Elasticity (Economics)

Elasticity is a measure of how strongly one economic variable responds to a change in another, expressed as a ratio of percentage changes. The best-known form, price elasticity of demand, compares the percentage change in the quantity buyers want with the percentage change in price. Businesses use it to set prices, governments use it to forecast tax revenue, and economists use it to describe almost every market.

Because it uses percentages, elasticity is unit-free: it can compare the market for petrol with the market for concert tickets. It complements the basic model of supply and demand, which shows the direction of a response but not its size. Separate entries cover the two extremes of elastic demand and inelastic demand, and the supply-side equivalents. The British economist Alfred Marshall popularized the concept in his Principles of Economics (1890).

Imagine two cafés raising prices by the same amount. One sells takeaway coffee on a street with five other coffee shops; customers simply walk next door, and sales fall sharply. The other is the only café inside a hospital; people grumble but keep buying. The first café faces elastic demand, the second inelastic demand.

Elasticity is a way of putting a number on that difference in reaction. A big number means customers are very sensitive and drift away quickly when the price moves. A small number means they stick around. Knowing which kind of customer you have tells you whether raising prices will bring in more money or less.

The price elasticity of demand is calculated as:

• $E_d$ is the price elasticity of demand. It is normally negative, because quantity falls when price rises; economists often quote its absolute value.
• $\%\Delta Q_d$ is the percentage change in quantity demanded.
• $\%\Delta P$ is the percentage change in price.

Because the percentage change from 10 to 12 is not the same as from 12 to 10, analysts often use the midpoint (arc) formula, which divides each change by the average of the two values:

Worked example: a cinema raises its ticket price from $10 to $12 and weekly sales fall from 1,000 to 800 tickets. The quantity change is $-200 \div 900 = -22.2\%$ and the price change is $2 \div 11 = 18.2\%$, so $E_d = -22.2 \div 18.2 \approx -1.22$. The absolute value is above 1, so demand is elastic, and revenue falls from $10,000 to $9,600.

The general rule, known as the total revenue test, follows from this:

• Absolute value above 1 (elastic). A price rise lowers total revenue.
• Absolute value below 1 (inelastic). A price rise raises total revenue.
• Exactly 1 (unit elastic). Revenue does not change.

• Availability of substitutes. The more close alternatives exist, the more elastic demand is; this is why demand for one brand is more elastic than for the product category.
• Necessity or luxury. Essentials such as basic food, medicine and heating are less elastic than discretionary purchases.
• Share of the budget. A price rise on salt is barely noticed; one on rent or a car forces a rethink.
• Time. Demand is usually more elastic in the long run, once people can change habits, equipment or suppliers. Studies of fuel demand consistently find a small short-run response and a larger long-run one.

• Price elasticity of supply. How much producers expand output when the price rises; see elastic supply and inelastic supply. It depends on spare capacity, stocks and how easily factors of production can be shifted.
• Income elasticity of demand. The response of demand to changes in income. Normal goods have a positive value, luxuries a value above 1, and inferior goods a negative value.
• Cross-price elasticity. The response of demand for one good to the price of another. It is positive for substitutes (tea and coffee) and negative for complements (printers and ink).

The split between how much of a response comes from switching to cheaper goods and how much from feeling poorer is analyzed through the substitution effect and the income effect. In rare cases, such as Giffen goods, the income effect is strong enough to make demand rise with price.

• Pricing. A firm with market power, such as a monopoly, never sets its price where demand is inelastic, because a higher price would then raise revenue and cut costs. The gap between price and marginal cost it can sustain shrinks as demand becomes more elastic.
• Taxation. Tax incidence analysis shows that the burden of a tax falls mostly on whichever side of the market, buyers or sellers, is less elastic. Excise taxes on tobacco, alcohol and fuel raise substantial revenue partly because demand for them is inelastic.
• Trade and exchange rates. Whether a currency depreciation improves the trade balance depends on how elastic export and import demand are, a result known as the Marshall–Lerner condition; the slow response is one reason for the J-curve.
• Policy evaluation. Estimates of labor supply elasticity inform debates over income tax rates, and estimates of demand elasticity inform antitrust market definition.

Elasticity is not constant along a straight demand curve; it changes at every point, so a single figure applies only near the price where it was measured. Estimates from econometrics also vary with the period, country and method used.

• OpenStax Principles of Economics: Price Elasticity of Demand and Price Elasticity of Supply