factors affecting: price elasticity of demand

Cambridge AS & A‑Level Economics (9708) – Elasticities of Demand and Supply

1. Learning Objectives

• Recall the basic demand‑supply model and the distinction between movements along a curve and shifts of the curve.
• Define price, income and cross‑elasticities of demand and price elasticity of supply.
• Derive and apply the point‑elasticity and arc‑elasticity (mid‑point) formulas.
• Identify and explain the determinants of price elasticity of demand (PED) and price elasticity of supply (PES).
• Calculate PED, YED, XED and PES from tabular data and interpret the results.
• Analyse the impact of elasticities on total‑revenue, consumer and producer surplus, and on government policy.
• Develop exam‑ready responses for typical AS & A‑Level questions.

2. Why Elasticities Matter – A Syllabus‑Wide Link

Elasticities measure the responsiveness of quantities to changes in price, income or related‑good prices. They are a quantitative expression of the margin – the idea that economic agents make decisions by comparing marginal benefits and marginal costs. Because the price system allocates scarce resources, understanding how quantity reacts to price signals is essential for:

• Evaluating the efficiency of market outcomes (Syllabus 2.1).
• Assessing the welfare effects of government intervention (Syllabus 3.1‑3.3).
• Linking micro‑behaviour to macro‑policy (e.g., labour‑supply elasticity in wage‑setting, export‑demand elasticity in balance‑of‑payments – Syllabus 4‑6).

3. The Demand‑Supply Framework (Syllabus 2.1)

Demand curve: Quantity of a good that consumers are willing and able to buy at each price, ceteris paribus (c.p.). Downward‑sloping because of the substitution and income effects.

Supply curve: Quantity that producers are willing and able to sell at each price, c.p. Upward‑sloping because higher prices raise profitability and attract resources.

Market equilibrium: Intersection of demand and supply (Q*, P*). At this price quantity demanded equals quantity supplied.

Movements vs. shifts:

• Movement along a curve – caused by a change in the good’s own price.
• Shift of the curve – caused by a change in any other determinant (income, tastes, input prices, technology, etc.).

4. Elasticities – Definitions & Formulas (Syllabus 2.2)

Elasticity	Variable that changes	Formula (percentage‑change form)
Price elasticity of demand (PED)	Quantity demanded ↔ own price	$$\varepsilon_{p}^{d}= \frac{\%\Delta Q_{d}}{\%\Delta P} =\frac{\Delta Q_{d}}{\Delta P}\times\frac{P}{Q_{d}}$$
Income elasticity of demand (YED)	Quantity demanded ↔ consumer income	$$\varepsilon_{y}= \frac{\%\Delta Q_{d}}{\%\Delta Y} =\frac{\Delta Q_{d}}{\Delta Y}\times\frac{Y}{Q_{d}}$$
Cross‑elasticity of demand (XED)	Quantity demanded of good x ↔ price of good y	$$\varepsilon_{xy}= \frac{\%\Delta Q_{x}}{\%\Delta P_{y}} =\frac{\Delta Q_{x}}{\Delta P_{y}}\times\frac{P_{y}}{Q_{x}}$$
Price elasticity of supply (PES)	Quantity supplied ↔ own price	$$\varepsilon_{p}^{s}= \frac{\%\Delta Q_{s}}{\%\Delta P} =\frac{\Delta Q_{s}}{\Delta P}\times\frac{P}{Q_{s}}$$

4.1 Point (Calculus) Elasticity – A‑Level Extension

If the demand (or supply) curve is expressed as a continuous function, the exact elasticity at price P is:

$$\varepsilon_{p}^{d}= \frac{dQ}{dP}\times\frac{P}{Q}\qquad \varepsilon_{p}^{s}= \frac{dQ_{s}}{dP}\times\frac{P}{Q_{s}}$$

This gives the elasticity at a single point, useful when a functional form is supplied in a data‑response.

4.2 Arc (Mid‑point) Elasticity – Preferred for exam data‑responses

$$\varepsilon_{arc}= \frac{\displaystyle\frac{Q_{2}-Q_{1}}{(Q_{1}+Q_{2})/2}} {\displaystyle\frac{P_{2}-P_{1}}{(P_{1}+P_{2})/2}}$$

The midpoint denominator removes the bias that arises from the direction of change.

5. Interpreting Elasticities

• |ε| > 1 → elastic (quantity changes proportionally more than price).
• |ε| < 1 → inelastic (quantity changes proportionally less than price).
• |ε| = 1 → unit‑elastic.
• YED: ε > 0 = normal good; ε < 0 = inferior good; ε > 1 = luxury; 0 < ε < 1 = necessity.
• XED: ε > 0 = substitutes; ε < 0 = complements; ≈ 0 = unrelated.

6. Determinants of Price Elasticity of Demand (PED) (Syllabus 2.3)

Determinant	Typical effect on |PED|	Reason
Availability of close substitutes	Higher elasticity	Consumers can switch easily when price rises.
Proportion of consumer’s income spent on the good	Higher elasticity for high‑budget items	A given price change represents a larger share of the budget.
Nature of the good (necessity vs. luxury)	Necessities → low elasticity; Luxuries → high elasticity	Consumers are less willing to cut back on essentials.
Definition of the market (broad vs. narrow)	Narrow definition → higher elasticity	Specific brands or varieties have more close substitutes than an entire product category.
Time horizon (short‑run vs. long‑run)	Long‑run elasticity > short‑run elasticity	More time allows habit adjustment and search for alternatives.
Addiction or habit formation	Lower elasticity	Strong preferences dampen response to price changes.

7. Determinants of Price Elasticity of Supply (PES) (Syllabus 2.4)

Determinant	Typical effect on |PES|	Reason
Availability of inputs	Higher elasticity when inputs are abundant	Producers can increase output quickly without large cost spikes.
Spare production capacity	Higher elasticity if firms have idle plant or labour	Output can be raised with little extra cost.
Time horizon	Long‑run elasticity > short‑run elasticity	Firms can adjust plant size, adopt new technology or relocate.
Complexity of the production process	Simple, flexible processes → higher elasticity	Complex, specialised processes constrain rapid output changes.
Mobility of factors of production	Higher elasticity when labour and capital can move easily between industries	Resources can be re‑allocated to respond to price signals.

8. Consumer and Producer Surplus – Elasticity Link (Syllabus 2.5)

• Consumer surplus (CS) – the area between the demand curve and the market price, up to the quantity purchased.
• Producer surplus (PS) – the area between the market price and the supply curve, up to the quantity sold.
• When a price change occurs, the magnitude of the change in CS or PS depends on the elasticity of the relevant curve:
  • If demand is elastic, a price rise causes a large fall in quantity, so CS falls sharply.
  • If supply is inelastic, a price rise leads to a small increase in quantity, so PS rises only modestly.

8.1 Worked Data‑Response – Change in Surplus after a Tax

Price (£)	Quantity demanded (units)
8	1 200
10	1 000

Suppose the government imposes a £2 per‑unit tax, shifting the supply curve upward by £2. Using the arc‑elasticity for demand (calculated from the table) we find |PED|≈1.1 (elastic). The tax therefore reduces CS substantially, while the tax revenue (price × quantity) is relatively small because quantity falls sharply. PS also falls, but the loss is shared between producers and consumers according to the relative elasticities (see AO‑3 evaluation).

9. Government Micro‑Intervention and Elasticities (Syllabus 3.1‑3.3)

Elasticities are central to evaluating the welfare impact of:

• Taxes – incidence depends on the relative PED and PES. The side with the more inelastic curve bears a larger burden.
• Subsidies – the dead‑weight loss is larger when either demand or supply is elastic.
• Price ceilings and floors – the size of the resulting surplus or shortage is determined by the slopes of the curves at the regulated price.

When answering an exam question, always:

1. State the relevant elasticity(s).
2. Explain how they affect the incidence or dead‑weight loss.
3. Evaluate the policy by weighing efficiency against equity (AO‑3).

10. Macro‑Economic Connections (Syllabus 4‑6)

11. A‑Level Preview – Extending Elasticity Concepts

For mixed AS/A‑Level classes, the following extensions are useful:

• Utility theory – marginal utility curves underpin the derivation of the demand curve; a flatter marginal‑utility curve corresponds to a more elastic demand.
• Market failure – when a negative externality is present, the social cost curve is steeper than the private supply curve, making the socially optimal tax depend on the PED of the affected good.
• Labour‑market elasticity – the responsiveness of labour supply to wage changes is crucial when evaluating policies such as welfare reforms or immigration.
• Growth and development – the elasticity of factor demand influences how quickly an economy can expand production capacity in response to investment.

12. Worked Data‑Response Examples (Syllabus 2.5)

12.1 Example 1 – Calculating PED (arc formula)

Price (£)	Quantity demanded (units)
12	800
15	650

Step 1 – Mid‑point percentages:

$$\Delta P = 3,\qquad \frac{\Delta P}{P_{mid}} = \frac{3}{13.5}=0.222$$ $$\Delta Q = -150,\qquad \frac{\Delta Q}{Q_{mid}} = \frac{-150}{725}= -0.207$$

Step 2 – PED:

$$\varepsilon_{p}^{d}= \frac{-0.207}{0.222}= -0.93$$

Interpretation: demand is slightly inelastic; a 1 % price rise reduces quantity demanded by 0.93 % and total revenue falls.

12.2 Example 2 – Calculating YED

Income (£ 000)	Quantity demanded of organic fruit (kg)
30	1 200
36	1 560

$$\varepsilon_{y}= \frac{\frac{1\,560-1\,200}{(1\,560+1\,200)/2}}{\frac{36-30}{(36+30)/2}} = \frac{360/1\,380}{6/33}= \frac{0.261}{0.182}= 1.44$$

Interpretation: organic fruit is a luxury good (YED > 1); demand rises faster than income.

12.3 Example 3 – Calculating XED

Price of coffee (£)	Quantity of tea demanded (cups)
2.00	1 000
2.50	1 300

$$\varepsilon_{xy}= \frac{\frac{1\,300-1\,000}{(1\,300+1\,000)/2}}{\frac{2.50-2.00}{(2.50+2.00)/2}} = \frac{300/1\,150}{0.50/2.25}= \frac{0.261}{0.222}= 1.18$$

Positive XED indicates tea and coffee are substitutes; the magnitude suggests a fairly strong substitution effect.

12.4 Example 4 – Calculating PES (arc formula)

Price (£ per unit)	Quantity supplied (units)
4	500
5	800

$$\varepsilon_{p}^{s}= \frac{\frac{800-500}{(800+500)/2}}{\frac{5-4}{(5+4)/2}} = \frac{300/650}{1/4.5}= \frac{0.462}{0.222}= 2.08$$

Supply is elastic; producers can increase output substantially when price rises.

13. Diagrammatic Guidance

• Demand curve with elasticity zones: draw a single downward‑sloping curve, shade the upper‑left (elastic), middle (unit‑elastic) and lower‑right (inelastic) sections. Add arrows to show total‑revenue behaviour in each zone.
• PED & PES on the same graph: plot demand and supply, then illustrate a rightward shift of supply. Use the steepness of each curve to explain why the price change is larger when demand is inelastic and supply is elastic (and vice‑versa).
• Point‑elasticity diagram: pick a point (P₀,Q₀) on a smooth demand curve, draw the tangent, label the slope dQ/dP and write the formula ε = (dQ/dP)(P/Q).
• Surplus diagram with a tax: show the original equilibrium, the upward shift of supply by the tax amount, and the resulting dead‑weight loss triangle. Annotate the areas representing CS, PS and tax revenue.

14. Exam Technique – “What to Do” Checklist

1. Read the question carefully. Identify which elasticity is required and whether the task is calculation, explanation or evaluation.
2. Select the appropriate formula. Use the midpoint (arc) formula for tabular data; use the point‑elasticity formula only when a functional form is given.
3. Show every step. Write down the numerator, denominator, mid‑point values and the final elasticity – this secures marks for method.
4. Interpret sign and magnitude. State “elastic”, “inelastic” or “unit‑elastic” and link to total‑revenue, CS or PS.
5. Connect to determinants. Explain why the calculated elasticity is likely high or low (e.g., presence of substitutes, time‑frame).
6. Evaluate policy implications. When the question involves a tax, subsidy, price ceiling or floor, discuss incidence, dead‑weight loss and equity using the relevant elasticities (AO‑3).
7. Conclude succinctly. End with a sentence that directly answers the command term (e.g., “In summary, the tax will fall mainly on consumers because demand is relatively inelastic”).

15. Summary

• Elasticities quantify the responsiveness of quantity demanded or supplied to changes in price, income or related‑good prices.
• Price elasticity of demand is shaped by substitutes, income share, necessity vs. luxury, market definition, time and habit.
• Price elasticity of supply depends on input availability, spare capacity, production flexibility, time and factor mobility.
• Point‑elasticity (calculus) gives the exact value at a single price; the arc (mid‑point) formula is the standard tool for exam data‑responses.
• Understanding elasticities is essential for analysing total‑revenue, consumer and producer surplus, and for evaluating government interventions and macro‑policy outcomes.