Elasticity of Demand
Price elasticity of demand (E_p) is the ratio of the percentage change in quantity demanded to the percentage change in price. Because price and quantity move in opposite directions, E_p is negative — but economists usually report the absolute value.
Price elasticity of demand (percentage method)
Degrees of Price Elasticity
Five Degrees of Price Elasticity of Demand
| Degree | Coefficient | Description | Example |
|---|---|---|---|
| Perfectly Inelastic | E_p = 0 | Quantity does not change at all | Life-saving insulin |
| Inelastic | 0 < E_p < 1 | Quantity changes less than price | Salt, basic food |
| Unitary Elastic | E_p = 1 | Quantity changes exactly with price | Theoretical benchmark |
| Elastic | E_p > 1 | Quantity changes more than price | Luxury goods, branded items |
| Perfectly Elastic | E_p = ∞ | Any price increase drops demand to zero | Perfectly competitive firm |
Arc Elasticity (Mid-point Method)
A practical problem with the percentage method is that elasticity differs depending on the direction of change (price rise vs price fall). The arc elasticity (mid-point method) solves this by using the average of the initial and final values as the base. It is the most appropriate method when the price change is large. The formula uses the midpoint of P and Q, giving a single elasticity value for the entire arc.
Arc (mid-point) elasticity formula
Factors Affecting Price Elasticity
Determinants of Price Elasticity of Demand
- Availability of substitutes — more substitutes mean more elastic demand (Coke vs Pepsi).
- Nature of the good — necessities (salt, medicine) are inelastic; luxuries are elastic.
- Proportion of income — goods taking a small share of income (salt) are inelastic; large-share goods (cars) are elastic.
- Time period — demand is more elastic in the long run as consumers find substitutes.
- Number of uses — multi-use goods (electricity) are more elastic than single-use goods.
- Habit goods — cigarettes, alcohol tend to be inelastic (addiction).
- Brand loyalty — strong brands face less elastic demand (Apple iPhone).
Nepal Example: LPG Gas and Salt
In Nepal, the demand for cooking gas (LPG) is relatively inelastic — when the Nepal Oil Corporation raises prices, households reduce consumption only modestly because alternatives (firewood, electric induction) are imperfect substitutes. The demand for iodised salt is even more inelastic — it is a necessity costing a tiny fraction of household income. In contrast, demand for restaurant meals in Kathmandu is elastic: when restaurant prices rise 20%, many middle-class families shift to home cooking, and quantity demanded falls sharply. This explains why the government taxes essentials less but restaurants more.
Point Elasticity and Total Expenditure Method
- Point elasticity measures elasticity at a specific point on the demand curve using the derivative. It is useful when the demand function is known mathematically. The total expenditure method compares the direction of change in total expenditure (price × quantity) with the direction of price change: if price and total expenditure move in opposite directions, demand is elastic
- same direction, inelastic
- no change in expenditure, unitary.
Point elasticity formula
Total Expenditure Method
Total Expenditure Method — Elasticity Diagnosis
| Price Change | Total Expenditure Change | Elasticity |
|---|---|---|
| Price rises | TE falls | Elastic (E_p > 1) |
| Price rises | TE rises | Inelastic (E_p < 1) |
| Price rises | TE unchanged | Unitary (E_p = 1) |
| Price falls | TE rises | Elastic (E_p > 1) |
| Price falls | TE falls | Inelastic (E_p < 1) |
| Price falls | TE unchanged | Unitary (E_p = 1) |
Income and Cross Elasticity
- Income elasticity of demand (E_y) measures the responsiveness of demand to a change in consumer income. If E_y > 0, the good is normal
- if E_y < 0, it is inferior
- if E_y > 1, it is a luxury
- if 0 < E_y < 1, it is a necessity. Cross elasticity of demand (E_xy) measures how the demand for good X responds to a change in the price of good Y. If E_xy > 0, X and Y are substitutes
- if E_xy < 0, they are complements
- if E_xy = 0, they are unrelated.
Income elasticity and cross elasticity
Cross Elasticity and Types of Goods
Cross Elasticity and Classification of Goods
| Sign of E_xy | Relationship | Example |
|---|---|---|
| E_xy > 0 (positive) | Substitutes | Tea and coffee |
| E_xy < 0 (negative) | Complements | Tea and sugar |
| E_xy = 0 | Unrelated | Tea and shoes |
| E_xy large positive | Close substitutes | Coke and Pepsi |
| E_xy small negative | Weak complements | Tea and biscuits |
Income Elasticity and Classification
Income Elasticity and Types of Goods
| Coefficient | Type of Good | Example |
|---|---|---|
| E_y > 1 | Luxury | Jewellery, sports car |
| E_y = 1 | Comfort | Clothing, furniture |
| 0 < E_y < 1 | Necessity | Rice, milk, education |
| E_y = 0 | Neutral | Matchsticks, salt |
| E_y < 0 | Inferior | Coarse grain, second-hand goods |
Uses of Elasticity
- Price elasticity helps firms decide whether to raise or lower prices to increase revenue.
- Government uses elasticity to set tax rates — inelastic goods are taxed more because demand barely falls.
- Income elasticity helps classify goods as normal, inferior, luxury, or necessity.
- Cross elasticity identifies whether goods are substitutes, complements, or unrelated.
- Advertisement elasticity measures the effectiveness of promotional spending.
Elasticity and Total Revenue
Relationship Between Price Elasticity and Total Revenue
| Elasticity | Price Cut Effect on TR | Price Rise Effect on TR |
|---|---|---|
| Elastic (E_p > 1) | TR rises | TR falls |
| Inelastic (E_p < 1) | TR falls | TR rises |
| Unitary (E_p = 1) | TR unchanged | TR unchanged |
Practical Applications of Elasticity
Pricing strategy: a Kathmandu cinema with inelastic demand for weekend shows can raise ticket prices; for weekday shows with elastic demand, it should offer discounts. Taxation: the Nepal government taxes cigarettes and alcohol heavily because their demand is inelastic — revenue rises despite modest quantity falls. Wage negotiations: unions demand higher wages when labour demand is inelastic (skilled workers). Farm income: a bumper harvest shifts supply rightward, but because food demand is inelastic, total farm revenue falls — explaining why farmers often suffer from good harvests.
Price Elasticity of Supply
Price elasticity of supply (E_s) is the ratio of the percentage change in quantity supplied to the percentage change in price. Because price and quantity supplied move in the same direction (law of supply), E_s is positive. The main determinant is time — in the short run, supply is inelastic because firms cannot easily expand capacity; in the long run, supply becomes more elastic as firms can build new plants and enter the industry.
Price elasticity of supply
Types of Elasticity of Supply
Five Degrees of Price Elasticity of Supply
| Degree | Coefficient | Supply Curve Shape | Example |
|---|---|---|---|
| Perfectly inelastic | E_s = 0 | Vertical line | Land, antique art |
| Inelastic | 0 < E_s < 1 | Steep upward | Perishable vegetables (short run) |
| Unitary elastic | E_s = 1 | Through origin | Theoretical benchmark |
| Elastic | E_s > 1 | Flat upward | Manufactured goods (long run) |
| Perfectly elastic | E_s = ∞ | Horizontal line | Perfectly competitive firm |
Revenue and Elasticity
If demand is elastic (E_p > 1), lowering price increases total revenue (quantity rises more than price falls). If demand is inelastic (E_p < 1), raising price increases total revenue (quantity barely falls). At unitary elasticity, revenue is maximised and price changes do not affect it. This is the key insight for pricing strategy.
Key Terms and Definitions / मुख्य शब्द र परिभाषा
- Elasticity: Responsiveness of one variable to a change in another — लोच: एक चर अर्कोमा परिवर्तनमा कति उत्तरदायी हुने।
- Price elasticity of demand: % change in Q_d ÷ % change in P — मागको मूल्य लोच: Q_d मा % परिवर्तन ÷ P मा % परिवर्तन।
- Income elasticity: % change in Q_d ÷ % change in income — आय लोच: Q_d मा % परिवर्तन ÷ आयमा % परिवर्तन।
- Cross elasticity: % change in Q_x ÷ % change in P_y — क्रस लोच: Q_x मा % परिवर्तन ÷ P_y मा % परिवर्तन।
- Arc elasticity: Elasticity using mid-point as base — चाप लोच: मध्य-बिन्दु आधार प्रयोग गर्ने लोच।
- Point elasticity: Elasticity at a specific point on the curve — बिन्दु लोच: वक्रको विशिष्ट बिन्दुमा लोच।
- Elastic demand: |E_p| > 1, quantity changes more than price — लोचदार माग: |E_p| > 1, मात्रा मूल्यभन्दा बढी परिवर्तन।
- Inelastic demand: |E_p| < 1, quantity changes less than price — अलोचदार माग: |E_p| < 1, मात्रा मूल्यभन्दा कम परिवर्तन।
- Unitary elasticity: |E_p| = 1, quantity changes exactly with price — एकाइ लोच: |E_p| = 1, मात्रा मूल्यसँग ठीक बराबर परिवर्तन।
- Substitutes: E_xy > 0, goods that replace each other — विकल्प: E_xy > 0, एकआपसमा प्रतिस्थापन हुने वस्तु।
- Complements: E_xy < 0, goods used together — पूरक: E_xy < 0, सँगै प्रयोग हुने वस्तु।
- Normal good: E_y > 0, demand rises with income — सामान्य वस्तु: E_y > 0, आयसँग माग बढ्ने।
Practice Problem
When the price of a commodity rises from Rs 10 to Rs 12, the quantity demanded falls from 100 units to 80 units. Calculate price elasticity of demand using the percentage method and classify the demand.
Practice Problem
The price of good X falls from Rs 20 to Rs 16 per unit, and as a result, its quantity demanded rises from 50 to 70 units. Calculate the price elasticity of demand using the arc (mid-point) method. Comment on the result.
Practice Problem
The price of tea (good Y) rises from Rs 100 to Rs 120 per kg. As a result, the demand for coffee (good X) rises from 50 to 80 kg per month. Calculate the cross elasticity of demand and identify the relationship between tea and coffee.