Welcome to Elasticity of Demand and Supply!
Welcome to one of the most exciting and practical topics in your CCEA AS Economics course: Elasticity! In earlier topics, you learned that when price goes up, demand falls and supply rises. But by how much? Does a 10% price hike cause sales to drop by a tiny trickle or a giant landslide?
That is exactly what elasticity measures: responsiveness. Think of an elastic band: some bands are super stretchy, while others are stiff and snap back with hardly any stretch at all. By the end of these notes, you will understand how consumers and firms stretch and react to changes in prices, incomes, and rival products.
Don't worry if the calculations seem intimidating at first! We will break down every single formula step by step with easy-to-remember rules and everyday examples.
1. Price Elasticity of Demand (PED)
What is PED?
Price Elasticity of Demand (PED) measures the responsiveness of the quantity demanded for a good or service to a change in its price.
The PED Formula
To calculate PED, use the percentage change formula:
\(PED = \frac{\% \text{ Change in Quantity Demanded}}{\% \text{ Change in Price}}\)
Where percentage change is calculated as:
\(\% \text{ Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\)
Step-by-Step Calculation Example
Imagine a local cinema raises the price of a movie ticket from £\(8\) to £\(10\). As a result, weekly attendance falls from \(1{,}000\) to \(700\) viewers.
Step 1: Calculate \(\% \text{ Change in Price}\):
\(\frac{10 - 8}{8} \times 100 = \frac{2}{8} \times 100 = +25\%\)
Step 2: Calculate \(\% \text{ Change in Quantity Demanded}\):
\(\frac{700 - 1000}{1000} \times 100 = \frac{-300}{1000} \times 100 = -30\%\)
Step 3: Put them into the formula:
\(PED = \frac{-30\%}{+25\%} = -1.2\)
Important Exam Note on the Minus Sign: Because of the Law of Demand (price and quantity move in opposite directions), PED is almost always a negative number. In CCEA exams, economists often ignore the minus sign and talk about the absolute value (e.g., treating \(-1.2\) as \(1.2\)). However, always show the minus sign in your working unless instructed otherwise!
The Five Numerical Ranges of PED
1. Perfectly Inelastic (\(PED = 0\)): Quantity demanded does not change at all when price changes. The demand curve is a vertical straight line. Example: Life-saving medicine like insulin.
2. Price Inelastic (\(0 < |PED| < 1\)): The percentage change in quantity demanded is smaller than the percentage change in price. Consumers are relatively unresponsive. Example: Petrol, milk, tap water.
3. Unitary Elastic (\(|PED| = 1\)): The percentage change in quantity demanded is exactly equal to the percentage change in price. Total spending remains unchanged.
4. Price Elastic (\(|PED| > 1\)): The percentage change in quantity demanded is greater than the percentage change in price. Consumers are very responsive to price changes. Example: Brand-name luxury clothes, specific chocolate brands.
5. Perfectly Elastic (\(|PED| = \infty\)): A tiny price increase causes quantity demanded to collapse to zero. The demand curve is horizontal.
Determinants of PED: Remember the Acronym "SPLAT"
Why are some goods elastic and others inelastic? Use the memory aid SPLAT:
• S - Substitutes: The more close substitutes available, the more elastic the demand (e.g., lots of fizzy drinks to choose from). If there are no substitutes, demand is inelastic.
• P - Percentage of Income: Goods that take up a huge chunk of your budget (like a car or a holiday) are price elastic. Cheap goods (like a box of matches or salt) are inelastic.
• L - Luxury vs. Necessity: Necessities (bread, heating) have inelastic demand; luxuries (sports cars, designer watches) have elastic demand.
• A - Addictive or Habit-Forming: Goods like cigarettes, alcohol, and caffeine create strong habits, making demand inelastic.
• T - Time Period: In the short run, consumers find it hard to change habits or find alternatives (inelastic). In the long run, consumers adjust and switch (more elastic).
PED and Total Revenue (TR)
Total Revenue (TR) is the total amount of money a business takes in from sales:
\(Total\ Revenue\ (TR) = Price\ (P) \times Quantity\ Demanded\ (Q)\)
Understanding PED is essential for business managers wanting to maximize revenue:
• If demand is INELASTIC (\(|PED| < 1\)):
Raising price leads to a proportionately smaller drop in quantity demanded. Total Revenue RISES.
Lowering price leads to a proportionately smaller rise in quantity demanded. Total Revenue FALLS.
Rule of thumb: To make more money from an inelastic good, raise the price!
• If demand is ELASTIC (\(|PED| > 1\)):
Raising price leads to a proportionately larger drop in quantity demanded. Total Revenue FALLS.
Lowering price leads to a proportionately larger rise in quantity demanded. Total Revenue RISES.
Rule of thumb: To make more money from an elastic good, cut the price!
• If demand is UNIT ELASTIC (\(|PED| = 1\)):
Any price change leaves total revenue completely unchanged. Total revenue is maximized at the point of unitary elasticity on a linear demand curve.
Key Takeaway for PED: PED tells us how sensitive buyers are to price changes. If \(|PED| > 1\), demand is elastic (cut price to raise revenue). If \(|PED| < 1\), demand is inelastic (raise price to raise revenue).
2. Income Elasticity of Demand (YED)
What is YED?
Income Elasticity of Demand (YED) measures the responsiveness of quantity demanded for a good to a change in consumer real income (\(Y\)).
The YED Formula
\(YED = \frac{\% \text{ Change in Quantity Demanded}}{\% \text{ Change in Real Income}}\)
Note: In economics, income is represented by the letter \(Y\).
Interpreting the Sign: Crucial Exam Skill!
Unlike PED, the sign (+ or -) in YED matters enormously. It tells you what type of good it is.
1. Normal Goods (\(YED > 0\), Positive Sign)
When income rises, demand increases. When income falls, demand decreases.
• Normal Necessity (\(0 < YED \le 1\)): Demand grows at a slower rate than income. Examples: basic groceries, electricity, tap water.
• Normal Luxury / Superior Good (\(YED > 1\)): Demand grows at a faster rate than income. Examples: foreign holidays, fine dining, designer clothing.
2. Inferior Goods (\(YED < 0\), Negative Sign)
When income rises, demand actually falls because consumers switch to higher-quality alternatives. Examples: supermarket value-brand baked beans, second-hand clothes, long-distance bus travel.
Why is YED Important to Businesses and Governments?
• Business Planning: During an economic boom (rising incomes), luxury goods producers can expand production, while inferior goods producers might struggle. In a recession (falling incomes), discount supermarkets and value brands thrive.
• Government Policy: Helps governments forecast indirect tax revenues (VAT) during different phases of the economic cycle.
Key Takeaway for YED: The plus or minus sign is everything! Positive means a normal good (necessity if between \(0\) and \(1\), luxury if \(>1\)). Negative means an inferior good.
3. Cross Elasticity of Demand (XED)
What is XED?
Cross Elasticity of Demand (XED) measures the responsiveness of quantity demanded for one good (Good A) to a change in the price of another good (Good B).
The XED Formula
\(XED = \frac{\% \text{ Change in Quantity Demanded of Good A}}{\% \text{ Change in Price of Good B}}\)
Interpreting the Sign of XED
Just like YED, the sign (+ or -) is vital in XED because it defines the economic relationship between two goods:
1. Substitutes (\(XED > 0\), Positive Sign)
These are competing goods in competitive demand. If the price of Good B rises, consumers switch to Good A, so demand for Good A increases.
• Example: If the price of Sony PlayStation consoles rises, the quantity demanded for Xbox consoles increases (\(XED > 0\)).
• Close substitutes have a large positive XED (e.g., \(+2.5\)). Weak substitutes have a small positive XED (e.g., \(+0.2\)).
2. Complements (\(XED < 0\), Negative Sign)
These are goods in joint demand that are bought together. If the price of Good B rises, people buy less of Good B, which also decreases demand for Good A.
• Example: If the price of printers rises, demand for printer ink cartridges falls (\(XED < 0\)).
• Strong complements have a large negative XED (e.g., \(-3.0\)). Weak complements have a small negative XED (e.g., \(-0.1\)).
3. Unrelated Goods (\(XED = 0\))
A change in the price of Good B has zero effect on the quantity demanded of Good A. Example: The price of golf clubs and the demand for milk.
Business Applications of XED
• Pricing Strategies: If a competitor lowers their price, knowing your positive XED helps you predict how many sales you might lose.
• Loss Leaders & Bundling: Supermarkets sell complementary goods together (e.g., selling turkeys cheaply at Christmas to boost high-margin cranberry sauce and stuffing sales).
Key Takeaway for XED: Positive (\(+\)) means Substitutes (they switch). Negative (\(-\)) means Complements (they go together). Zero (\(0\)) means Unrelated.
4. Price Elasticity of Supply (PES)
What is PES?
Price Elasticity of Supply (PES) measures the responsiveness of the quantity supplied of a good to a change in its own price.
The PES Formula
\(PES = \frac{\% \text{ Change in Quantity Supplied}}{\% \text{ Change in Price}}\)
Because higher prices incentivize producers to supply more (Law of Supply), PES is virtually always positive.
Numerical Ranges of PES
• Perfectley Inelastic Supply (\(PES = 0\)): Supply is completely fixed. A vertical supply line. Example: Stadium seating for a specific match, original artwork by Leonardo da Vinci.
• Inelastic Supply (\(0 < PES < 1\)): Percentage change in quantity supplied is less than the percentage change in price. Producers struggle to respond quickly to price rises. Example: Agricultural crops, fresh fish, nuclear power plants.
• Unitary Elastic Supply (\(PES = 1\)): Percentage change in quantity supplied is identical to percentage change in price. Any straight-line supply curve passing through the origin has \(PES = 1\).
• Elastic Supply (\(PES > 1\)): Percentage change in quantity supplied is greater than the percentage change in price. Producers can easily ramp up production. Example: Mass-manufactured items like plastic bottles or printed t-shirts.
• Perfectly Elastic Supply (\(PES = \infty\)): A horizontal supply curve where suppliers provide infinite amounts at a specific price, but none below it.
Determinants of PES
What makes a producer flexible and quick to react? Remember these key factors:
• Spare Capacity: If a factory is operating at only \(60\%\) capacity, it can easily boost output if price rises (Elastic). If working at \(100\%\) capacity, supply is Inelastic.
• Stocks / Inventories: Firms with large warehouses of non-perishable finished goods can release them onto the market instantly (Elastic). Perishable goods like fresh strawberries cannot be stored easily (Inelastic).
• Time Horizon: Supply is very inelastic in the immediate momentary run because production takes time. Over the long run, firms can build new factories and hire more workers, making supply much more elastic.
• Mobility of Factors of Production: If workers and machinery can easily be switched from making one product to another, supply is elastic.
• Barriers to Entry & Production Lead Time: Goods that take months or years to produce (like passenger planes or fine wine) have inelastic supply.
Key Takeaway for PES: PES is always positive. The more flexible and prepared a firm is (spare capacity, stockpiles, time to adjust), the more elastic its supply (\(PES > 1\)).
Quick Summary & Common Exam Traps
Master Summary Table of Elasticities
• PED (\(PED = \frac{\% \Delta QD}{\% \Delta P}\)): Usually negative. Value \(> 1\) = Elastic; Value \(< 1\) = Inelastic.
• YED (\(YED = \frac{\% \Delta QD}{\% \Delta Y}\)): Positive = Normal good (\(>1\) luxury, \(0\text{ to }1\) necessity); Negative = Inferior good.
• XED (\(XED = \frac{\% \Delta QD_A}{\% \Delta P_B}\)): Positive = Substitutes; Negative = Complements; Zero = Unrelated.
• PES (\(PES = \frac{\% \Delta QS}{\% \Delta P}\)): Always positive. Value \(> 1\) = Elastic; Value \(< 1\) = Inelastic.
Top 3 Common Mistakes to Avoid:
Mistake 1: Putting the price change on top of the formula. Correction: Always put the Quantity change on TOP and the Price or Income change on the BOTTOM (\(\frac{Q}{P}\) or \(\frac{Q}{Y}\)).
Mistake 2: Forgetting that regular changes are not percentage changes. If price rises from £\(10\) to £\(12\), that is a £\(2\) increase, but a \(\frac{2}{10} \times 100 = 20\%\) increase!
Mistake 3: Confusing the signs for YED and XED. Remember: In YED, minus means inferior. In XED, minus means complementary.