Welcome to the World of Elasticities!
Hello future economist! This chapter is one of the most practical and useful parts of market analysis. We are moving beyond simply knowing that demand falls when price rises; we are learning how much it falls. Elasticities are measurement tools—they tell us about the responsiveness, or 'stretchiness', of demand when factors like price or income change.
Why is this important? Because understanding elasticity is the secret weapon for businesses deciding how to price a product, and for governments deciding which goods to tax!
Don't worry if the formulas look scary at first. Elasticity is just a ratio of two percentage changes, and we'll break down how to interpret every number.
1. Price Elasticity of Demand (PED)
Price Elasticity of Demand (PED) measures the responsiveness of the quantity demanded of a good to a change in its own price.
The PED Formula: Calculating Responsiveness
We calculate PED using the following ratio:
$$PED = \frac{\text{Percentage change in Quantity Demanded (QD)}}{\text{Percentage change in Price (P)}}$$
$$\text{or}$$
$$PED = \frac{\% \Delta Q_D}{\% \Delta P}$$
Key Point: Using the Absolute Value
Since the demand curve is almost always downward sloping (Law of Demand), the PED calculation will usually give you a negative number (Price goes up, Quantity goes down). To make interpretation easier, economists usually ignore the negative sign and use the absolute value. We focus only on the magnitude of the number.
Interpreting the PED Coefficient
The value of the coefficient tells us exactly how "stretchy" demand is:
- Elastic Demand: \(|PED| > 1\)
- Inelastic Demand: \(|PED| < 1\)
- Unitary Elasticity: \(|PED| = 1\)
- Perfectly Inelastic Demand: \(|PED| = 0\)
- Perfectly Elastic Demand: \(|PED| = \infty\) (Infinity)
This means Quantity Demanded changes by a larger percentage than the price change. The product is highly responsive to price changes. Example: If price rises by 10%, demand falls by 20%.
This means Quantity Demanded changes by a smaller percentage than the price change. The product is not very responsive to price changes. Example: If price rises by 10%, demand only falls by 5%.
The percentage change in quantity demanded is exactly equal to the percentage change in price. (A rare, theoretical benchmark).
Quantity demanded does not change at all, regardless of price changes. (Think life-saving medicine).
A tiny change in price causes demand to collapse to zero. (Commonly used in pure competition models).
Memory Aid (The Slope Test): Look at the demand curve. A flatter curve looks more "stretchy" or elastic. A steeper curve looks more "stiff" or inelastic.
The Crucial Link: PED and Total Revenue (TR)
The main reason firms care about PED is its relationship with Total Revenue (TR) (which is also the consumer's total expenditure).
$$TR = \text{Price} \times \text{Quantity Sold}$$
If a firm wants to increase its revenue, should it raise or lower the price?
1. If Demand is Elastic (\(|PED| > 1\)):
- If you lower the price, the resulting increase in quantity demanded will be proportionally larger, so TR rises.
- If you raise the price, the resulting fall in quantity demanded will be proportionally larger, so TR falls.
Think of expensive gadgets: a small price cut attracts masses of new buyers.
2. If Demand is Inelastic (\(|PED| < 1\)):
- If you raise the price, the resulting decrease in quantity demanded will be proportionally smaller, so TR rises.
- If you lower the price, the resulting increase in quantity demanded will be proportionally smaller, so TR falls.
Think of essential petrol: you can raise the price, and people still have to buy nearly the same amount to drive to work.
Quick Review: PED
PED is always positive (using absolute value). If PED > 1, lowering price increases TR. If PED < 1, raising price increases TR.
Factors Influencing Price Elasticity of Demand (Determinants)
What makes demand for a product elastic or inelastic?
- Availability of Substitutes (Most Important Factor):
The more substitutes available (e.g., different brands of breakfast cereal), the more elastic demand is. If the price of one cereal rises, consumers easily switch. If there are few substitutes (e.g., tap water), demand is inelastic.
- Necessity vs. Luxury:
Necessities (e.g., toothpaste, basic food) have highly inelastic demand because you need them regardless of price. Luxuries (e.g., yachts, holidays) tend to have highly elastic demand.
- Proportion of Income Spent:
If the good takes up a large percentage of your income (e.g., a car), demand is elastic, as a small price change has a big impact on your budget. If it's a tiny percentage (e.g., a box of matches), demand is inelastic.
- Time Horizon:
In the short run, demand is often more inelastic because consumers don't have time to adjust their habits or find substitutes. In the long run, they can adjust (e.g., switching from petrol cars to electric cars if petrol prices stay high), making demand more elastic.
- Habit-forming Goods (Addiction):
Goods that are addictive (e.g., tobacco, certain prescription drugs) often have very inelastic demand because consumers cannot easily stop buying them.
2. Income Elasticity of Demand (YED)
Income Elasticity of Demand (YED) measures the responsiveness of the quantity demanded of a good to a change in consumer income (Y).
The YED Formula:
$$YED = \frac{\text{Percentage change in Quantity Demanded (QD)}}{\text{Percentage change in Income (Y)}}$$
$$YED = \frac{\% \Delta Q_D}{\% \Delta Y}$$
The Significance of the Sign
Unlike PED, we must keep the sign for YED! The sign tells us the relationship between the good and income.
Interpreting the YED Coefficient
YED classifies goods based on how demand changes when we get richer (or poorer):
- Normal Goods: \(YED > 0\) (Positive)
- Necessity Goods (Income Inelastic): \(0 < YED < 1\)
Demand rises slower than the rise in income. We need these goods, but we don't buy twice as much bread just because our salary doubled. (Example: Basic groceries, utility services.)
- Luxury Goods (Income Elastic): \(YED > 1\)
Demand rises faster than the rise in income. These are "treats" we splash out on when we earn more. (Example: Designer clothing, international holidays.)
- Inferior Goods: \(YED < 0\) (Negative)
As income rises, demand for the good also rises. This is the typical relationship.
As income rises, demand for the good falls. Consumers swap these cheaper options for better quality alternatives when they can afford to. (Example: Generic supermarket brands, public bus transport instead of a taxi.)
Did you know? A product can be classified as normal for a low-income family but become inferior once that family becomes very wealthy (e.g., they stop buying fast food).
Quick Review: YED Sign
The sign is your key:
POSITIVE (+) = Normal Good (Demand rises with income).
NEGATIVE (-) = Inferior Good (Demand falls with income).
3. Cross Elasticity of Demand (XED)
Cross Elasticity of Demand (XED) measures the responsiveness of the quantity demanded of one good (Good A) to a change in the price of another good (Good B).
The XED Formula:
$$XED = \frac{\text{Percentage change in Quantity Demanded of Good A}}{\text{Percentage change in Price of Good B}}$$
$$XED = \frac{\% \Delta Q_D \text{ of A}}{\% \Delta P \text{ of B}}$$
The Significance of the Sign (Again!)
Just like YED, the sign of XED is crucial. It tells us the economic relationship between the two goods (A and B).
Interpreting the XED Coefficient
XED helps firms understand which products are their rivals (substitutes) or their partners (complements).
- Substitutes: \(XED > 0\) (Positive)
- Complements: \(XED < 0\) (Negative)
- Unrelated Goods: \(XED = 0\)
If the price of Good B rises, the demand for Good A rises (consumers switch). The goods compete with each other.
Example: If the price of Pepsi goes up, the demand for Coke goes up.
Note on Strength: The higher the positive XED value, the closer the substitutes are (e.g., Coke and Pepsi have a very high XED, whereas Coke and Milk have a low XED).
If the price of Good B rises, the demand for Good A falls (consumers stop buying both). The goods are consumed together.
Example: If the price of printers increases, the demand for printer ink cartridges falls.
Note on Strength: The larger the negative XED value, the stronger the complementary relationship.
A change in the price of Good B has no impact on the demand for Good A. (Example: The price of car tyres changes the demand for umbrellas.)
Analogy: XED as a Social Network Map
Imagine you change the price of Product B. If Product A reacts positively (more demand for A), they are Substitutes (like rivals). If Product A reacts negatively (less demand for A), they are Complements (like partners).
Quick Review: XED Sign
POSITIVE (+) = Substitutes (Rivals).
NEGATIVE (-) = Complements (Partners).
Common Mistakes to Avoid in Calculations
Don't worry if this seems tricky at first, calculation requires careful attention to detail!
Mistake 1: Getting the order wrong
Always use the *percentage change in quantity* as the numerator (top number) and the *percentage change in the factor* (Price, Income, or Price of other good) as the denominator (bottom number).
Mistake 2: Confusing absolute value and sign
PED: Use the absolute value (ignore the minus sign). The number tells you if it's elastic or inelastic.
YED & XED: The sign matters entirely! The sign tells you the type of good (Normal/Inferior or Substitute/Complement).
Step-by-Step Calculation Tip (Example):
Suppose income rises by 10% and demand for luxury chocolate rises by 15%.
1. Identify the factor and the response: Factor (Y) changes by +10%. Response (QD) changes by +15%.
2. Apply the formula: \(YED = \frac{+15\%}{+10\%} = +1.5\).
3. Interpretation: Since YED is positive (+1.5), it is a Normal Good. Since \(|YED| > 1.0\), it is specifically a Luxury Good. Perfect!