Measuring responsiveness

Elasticity is a measure of responsiveness that compares the percentage change in one economic variable with the percentage change in another. It uses percentage changes rather than absolute changes, so goods with very different prices and quantities can still be compared meaningfully.

Use the language precisely. When one variable changes by a greater percentage than another, the response is more than proportionate. If the percentage change is smaller, it is less than proportionate. Describing a change as merely “large” or “small” ignores the relative nature of elasticity.

Relatively elastic demand is demand for which quantity demanded is comparatively responsive to a change in the relevant determinant. Relatively inelastic demand is demand for which quantity demanded is comparatively unresponsive to that change. On otherwise comparable price–quantity diagrams, a flatter demand curve often illustrates relatively elastic demand, while a steeper curve illustrates relatively inelastic demand.

Be careful with this comparison: slope and elasticity aren’t identical. Slope measures absolute changes and depends on the units and scale used on the axes. Elasticity measures percentage changes. Comparing steeper and flatter curves is safest when both diagrams use the same scales and the curves are compared at corresponding prices and quantities.

Definition and calculation

Price elasticity of demand (PED) is an elasticity coefficient that measures the responsiveness of quantity demanded for a good or service to a change in its price, ceteris paribus.

To calculate a percentage change, subtract the original value from the new value. Divide the result by the original value, then multiply by $100$. Follow this method for both variables. Because it uses the original value, reversing a change can give a different coefficient. Always check the data to identify the starting values.

Under the law of demand, PED normally has a negative sign because price and quantity demanded move in opposite directions. Economists commonly use its absolute value when discussing the degree of PED. For calculations, though, show the substitution and keep the negative sign unless the question or data convention asks only for the magnitude.

The formula can be rearranged too. The percentage change in quantity demanded equals $PED \times \%\Delta P$, while the percentage change in price equals $\%\Delta Q_d/PED$. Use the signs to work out the direction of change. If the direction is already given, magnitudes are enough.

Degrees of PED

The theoretical range of PED runs from zero to negative infinity. In practice, its degrees are usually classified using the absolute value:

• Price-inelastic demand is demand for which the percentage change in quantity demanded is less than the percentage change in price, so $0 < |PED| < 1$.
• Unit-price-elastic demand is demand for which quantity demanded changes by the same percentage as price, so $|PED| = 1$.
• Price-elastic demand is demand for which the percentage change in quantity demanded is greater than the percentage change in price, so $1 < |PED| < \infty$.
• Perfectly price-inelastic demand is demand for which quantity demanded does not change when price changes, so $PED = 0$; its demand curve is vertical.
• Perfectly price-elastic demand is demand for which any price increase reduces quantity demanded to zero while, at the given price, any quantity can be demanded, so $|PED| = \infty$; its demand curve is horizontal.

A demand curve with constant unitary PED forms a rectangular hyperbola, with every point showing the same total spending. Perfectly elastic and perfectly inelastic demand also have constant PED throughout.

Determinants of PED

PED depends on the choices consumers can realistically make.

• Number and closeness of substitutes: When substitutes are more numerous or closer, consumers can switch more easily, making demand more price elastic. Demand for a narrowly defined product is therefore usually more elastic than demand for its broad product category.
• Degree of necessity: Necessities tend to have relatively inelastic demand because consumers find it difficult to reduce consumption. They can postpone or abandon non-essential purchases more readily. Habit-forming consumption may also be relatively inelastic.
• Proportion of income spent: Consumers respond more strongly to a price change when a good takes up a substantial share of their income. A low-cost item that absorbs only a tiny budget share is likely to have less elastic demand.
• Time: Demand is usually more elastic in the long run. Given more time, consumers can find information, change routines, leave contracts or replace equipment with an alternative.

These determinants can interact. A necessary good may still have elastic demand for low-income households if it takes up a large share of their income. The availability of substitutes can also change over time.

PED and total revenue

Total revenue is the monetary receipt earned from selling a given quantity of output over a period.

With price-elastic demand, quantity changes proportionately more than price. A price reduction raises total revenue, whereas a price increase lowers it. With price-inelastic demand, quantity changes proportionately less than price. A price increase therefore raises total revenue, while a price reduction lowers it. Under unit-price-elastic demand, the two percentage effects exactly offset each other, leaving total revenue unchanged.

Comparison of total revenue changes under different demand elasticities.

A revenue-area diagram shows why. After a price decrease, the firm loses revenue on units it was already selling but gains revenue from the extra units sold. If demand is elastic, the gain exceeds the loss. If demand is inelastic, the loss exceeds the gain.

When using numerical data, calculate $PED$ by showing both percentage changes before dividing. If total revenue isn’t given, multiply price by quantity. If one component is missing, use $Q = TR/P$ or $P = TR/Q$. You can then apply a percentage change to the original value to find the new price, quantity demanded or total revenue.

Why PED changes even though slope does not

A straight-line demand curve slopes downwards at a constant rate, yet its PED varies. The reason is simple: slope measures absolute changes, whereas PED measures percentage changes.

The point form shows the difference:

Along a straight line, $\Delta Q_d/\Delta P$ stays constant. However, $P/Q_d$ changes at each point.

Close to the price-axis intercept, price is high and quantity demanded is near zero. As a result, $P/Q_d$ is very large and demand approaches perfect elasticity. Further down the curve, price falls as quantity demanded rises, so the absolute value of PED declines. Demand is unit-price elastic at the midpoint. Below this point, it is price inelastic. At the quantity-axis intercept, where price is zero, PED equals zero.

The same pattern explains what happens to total revenue. A price reduction in the elastic upper section raises total revenue. At the midpoint, where $|PED| = 1$, total revenue reaches its maximum. Any further price reductions take place in the inelastic section and reduce total revenue. An entire straight-line demand curve should therefore not be labelled “elastic” or “inelastic”; that classification applies to a point or range on the curve.

Decisions by firms

PED helps firms predict how a proposed price change could affect sales and total revenue. When demand is price elastic, cutting the price may increase revenue because sales rise by a more than proportionate amount. With price-inelastic demand, a price rise may increase revenue since sales fall by a smaller percentage.

Revenue, though, is not the same as profit. Profit is the financial surplus remaining when total costs are subtracted from total revenue. Even if a price cut raises revenue, it could reduce profit when the extra output costs substantially more to supply. Firms therefore need to consider PED estimates alongside costs, capacity and strategic information.

Firms can also use PED when segmenting markets and making product decisions. Customer groups may differ in their access to substitutes, their incomes or the time they have to adjust. For instance, a transport operator may discover that time-sensitive business travellers have less elastic demand than leisure travellers, then set separate fares for each group.

Decisions by governments

Governments use PED to forecast the effects of indirect taxes. If demand is relatively inelastic, consumers cut their purchases by a smaller proportion after the tax raises the price. Tax revenue may therefore be comparatively dependable. Producers may also pass a larger share of the tax on to consumers through a higher market price. When demand is elastic, quantity demanded contracts more sharply, which limits revenue and puts greater pressure on sellers to absorb the tax.

PED matters when a policy is intended to reduce consumption as well. If demand is strongly inelastic, especially in the short run, raising the price of a harmful product will have only a limited effect on quantity demanded. Governments may respond by combining taxation with information or regulation, or by making substitutes easier to access. Over time, these measures may make demand more elastic.

How reliable is PED for decision-making?

Looking at how far firms actually use elasticity in pricing exposes several limitations. PED estimates come from past data, surveys or market experiments, yet consumer preferences may change, as can competitors’ prices and incomes. The coefficient may also vary between customer groups, locations and time periods. A large price change can move a firm to another part of its demand curve, where PED is different.

PED should therefore inform a decision rather than act as an automatic pricing rule. It is most useful when the market has been defined carefully and the estimates are current. Revenue predictions must also be weighed against costs, competitors’ likely reactions, long-term objectives and uncertainty.

Why their responsiveness tends to differ

A primary commodity is a good obtained directly from natural resources with little or no processing. Examples are unprocessed crops, timber and metal ores. A manufactured product is a good created by transforming raw materials or components through a production process.

Demand for primary commodities tends to be more price inelastic than demand for manufactured products. Several factors explain this pattern:

• Many primary commodities satisfy basic food, energy or industrial-input needs. Buyers therefore can’t easily stop purchasing them.
• In the short run, a commodity required for a specific production process may have few close technical substitutes.
• Individual primary inputs often account for only a small share of the final buyer’s total expenditure or production cost, so buyers respond less to price changes.
• Manufactured products are often differentiated by brand, design and specification. This creates many competing substitutes.
• Consumers can frequently postpone buying durable manufactured products, which gives them another way to respond when prices rise.
• Manufactured products may take up a larger share of household income, making a change in price more noticeable.

This is a general tendency rather than a fixed rule. Demand for a rare collectible raw material may be highly elastic if buyers can abandon the purchase. By contrast, an essential manufactured medical device with no substitute may have highly inelastic demand. The analysis depends on substitutes, necessity, budget share and time.

Low PED also explains why a change in supply can cause a large price movement in a primary-commodity market. Suppose harvest conditions reduce supply. If buyers reduce quantity demanded only slightly, most of the adjustment comes through a steep price rise. For a comparable supply shift, the more elastic demand for a manufactured product would lead to a larger quantity response and a smaller price movement.

Definition and calculation

Income elasticity of demand (YED) is an elasticity coefficient that measures the responsiveness of quantity demanded for a good or service to a change in consumer income, ceteris paribus.

Calculate YED by dividing the percentage change in quantity demanded by the percentage change in income. If a percentage change is missing, rearrange the formula: $\%\Delta Q_d = YED \times \%\Delta Y$, or $\%\Delta Y = \%\Delta Q_d/YED$. When a new quantity or income value is needed, apply the result to the original figure.

The sign of YED matters. Unlike PED, it must not be discarded.

Sign and magnitude

A normal good is a good for which demand increases when consumer income increases, ceteris paribus. It has $YED > 0$. The magnitude of YED divides normal goods into the following categories:

• Income-inelastic demand is demand for which quantity demanded changes by a smaller percentage than income, so $0 < YED < 1$. Necessities often fall into this category. Consumers already buy them, so consumption rises only modestly when income increases.
• Income-elastic demand is demand for which quantity demanded changes by a greater percentage than income, so $YED > 1$. This often applies to services and luxury goods, since extra income can make previously unaffordable or discretionary purchases possible.
• Where $YED = 1$, quantity demanded changes in the same proportion as income.

An inferior good is a good for which demand decreases when consumer income increases, ceteris paribus. It has $YED < 0$ because rising purchasing power leads consumers to switch towards preferred alternatives. The word “inferior” describes the income–demand relationship; it doesn’t mean that the product is objectively poor quality.

Engel curves

An Engel curve is a curve showing the relationship between consumer income and the quantity demanded of a good, ceteris paribus. Under the IB convention, income goes on the vertical axis and quantity demanded on the horizontal axis.

A normal good has an upward-sloping curve: higher income is associated with a greater quantity demanded. For an income-inelastic necessity, a given percentage increase in income leads to a smaller percentage increase in quantity demanded. With an income-elastic service or luxury, the percentage increase in quantity demanded is larger, often after consumers reach an income threshold. Over the relevant income range, an inferior good has a downward-sloping Engel curve.

A good’s classification can shift as income changes. It may be normal at lower incomes, then become inferior once consumers can afford a preferred alternative. Engel curves should therefore be read over the range shown, rather than treated as permanent labels for every household and income level.

Importance for firms

YED allows firms to anticipate shifts in demand as the economy grows or contracts. Average household income tends to rise during periods of economic growth, increasing demand for normal goods. Products with high positive YED are likely to see the strongest proportionate growth. In a recession, demand for income-elastic luxuries may drop sharply. Demand for necessities falls less, while demand for some inferior goods may rise.

Firms can use these forecasts when planning capacity, staffing, inventories and product mix. For example, a food retailer that sells basic own-label products alongside premium prepared meals might focus more on its basic range during a downturn, then expand the premium range as incomes recover.

Forecasts based on YED aren’t certain. Estimates can vary among income groups and over time. Tastes, demographic change, prices and expectations also affect demand. If a firm expands capacity solely because income is expected to rise, it risks overproduction when consumer preferences change or the increase in income is unevenly distributed.

Explaining changes in sectoral structure

Sectoral structure is the composition of an economy’s output and employment across different categories of production. The primary sector is the category of economic activity that extracts or harvests natural resources; the secondary sector is the category that transforms materials into manufactured output; and the tertiary sector is the category that supplies services.

As an economy develops and average income rises, demand for necessities with low positive YED increases more slowly than income. Agricultural output may still increase in absolute terms, but its share of total expenditure and output can fall. At first, demand for manufactured consumer goods may grow faster as households acquire durable products. Once incomes reach higher levels, demand for many services—such as recreation, specialist healthcare and financial advice—often rises more than proportionately.

This pattern helps explain the broad shift from primary activity to manufacturing and, later, towards services. The mechanism comes from the demand side: as incomes rise, sectors that produce goods and services with higher YED tend to grow faster.

YED doesn’t explain the entire change. Sectoral structure is also shaped by productivity differences, technology, trade, natural-resource endowments, education and government policy. Manufactured goods and services don’t all share the same YED either. YED therefore helps explain the pattern of structural transformation, but it doesn’t determine that pattern by itself.