Price Elasticity of Demand (PED) & Price Elasticity of Supply (PES) Calculations
While the laws of demand and supply tell us the direction in which quantity changes when price changes, Price Elasticity of Demand (PED) and Price Elasticity of Supply (PES) measure the responsiveness (sensitivity) of quantity demanded or supplied to a change in price. Both elasticities are calculated using the exact same structure: $\text{Elasticity} = (\% \text{ Change in Quantity}) \div (\% \text{ Change in Price})$ (Always 'Quantity on top of Price'). Understanding whether a product is price elastic ($|\text{PED}| > 1$, flat curve) or price inelastic ($|\text{PED}| < 1$, steep curve) is essential for businesses deciding whether to raise or lower prices to maximise Total Revenue ($\text{TR} = P \times Q$), and for governments deciding which goods to tax.
- Price Elasticity of Demand (PED) Formula
- Measures the responsiveness of quantity demanded to a change in price. Formula: $\text{PED} = \frac{\% \text{ Change in Quantity Demanded}}{\% \text{ Change in Price}}$. Because price and quantity demanded move in opposite directions, PED is always negative (though economists often compare the magnitude $|\text{PED}|$).
- Price Elastic vs Price Inelastic Demand
- 1. Price Elastic Demand ($|\text{PED}| > 1$, e.g., $\text{PED} = -2.4$): A change in price leads to a more than proportionate percentage change in quantity demanded; the demand curve is shallow/flat. 2. Price Inelastic Demand ($0 < |\text{PED}| < 1$, e.g., $\text{PED} = -0.3$): A change in price leads to a less than proportionate percentage change in quantity demanded; the demand curve is steep. 3. Unitary Elastic ($|\text{PED}| = 1$): Total revenue stays constant when price changes. 4. Perfectly Inelastic ($\text{PED} = 0$, vertical line) vs Perfectly Elastic ($\text{PED} = \infty$, horizontal line).
- Determinants of PED & Total Revenue ($\text{TR} = P \times Q$)
- Demand is price inelastic when a good has few close substitutes (e.g., Apple iPhone ecosystem, mains water), is a necessity or habit-forming/addictive (petrol, cigarettes, coffee), takes up a tiny proportion of income, or is in the short run. To increase Total Revenue ($\text{TR} = \text{Price} \times \text{Quantity}$): Increase price if demand is inelastic; Decrease price if demand is elastic.
Price Elasticity of Demand (PED) & Price Elasticity of Supply (PES) Calculations: Supply, Demand, Elasticity & Welfare Shift Lab
Trigger a market shock or adjust price elasticity below to watch the curves shift and inspect the new equilibrium price, output, and welfare triangles.
Baseline Free-Market Equilibrium
Market clears at P₁, Q₁ where Quantity Demanded equals Quantity Supplied (allocative efficiency; social welfare is maximised).
Key Concepts & Exam Definitions (6)
- Price Elasticity of Demand (PED) Formula
- Measures the responsiveness of quantity demanded to a change in price. Formula: $\text{PED} = \frac{\% \text{ Change in Quantity Demanded}}{\% \text{ Change in Price}}$. Because price and quantity demanded move in opposite directions, PED is always negative (though economists often compare the magnitude $|\text{PED}|$).
- Price Elastic vs Price Inelastic Demand
- 1. Price Elastic Demand ($|\text{PED}| > 1$, e.g., $\text{PED} = -2.4$): A change in price leads to a more than proportionate percentage change in quantity demanded; the demand curve is shallow/flat. 2. Price Inelastic Demand ($0 < |\text{PED}| < 1$, e.g., $\text{PED} = -0.3$): A change in price leads to a less than proportionate percentage change in quantity demanded; the demand curve is steep. 3. Unitary Elastic ($|\text{PED}| = 1$): Total revenue stays constant when price changes. 4. Perfectly Inelastic ($\text{PED} = 0$, vertical line) vs Perfectly Elastic ($\text{PED} = \infty$, horizontal line).
- Determinants of PED & Total Revenue ($\text{TR} = P \times Q$)
- Demand is price inelastic when a good has few close substitutes (e.g., Apple iPhone ecosystem, mains water), is a necessity or habit-forming/addictive (petrol, cigarettes, coffee), takes up a tiny proportion of income, or is in the short run. To increase Total Revenue ($\text{TR} = \text{Price} \times \text{Quantity}$): Increase price if demand is inelastic; Decrease price if demand is elastic.
- Price Elasticity of Supply (PES) Formula
- Measures the responsiveness of quantity supplied by producers to a change in price. Formula: $\text{PES} = \frac{\% \text{ Change in Quantity Supplied}}{\% \text{ Change in Price}}$. Because higher prices incentivize firms to supply more, PES is always positive ($+$). If $\text{PES} > 1$, supply is price elastic (steepness is shallow); if $0 < \text{PES} < 1$, supply is price inelastic (steep curve).
- Determinants of PES (Short Run vs Long Run)
- Supply is price elastic ($\text{PES} > 1$) when firms have: 1. Plenty of spare capacity (idle machines/workers ready to switch on). 2. High levels of unsold stocks/inventories in warehouses (durable manufactured goods). 3. Short, fast production times. 4. Mobile factors of production. Supply is price inelastic ($\text{PES} < 1$) for agricultural harvests (takes a year to grow wheat/cocoa), housing (takes years to get planning permission and build houses), and stadium/concert seats (fixed capacity, $\text{PES} = 0$).
- Elasticity & Government Indirect Taxes / Subsidies
- Governments place indirect taxes (excise duties) on demerit goods with price inelastic demand (such as tobacco, alcohol, and petrol/fuel duty). Because demand is inelastic, consumers continue buying the product despite the higher price: this is highly effective at raising huge tax revenue for the government, but less effective at reducing consumption unless the tax is very large.
Quick-Fire Flashcards (6)
Click any card to check the answer, then mark it as Known to track your progress.
State the formulas for Price Elasticity of Demand (PED) and Price Elasticity of Supply (PES).
A cinema raises ticket prices from £10 to £12, and weekly ticket sales fall from 2,000 to 1,400. Calculate the PED and state whether demand is elastic or inelastic.
In the cinema question above, what happened to the cinema's Total Revenue when it raised the price from £10 to £12, and why?
List four factors that determine the Price Elasticity of Demand (PED) of a good.
Why is the Price Elasticity of Supply (PES) of fresh strawberries much lower (more inelastic) than the PES of plastic biro pens?
Why does the government tax cigarettes and petrol so heavily, and what is the trade-off?
Exam-Style Questions & Mark Schemes (4)
Write or think through your answer first, then click Check Mark Scheme to see the exact points examiners award marks for.
- Q1
A coffee shop increases the price of its flat white coffee from £3.00 to £3.60. As a result, daily sales fall from 500 cups to 450 cups. (a) Calculate the Price Elasticity of Demand (PED) for the coffee. (b) Calculate the change in the coffee shop's daily Total Revenue and explain why Total Revenue changed in this direction. [5 marks]
Click “Check Mark Scheme” to compare your answer, 1. (a) Calculate the percentage change in price: ((3.60 - 3.00) ÷ 3.00) x 100 = (0.60 ÷ 3.00) x 100 = +20% [1 mark]. 2. Calculate the percentage change in quantity demanded: ((450 - 500) ÷ 500) x 100 = (-50 ÷ 500) x 100 = -10% [1 mark]. 3. Calculate PED: PED = -10% ÷ +20% = -0.5 [1 mark]. 4. (b) Old Total Revenue = £3.00 x 500 = £1,500; New Total Revenue = £3.60 x 450 = £1,620, so daily Total Revenue increased by £120 [1 mark]. 5. Explanation: Because demand for coffee is price inelastic (|PED| = 0.5 < 1, due to habitual/addictive consumption and brand loyalty), the 10% drop in quantity sold was proportionately smaller than the 20% increase in price, raising Total Revenue [1 mark].
- Q2
When the market price of hand sanitiser rose by 40% at the start of a health scare, Manufacturer A increased its weekly quantity supplied from 10,000 bottles to 11,500 bottles, while six months later Manufacturer A was able to supply 22,000 bottles at that same price. Calculate the short-run and long-run Price Elasticity of Supply (PES) and explain two reasons why PES increased over time. [5 marks]
Click “Check Mark Scheme” to compare your answer, 1. Short-run % change in quantity supplied = ((11,500 - 10,000) ÷ 10,000) x 100 = +15%, so short-run PES = +15% ÷ +40% = +0.375 (price inelastic supply) [1 mark]. 2. Long-run % change in quantity supplied = ((22,000 - 10,000) ÷ 10,000) x 100 = +120% [1 mark]. 3. Long-run PES = +120% ÷ +40% = +3.0 (price elastic supply) [1 mark]. 4. Reason 1 (Spare capacity & Stocks): Immediately after the price surge, the factory was already running near full capacity and warehouse stocks quickly ran out, so output could only rise by 15% [1 mark]. 5. Reason 2 (Factor mobility over time): Over six months (the long run), the manufacturer had time to buy and install new bottling machinery, build factory extensions, and hire/train extra shift workers, making supply much more elastic [1 mark].
- Q3
A train operating company wants to increase its total ticket revenue. It sells two types of tickets: Peak-time commuter tickets (8:00 am Monday-Friday) and Off-peak leisure tickets (weekends). Evaluate how the train company should use Price Elasticity of Demand (PED) to set the prices of these two ticket types. [6 marks]
Click “Check Mark Scheme” to compare your answer, 1. Peak-time commuter tickets have price inelastic demand (|PED| < 1) because commuters must arrive at work by 9:00 am (it is a necessity) and have very few substitutes at that specific time (roads are congested and parking is expensive) [1 mark]. 2. Therefore, the train company should increase the price of Peak-time commuter tickets: the percentage fall in passenger numbers will be much smaller than the percentage rise in fare, causing Total Revenue from commuters to increase [1 mark]. 3. Off-peak leisure tickets have price elastic demand (|PED| > 1) because weekend leisure travel is a non-essential luxury and travellers have many close substitutes (driving by car, taking a coach, travelling at a different time, or staying home) [1 mark]. 4. Therefore, the train company should decrease the price of Off-peak leisure tickets (offer discounted savers/railcards): the percentage increase in leisure passengers will be much greater than the percentage fare cut, increasing Total Revenue and filling otherwise empty seats [1 mark]. 5. Evaluation (Long-run PED & Working from home): However, if peak fares are raised too aggressively, demand becomes more elastic in the long run as commuters switch to working from home, cycling, or finding jobs closer to home [1 mark]. 6. Evaluation (Government regulation): Furthermore, many peak commuter rail fares in the UK are regulated by the government (capped in line with inflation) to prevent monopoly exploitation and road congestion, limiting how much the firm can raise peak prices [1 mark].
- Q4
Explain why the price of tickets for a Cup Final at a 90,000-seat stadium or the price of new houses in the UK is largely determined by changes in demand, referring to Price Elasticity of Supply (PES) in your answer. [4 marks]
Click “Check Mark Scheme” to compare your answer, 1. A football stadium has a fixed maximum physical capacity of 90,000 seats; no matter how high the ticket price rises, the stadium cannot supply a single extra seat, so supply is perfectly price inelastic (PES = 0, a vertical supply curve) [1 mark]. 2. Similarly, the supply of new houses in the UK is highly price inelastic (PES < 1) because of strict greenbelt planning laws, a shortage of skilled bricklayers, and the long time period (1-2 years) required to build a house [1 mark]. 3. Because the supply curve is vertical or very steep, producers cannot respond to rising demand by significantly increasing quantity supplied [1 mark]. 4. Consequently, when demand shifts to the right (due to cup final excitement or lower mortgage rates/population growth), almost the entire market adjustment occurs via a sharp increase in equilibrium price rather than an increase in quantity [1 mark].
Common Exam Questions (4)
How do you remember whether Quantity or Price goes on the top of the PED and PES formulas?
Think of a 'Queen on a Pony' (Q over P): Percentage change in quantity ($Q$) always goes in the numerator (top), and Percentage change in price ($P$) always goes in the denominator (bottom). Remember that to calculate any percentage change first, use: $\% \text{ Change} = ((\text{New} - \text{Original}) \div \text{Original}) \times 100$.
How do you interpret the number you get for PED or PES (Elastic vs Inelastic)?
Note that PED is always negative (because of the inverse law of demand), while PES is always positive. Look at the size (absolute value) of the number compared to 1: 1. If $|\text{Elasticity}| > 1$ (e.g., -2.5 or +1.8), demand/supply is price elastic (quantity changes by a larger percentage than price; shallow/flat curve). 2. If $|\text{Elasticity}| < 1$ (between 0 and 1, e.g., -0.4 or +0.3), demand/supply is price inelastic (quantity changes by a smaller percentage than price; steep curve). 3. If $|\text{Elasticity}| = 1$, it is UNITARY elastic; if $0$, it is perfectly inelastic (vertical line).
How should a business change its price to increase Total Revenue when demand is Elastic vs Inelastic?
This is the #1 6-mark business application question in GCSE Economics. 1. If demand is price inelastic ($|\text{PED}| < 1$, e.g., addictive goods, petrol, peak rail tickets, branded necessities): the firm should raise its price. Because consumers are unresponsive, the % drop in quantity sold is much smaller than the % rise in price, so Total Revenue ($P \times Q$) increases. 2. If demand is price elastic ($|\text{PED}| > 1$, e.g., luxury goods or goods with lots of close substitutes): the firm should lower its price (run a sale). The % surge in quantity sold is much larger than the % price cut, so Total Revenue increases.
What are the main factors that determine PED and PES?
Determinants of PED (mnemonic 'SPLAT'): 1. Substitutes (more close substitutes = more elastic). 2. Proportion of income spent (expensive cars = elastic; cheap matches/salt = inelastic). 3. Luxury vs Necessity (luxuries = elastic; necessities/addictive goods like tobacco = inelastic). 4. Time period (more elastic in the long run as consumers find alternatives). Determinants of PES (mnemonic 'PSSST'): Production lag/Perishability, Stocks/inventories available, Spare capacity in factories, Substitutability of factors of production, and Time (agricultural crops are inelastic in the short run because they take months to grow).
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