Price elasticity, income elasticity and cross elasticity of demand

Price elasticity of demand (PED) measures the responsiveness of quantity demanded to a change in the good's own price (%ΔQd ÷ %ΔP). Several factors determine how elastic or inelastic a good's demand is.

The most important is the availability of close substitutes. If many close substitutes exist, a rise in the good's price causes consumers to switch easily to alternatives, so demand is elastic; if there are few substitutes (e.g. a life-saving medicine), demand is inelastic.

A second factor is the proportion of income the good takes up. Goods that absorb a large share of income (e.g. cars, holidays) tend to have elastic demand, because a price change has a noticeable effect on the consumer's budget, whereas cheap items (e.g. salt) have inelastic demand.

A third is whether the good is a necessity or a luxury. Necessities (such as basic food) tend to be inelastic because people must buy them regardless of price, while luxuries are more elastic. Closely related is addiction or habit: addictive goods such as cigarettes have inelastic demand.

Finally, the time period matters: demand is usually more elastic in the long run, because consumers have more time to find substitutes or change their habits. The definition of the market also matters — demand for a narrowly defined brand is more elastic than demand for the product category as a whole.

Together these factors explain why some goods respond strongly to price changes while others barely respond at all.

Coffee chain: PED = %ΔQd ÷ %ΔP = −3% ÷ +8% = −0.375. Since |PED| = 0.375 < 1, its demand is inelastic.

Rival firm: PED = −12% ÷ +8% = −1.5. Since |PED| = 1.5 > 1, its demand is elastic.

This difference suggests the two firms face very different market conditions. The coffee chain's inelastic demand implies it has strong brand loyalty or few close substitutes that its customers consider acceptable, so customers keep buying despite the higher price. Its decision to raise prices would therefore increase total revenue, because the small fall in volume is outweighed by the higher price.

The rival's elastic demand implies its customers see many close substitutes and switch away readily when its price rises — so raising prices was a poor decision, as the large fall in volume would reduce total revenue. To raise revenue, the rival should instead lower its price.

The contrast shows how the same price rise can help one firm and harm another, depending on the elasticity of demand each faces.

Income elasticity of demand (YED) measures how demand responds to changes in income (%ΔQd ÷ %ΔY). Its sign classifies a good as normal (positive) or inferior (negative), and its size as a luxury (YED > 1) or a necessity (0 < YED < 1). This information can be valuable to a firm planning ahead.

The case for usefulness. Knowing its product's YED helps a firm anticipate the effect of the economic cycle. A firm selling an income-elastic luxury (e.g. foreign holidays) can expect demand to grow strongly in a boom but fall sharply in a recession, so it can plan capacity, stock and staffing accordingly, and perhaps diversify to reduce risk. A firm selling an inferior good may expect demand to rise in a downturn, which is useful for counter-cyclical planning. YED also guides long-term strategy: as economies grow and incomes rise over time, demand for income-elastic goods will expand, signalling where to invest.

Limitations. YED values are estimates based on past data and may not hold in future, especially if tastes change. The relationship can be non-linear — a good may be a luxury at low incomes but a necessity at high incomes. YED also tells the firm nothing about the effect of price changes or competitors' actions, which also affect demand. Forecasts of future income growth are themselves uncertain, so even an accurate YED gives an uncertain demand forecast. Finally, other factors (advertising, new products) may swamp the income effect.

Judgement. YED is a useful planning tool, particularly for anticipating how demand will move over the economic cycle and as incomes grow, which helps a firm manage risk and target investment. However, it is not sufficient on its own: it must be combined with knowledge of PED, competitors and reliable income forecasts, and treated with caution because the coefficient can change. YED is most useful for firms whose products are strongly income-sensitive and operating in stable conditions, and least useful where tastes are volatile or income forecasts unreliable. On balance it is a valuable input to planning rather than a complete guide.

If demand is price-inelastic (|PED| < 1), a price rise causes a less-than-proportionate fall in quantity, so total revenue rises (TR = P × Q). This is the basis for the claim that a firm with inelastic demand should raise price.

The case for raising price. Higher revenue from the same or only slightly lower volume directly improves the firm's sales income. If costs do not rise (and may even fall with lower output), profit rises too. Goods with inelastic demand often have strong brand loyalty or few substitutes, so the firm can exploit this pricing power. For a firm focused on short-term revenue and profit, raising price looks attractive.

The case against / qualifications. First, the firm should care about profit, not just revenue: raising price raises revenue, but the profit effect depends on costs — though with lower output costs usually fall, reinforcing the case, so this point is weaker here. More importantly, inelastic demand may be only short-run: over time consumers find substitutes, so demand becomes more elastic and the higher price drives customers away. Repeated price rises can damage brand reputation and customer goodwill, attract new competitors into a profitable market, or provoke government/regulatory intervention if the good is essential. If rivals do not follow the price rise, the firm may lose market share even with inelastic industry demand. There may also be ethical or PR costs to raising the price of a necessity.

Judgement. Raising price is likely to raise revenue and probably profit in the short run when demand is genuinely inelastic, so the advice has real merit. However, 'always' is too strong. The decision should depend on: whether the inelasticity will persist (long-run elasticity), the likely reaction of rivals and regulators, the effect on long-term reputation and competition, and the firm's objectives (profit vs market share vs growth). The most defensible conclusion is that a firm with inelastic demand has a strong case to raise price for short-run revenue, but should not do so automatically — it must weigh the long-run and competitive consequences first.