Elasticity measures how strongly buyers or sellers respond when an economic variable changes. This cheat sheet covers price elasticity of demand, income elasticity of demand, and cross elasticity of demand. Students need these tools to interpret markets, predict behavior, and explain real-world changes in revenue, spending, and demand.
It is especially useful for comparing goods, classifying products, and analyzing graphs or data tables.
The core idea is percent change: elasticity compares the percent change in one variable to the percent change in another. Price elasticity of demand measures how quantity demanded responds to price, income elasticity measures how demand responds to income, and cross elasticity measures how demand for one good responds to the price of another good. Values greater than 1 in absolute value usually mean elastic, values less than 1 mean inelastic, and values equal to 1 mean unit elastic.
The sign of an elasticity often reveals the relationship, such as normal versus inferior goods or substitutes versus complements.
Key Facts
- Price elasticity of demand is Ed = percent change in quantity demanded / percent change in price.
- Using the midpoint method, percent change = (new value - old value) / average of the two values x 100.
- Midpoint price elasticity of demand is Ed = [(Q2 - Q1) / ((Q1 + Q2) / 2)] / [(P2 - P1) / ((P1 + P2) / 2)].
- Demand is elastic when absolute value of Ed > 1, inelastic when absolute value of Ed < 1, and unit elastic when absolute value of Ed = 1.
- Total revenue is TR = price x quantity, and when demand is elastic, a price increase lowers total revenue.
- Income elasticity of demand is Ey = percent change in quantity demanded / percent change in income.
- Cross elasticity of demand is Exy = percent change in quantity demanded of good X / percent change in price of good Y.
- A positive cross elasticity means substitutes, a negative cross elasticity means complements, and a cross elasticity near 0 means unrelated goods.
Vocabulary
- Elasticity
- Elasticity is a measure of how responsive one economic variable is to a change in another variable.
- Price Elasticity of Demand
- Price elasticity of demand measures how much quantity demanded changes when the price of the good changes.
- Income Elasticity of Demand
- Income elasticity of demand measures how much demand changes when consumer income changes.
- Cross Elasticity of Demand
- Cross elasticity of demand measures how demand for one good changes when the price of another good changes.
- Elastic Demand
- Elastic demand means quantity demanded changes by a larger percentage than price, so absolute value of Ed is greater than 1.
- Inelastic Demand
- Inelastic demand means quantity demanded changes by a smaller percentage than price, so absolute value of Ed is less than 1.
Common Mistakes to Avoid
- Ignoring the negative sign for price elasticity of demand, which is wrong because demand usually moves opposite price. In many problems, use the absolute value to classify elasticity but keep the sign when interpreting direction.
- Using simple percent change instead of the midpoint method when comparing two points, which can give different answers depending on the direction of change. The midpoint method avoids this inconsistency.
- Confusing elastic with steep and inelastic with flat, which is wrong because elasticity depends on percentage changes, not just visual slope. A straight demand curve can have different elasticity values at different points.
- Mixing up income elasticity and cross elasticity, which leads to the wrong interpretation of the sign. Income elasticity classifies normal and inferior goods, while cross elasticity classifies substitutes and complements.
- Forgetting to connect elasticity to total revenue, which misses an important business implication. If demand is inelastic, raising price increases total revenue, but if demand is elastic, raising price decreases total revenue.
Practice Questions
- 1 A product's price rises from 12, and quantity demanded falls from 100 units to 80 units. Use the midpoint method to calculate price elasticity of demand and classify it.
- 2 Consumer income rises from 44,000, and demand for a good rises from 50 units to 60 units. Calculate the income elasticity of demand and identify whether the good is normal or inferior.
- 3 The price of Good Y rises by 8%, and the quantity demanded of Good X rises by 12%. Calculate the cross elasticity of demand and identify whether the goods are substitutes or complements.
- 4 Explain why a firm with inelastic demand might raise price, while a firm with elastic demand might avoid raising price.
Understanding Elasticity Reference (Price, Income, Cross)
Elasticity is shaped by the choices people have. Demand tends to be more responsive when a product has many close alternatives. A shopper can switch easily between brands of cereal, streaming services, or restaurants.
Demand is less responsive for a medicine, a basic utility, or a product with no close replacement. Time matters too. Right after a gasoline price rise, many drivers still need to commute.
Over several months, they can carpool, use transit, move closer to work, or choose a more efficient car. This makes long run demand often more elastic than short run demand.
A product’s share of a buyer’s budget matters. A small rise in the price of pencils rarely changes how many pencils a family buys. A similar percentage rise in rent, tuition, or a vehicle can change plans sharply.
Necessities are often less elastic than luxuries, though this depends on the person and situation. A winter coat may be essential in a cold climate. A second designer coat is easier to delay.
Do not treat categories as fixed rules. Evidence about available choices, urgency, income, and time gives a stronger explanation than simply naming a good a necessity.
Revenue results can seem backwards at first. When demand is responsive, a lower price can bring in enough extra buyers to raise a seller’s total revenue. A higher price can lose enough sales to reduce it.
When demand is not very responsive, buyers cut back only a little after a price increase, so total revenue may rise. This idea helps explain sale prices, concert tickets, airline fares, and public policy debates about taxes.
It does not prove that a lower price always raises profit. Profit depends on costs, including wages, materials, rent, and the cost of producing additional units.
The midpoint method is useful because it gives the same percentage change whether a movement is described from the first point to the second or in reverse. Using only the starting value creates different answers for an increase and an equal decrease. When reading a demand graph, do not confuse a steep line with inelastic demand or a flat line with elastic demand.
The slope uses changes in units and prices. Elasticity uses percentage changes, so the same straight demand curve can have different elasticity at different points. For income and cross effects, focus on the real relationship.
A negative income result can occur for lower cost goods that people buy less of as their income rises. A cross result may be weak when products are only distant alternatives. Always identify which variable changed, hold other influences in mind, and state what the calculated value means in words.