Elasticity of Demand and Supply

The law of demand says quantity falls when price rises; elasticity says by how much. A firm deciding whether to cut a price, a government deciding which good to tax, and a cloud provider changing a subscription fee all need it.

2.1 Price elasticity of demand

Price elasticity of demand (e_d) = percentage change in quantity demanded ÷ percentage change in price. Because price and quantity move in opposite directions e_d is negative; we usually quote the absolute value |e_d|.

| Type | |e_d| | Meaning | Example | |---|---|---|---| | Perfectly inelastic | 0 | quantity does not change | life-saving drug (vertical demand) | | Inelastic | 0 < |e| < 1 | quantity changes proportionally less than price | salt, electricity, petrol in the short run | | Unitary elastic | = 1 | proportional change | | | Elastic | > 1 | proportionally more | luxuries, restaurant meals, branded goods with substitutes | | Perfectly elastic | ∞ | any price rise loses all sales (horizontal demand) | one farmer's wheat in a perfect market |

Determinants: availability and closeness of substitutes (more substitutes → more elastic); necessity versus luxury; share of income spent (matchboxes vs cars); time period (longer → more elastic); definition of the market (demand for "food" is inelastic, for "one brand of noodles" elastic); habit.

Measurement 1: Total outlay (expenditure) method

Compare total expenditure TE = P × Q before and after a price change.

Price change	Total outlay rises	Total outlay unchanged	Total outlay falls
Price falls	elastic (	e	> 1)
Price rises	inelastic	unitary	elastic

In words: if price and total outlay move in opposite directions, demand is elastic; in the same direction, inelastic; if outlay is unchanged, unitary.

Measurement 2: Point method

At one point on the demand curve, e = (dQ/dP) × (P/Q) = (1/slope) × P/Q. For linear demand it varies along the curve: elastic at high prices, unit elastic at the midpoint, inelastic at low prices.

Measurement 3: Arc (midpoint) method

For a discrete change use the averages so that the answer does not depend on the direction: e = (ΔQ/Q̄) ÷ (ΔP/P̄), with Q̄ and P̄ the midpoints.

For the example above: ΔQ = 30, Q̄ = 115 → 26.09%; ΔP = −2, P̄ = 9 → −22.22%; e = −1.174 (elastic, agrees with the outlay test).

2.2 Income and cross elasticity of demand

Income elasticity e_y = %ΔQ ÷ %ΔIncome. Positive for normal goods (>1 luxury, 0–1 necessity); negative for inferior goods (instant noodles, public transport as income rises). Used to forecast demand as the economy grows and to decide which industries expand.

Cross elasticity e_xy = %ΔQ_x ÷ %ΔP_y. Positive for substitutes (tea and coffee), negative for complements (cars and petrol, printers and ink), zero for unrelated goods. Firms use it to see competition and to price product lines.

2.3 Uses of elasticity

• Business pricing: if demand is elastic, a price cut raises revenue; if inelastic, a price rise raises revenue. A software seller with many competitors (elastic) cuts price to grow; a monopoly utility (inelastic) can raise price.
• Taxation: governments tax inelastic goods (fuel, tobacco) for stable revenue; the tax burden falls more on the side with the less elastic curve.
• Agriculture: a bumper harvest can lower farmers' income because food demand is inelastic (price falls proportionally more than quantity rises).
• International trade: devaluation helps the trade balance only if import and export demands are sufficiently elastic (Marshall–Lerner condition: sum of elasticities > 1).
• Planning: income elasticity guides forecasts and investment; cross elasticity guides competition policy.

2.4 Elasticity of supply

e_s = %ΔQ_s ÷ %ΔP, positive. Determinants: time (supply is more elastic in the long run), availability of inputs and spare capacity, storability, flexibility of production.

Perfectly inelastic supply is vertical (land, a concert hall's seats); perfectly elastic is horizontal.

(a) Spice stalls, Asan Bazaar, Kathmandu

(b) Inelastic demand and a supply increase

(a) Ernst Engel (1821-1896)

(b) Engel curve for food (illustrative household)

(a) A petrol pump of 1952

(b) A Rs 12 tax: buyers carry 2/3

2.6 Eight uses of elasticity in business, government and Nepal

1. Setting the price of a product. If demand is elastic, a small price cut brings a large rise in sales, so total revenue grows. A Nepali mobile-data company with many rivals therefore offers cheap packs to win users. If demand is inelastic, a price cut only loses revenue, so a seller of an essential item keeps the price firm.
2. Choosing which goods to tax. Governments prefer to tax goods with inelastic demand, such as fuel, cigarettes and alcohol, because buyers keep buying and the revenue is steady. Nepal's excise duties follow this logic. Heavy taxes on an elastic luxury would simply push buyers to stop or to smuggle.
3. Sharing the burden of a tax. The side of the market with the less elastic curve pays the larger part of a tax. When demand for petrol is inelastic, nearly all of a new tax passes to the motorist. Knowing this lets a student predict who will really pay, whatever the law says.
4. Understanding the farmers' paradox. Food has inelastic demand, so a bumper harvest lowers the price by more than it raises the quantity sold. The farmers of the Terai may earn less from a record rice crop than from an average one. This is why support prices and storage are discussed every season.
5. Exchange rate and trade policy. A weaker currency makes exports cheaper and imports dearer, but the trade balance improves only if demand elasticities are high enough (Marshall-Lerner: the sum is above 1). Nepal's imports of fuel and medicine are inelastic, so a depreciation helps little. The rule explains why trade policy needs more than a change in the rate.
6. Forecasting demand as incomes grow. Income elasticity shows how fast demand rises when incomes rise. Luxuries, such as smartphones and air travel, grow faster than income, while inferior goods, such as cheap noodles, fall. Banks and telecom firms use this to decide where to expand.
7. Reading competition between products. Cross elasticity is large and positive for close substitutes, such as two mobile-wallet apps. A firm that sees this knows a price rise will send customers to its rival. For complements, such as printers and ink, a fall in one price raises sales of the other.
8. Timing and planning supply. Supply is more elastic over a longer period because factories, farms and servers can be expanded. A hydropower plant cannot respond to a price signal this year, but it can in ten years. Planners use the idea to decide whether a shortage is temporary or needs investment.

Formula and fact sheet

• e_d = %ΔQ/%ΔP; point: (dQ/dP)(P/Q); arc: \dfrac{\Delta Q/Q̄}{\Delta P/P̄}.
• Total outlay: price and outlay opposite directions → elastic; same → inelastic; unchanged → unitary.
• Linear demand: elastic above the midpoint, e = 1 at the midpoint, inelastic below.
• e_y > 0 normal (>1 luxury), < 0 inferior. e_xy > 0 substitutes, < 0 complements.
• Supply elasticity grows with time.

Chapter summary

• Elasticity measures responsiveness; price elasticity is classified from perfectly inelastic to perfectly elastic and depends on substitutes, necessity, income share and time.
• Total outlay, point and arc methods measure it; income and cross elasticities classify goods and relationships.
• Elasticity guides pricing, taxation and policy.

Practice

1. A price rises from 20 to 25 and the quantity demanded falls from 200 to 150. Find the arc elasticity and classify demand. Check with the total outlay method.
2. For Q = 80 − 4P find the point elasticity at P = 5 and P = 15, and the price of unit elasticity.
3. Income rises 10% and the demand for a good falls 4%. Find e_y and classify the good.
4. The price of petrol rises 20% and the demand for cars falls 6%. Find e_xy and the relationship.
5. Explain why a bumper crop may reduce farmers' income.
6. List four determinants of price elasticity of demand.
7. Price rises from 100 to 110 and Q_s from 500 to 560. Find e_s (midpoint).

Answers and worked solutions

1. ΔQ = −50, Q̄ = 175 → −28.57%; ΔP = 5, P̄ = 22.5 → 22.22%; e = −1.286 → elastic. TE: 20 × 200 = 4,000 → 25 × 150 = 3,750: price up, outlay down (opposite) → elastic ✓.

2. dQ/dP = −4. At P = 5, Q = 60: e = −4 × 5/60 = −0.333. At P = 15, Q = 20: e = −4 × 15/20 = −3. Unit elasticity: −4P/(80 − 4P) = −1 → 4P = 80 − 4P → P = 10.

3. e_y = −4/10 = −0.4: inferior good.

4. e_xy = −6/20 = −0.3: complements.

5. Demand for food is inelastic, so the price falls proportionally more than output rises and total revenue falls.

6. Substitutes, necessity vs luxury, share of income, time period (also market definition).

7. ΔQ = 60, Q̄ = 530 → 11.32%; ΔP = 10, P̄ = 105 → 9.52%; e_s = 1.19.

Model answers: medium (5 marks) and long (10 marks) questions

Q1 (5 marks). Explain the total outlay method of measuring price elasticity of demand. A price falls from NPR 10 to 8 and quantity rises from 100 to 130; what do you conclude?

Introduction. Price elasticity of demand measures how strongly the quantity demanded responds to a change in price.

The total outlay (expenditure) method, due to Marshall, finds it without any formula by comparing what buyers spend, TE = P × Q, before and after the price change.

Rule.

Price change	Outlay rises	Outlay unchanged	Outlay falls
Price falls	elastic (e > 1)	unitary (e = 1)	inelastic (e < 1)
Price rises	inelastic	unitary	elastic

In words: if price and outlay move in opposite directions the demand is elastic; in the same direction, inelastic; if outlay does not change, unitary.

Numerical case. Before: TE = 10 × 100 = 1,000. After: TE = 8 × 130 = 1,040. Price fell and outlay rose, which is the opposite direction, so demand is elastic.

A cross-check by the midpoint formula gives %ΔQ = 30/115 = 26.09% and %ΔP = −2/9 = −22.22%, so e = −1.174, which agrees (Figure 2.2b shows the same idea: revenue rises while e > 1).

Merit and limit. The method is simple and needs no calculus, but it gives only the class of elasticity, not its numerical value.

Conclusion. Outlay rose after the price fell, so demand is elastic and the seller gains by the cut.

Q2 (5 marks). Define income elasticity and cross elasticity of demand. Show how they classify goods, with a numerical example of each.

Introduction. Price is not the only determinant of demand. Income elasticity and cross elasticity measure the response of quantity to income and to another good's price.

Income elasticity e_y = %ΔQ ÷ %ΔIncome.

1. e_y > 1: luxury (smartphones, air travel); demand rises faster than income.
2. 0 < e_y < 1: necessity (books, rice); demand rises more slowly.
3. e_y < 0: inferior good (cheap noodles); demand falls as income rises.

Example. Income rises from NPR 20,000 to 24,000 and book purchases from 50 to 56. %ΔQ = 6/53 = 11.32% and %ΔIncome = 4,000/22,000 = 18.18%, so e_y = 0.623, a necessity.

Cross elasticity e_xy = %ΔQ_x ÷ %ΔP_y.

1. e_xy > 0: substitutes (tea and coffee).
2. e_xy < 0: complements (printers and ink).
3. e_xy = 0: unrelated goods.

Example. The price of tea rises from 10 to 12 and coffee sales rise from 80 to 88. %ΔQ = 8/84 = 9.52% and %ΔP = 2/11 = 18.18%, so e_xy = +0.524: substitutes.

Conclusion. Firms use e_y to forecast growth of demand and e_xy to measure rivalry and set the prices of related products.

Q3 (10 marks). Define price elasticity of demand. Explain its types and determinants, describe the three methods of measuring it, and discuss its practical uses.

Introduction. Price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price. Since price and quantity move in opposite directions the value is negative, and we usually quote its absolute value |e|.

Types (Figure 2.1). (1) Perfectly inelastic, e = 0: vertical curve, as for a life-saving drug. (2) Inelastic, 0 < e < 1: steep curve, as for salt or electricity. (3) Unitary, e = 1: a rectangular hyperbola with constant outlay.

(4) Elastic, e > 1: flat curve, as for restaurant meals or a branded phone with many rivals. (5) Perfectly elastic, e = ∞: horizontal curve, as for one wheat farmer in a perfect market.

Determinants. Number and closeness of substitutes; necessity or luxury; share of income spent; time period (longer means more elastic); breadth of the market definition; and habit.

Measurement.

1. Total outlay method: compare P × Q before and after (Q1). Opposite movement means elastic.
2. Point method: e = (dQ/dP) × (P/Q). For Q = 100 − 2P, dQ/dP = −2, so e = −2 × 30/40 = −1.5 at P = 30 (elastic), −1 at P = 25 (midpoint, revenue 1,250 is maximum) and −0.667 at P = 20 (inelastic); see Figure 2.2.
3. Arc method: e = (ΔQ/Q̄) ÷ (ΔP/P̄), for example −1.174 for the move from (10, 100) to (8, 130).

Uses. (1) Pricing: cut price if demand is elastic, raise it if inelastic. (2) Taxation: tax inelastic goods such as fuel for steady revenue.

(3) Agriculture: a bumper harvest lowers farm income because food demand is inelastic (Plate 2.1). (4) Trade: devaluation helps only if elasticities sum to more than 1.

(5) Planning: income and cross elasticities guide investment and competition policy.

Elasticity	Price rise by 10%	Revenue effect	Best seller action
e = 2 (elastic)	quantity falls 20%	revenue falls	cut price
e = 1	quantity falls 10%	unchanged	hold price
e = 0.5 (inelastic)	quantity falls 5%	revenue rises	raise price

Conclusion. Elasticity turns the shape of the demand curve into a number that managers and governments can act on.