Elasticities of Demand
Definition
Price elasticity of demand (PED): the responsiveness of quantity demanded of a good to a change in its own price, found by comparing the percentage change in quantity demanded with the percentage change in price.
Income elasticity of demand (YED): the responsiveness of quantity demanded of a good to a change in consumers' real income, found by comparing the percentage change in quantity demanded with the percentage change in income.
Cross elasticity of demand (XED): the responsiveness of quantity demanded of one good to a change in the price of another good, found by comparing the percentage change in quantity demanded of the first good with the percentage change in the price of the second.
- An elasticity of demand measures how responsive quantity demanded is to a change in one of its determinants.
- There are three demand elasticities: price elasticity (PED), income elasticity (YED) and cross elasticity (XED).
- Each one isolates a single cause of a change in quantity demanded while all other influences are held constant, so the three never overlap.
Key Idea
- PED measures the response to the good's own price, YED the response to consumers' income, and XED the response to the price of a related good.
- The sign of each coefficient reveals the type of good or relationship and must never be dropped, while the size reveals how strong the response is.
Price Elasticity of Demand
- Because price and quantity demanded move in opposite directions along a demand curve, a price rise causes quantity demanded to fall, so numerator and denominator carry opposite signs and PED is normally negative.
- The larger the coefficient in absolute size, the more strongly buyers react: petrol and cigarettes have few substitutes and are habit-forming, so a price rise barely dents quantity demanded (inelastic, |PED| < 1), whereas one brand of chocolate or a luxury holiday has many alternatives, so buyers desert it fast (elastic, |PED| > 1).
Income Elasticity of Demand
- YED is positive for a normal good, because higher income raises its demand: as real incomes rise, UK households buy more restaurant meals and foreign holidays.
- YED is negative for an inferior good, because higher income leads buyers to switch away from it: supermarket value-range food and long-distance bus travel lose demand as consumers trade up to branded goods and rail or car.
- Among normal goods, a luxury such as a sports car has a YED above 1 (demand grows faster than income), while a necessity such as bread has a YED between 0 and 1 (demand grows, but slowly).
Cross Elasticity of Demand
- XED is positive for substitutes, because a rise in the price of one good pushes buyers towards the other: if Pepsi raises its price, quantity demanded of Coca-Cola rises.
- XED is negative for complements, because a rise in the price of one good reduces demand for the other: dearer petrol lowers demand for cars, and dearer printers lower demand for ink cartridges.
- A value near 0 means the two goods are unrelated, such as salt and cars, where a price change in one has no effect on demand for the other.
Sign Versus Size
- The sign of a coefficient shows the direction of the relationship being measured.
- The size, read as an absolute value, shows how strong the response is.
- Both pieces of information are needed to interpret any elasticity correctly.
Exam technique
- State each formula as a percentage change in quantity demanded over a percentage change in the cause.
- Always give the expected sign: negative for PED, and positive or negative for YED and XED.
- Name the good or relationship from the sign: normal, inferior, substitute or complement.
Common Mistake
- Do not drop the negative sign on PED, as it shows that price and quantity demanded move in opposite directions.
- Do not confuse the sign conventions: the YED sign classifies the good, while the XED sign classifies the relationship between two goods.
Self review
- Define price elasticity of demand.
- What does a negative YED tell you about a good?
- What does a positive XED indicate about two goods?
- Why is PED normally negative?
- Distinguish between the sign and the size of an elasticity coefficient.
