Price, Income and Cross-Elasticities of Demand -(Consumer Behavior, Demand and Supply)

Price elasticity of demand (PED) measures the responsiveness of quantity demanded to a change in the good's own price (1). It is calculated as the percentage change in quantity demanded divided by the percentage change in price (1).

% change in price = (15.06 − 11.28)/11.28 × 100 = +33.5% (1).

% change in quantity demanded = (171 600 − 172 620)/172 620 × 100 = −0.59% (1).

PED = %ΔQd ÷ %ΔP = −0.59% ÷ +33.5% = −0.018 (to 3 d.p.) (1).

Since |PED| = 0.018 < 1, demand for sugar is highly (price) inelastic (1).

Demand is price inelastic when |PED| < 1 — quantity demanded changes proportionately less than price. Two reasons explain why this holds for petrol.

Reason 1 — few close substitutes. Most motorists cannot easily switch away from petrol in the short run: the car they already own requires it, and public transport is often not a convenient alternative. With few close substitutes, a rise in the petrol price causes only a small contraction in quantity demanded, so demand is inelastic.

Reason 2 — petrol is a necessity/derived demand. For commuters and businesses, petrol is needed to get to work or to transport goods, so it is close to a necessity and its demand is derived from these essential activities. Consumers therefore keep buying broadly the same quantity despite a higher price, again giving a low PED.

On a demand and supply diagram this is shown by a steep (relatively vertical) demand curve: a large rise in price from P₁ to P₂ produces only a small fall in quantity from Q₁ to Q₂ — confirming inelastic demand.

Total revenue is price × quantity (TR = P × Q), and the effect of each fare change depends on the elasticity of demand it faces.

Peak fares — inelastic (PED = −0.4). |PED| = 0.4 < 1, so a rise in the peak fare causes a less-than-proportionate fall in the number of commuters. For example, a 10% fare rise reduces peak journeys by only about 4%. Because the percentage rise in price outweighs the percentage fall in quantity, total revenue from peak travel rises. This works because commuters have few alternatives at rush hour (work start-times are fixed), so demand is inelastic.

Off-peak fares — elastic (PED = −1.8). |PED| = 1.8 > 1, so a cut in the off-peak fare causes a more-than-proportionate rise in leisure journeys — a 10% fare cut raises journeys by about 18%. The percentage rise in quantity outweighs the percentage fall in price, so total revenue from off-peak travel also rises. Leisure travellers are price-sensitive (they can retime trips, drive, or not travel), giving elastic demand.

Taken together, both moves are likely to increase the firm's total revenue, because the firm is exploiting the difference in elasticity between the two markets — charging more where demand is inelastic and less where it is elastic (the logic of price discrimination).

A minimum price is a price floor set above the free-market equilibrium, below which alcohol cannot legally be sold. Its effectiveness at cutting consumption depends heavily on the price elasticity of demand (PED) for alcohol.

The case that it is effective. A minimum price raises the price of the cheapest, strongest alcohol. By the law of demand, a higher price reduces the quantity demanded, so consumption falls — this can be shown on a demand and supply diagram with the price floor above equilibrium and a contraction along the demand curve. The policy is targeted: it bites hardest on cheap, high-strength drinks favoured by the heaviest and youngest drinkers, so it can cut the most harmful consumption and reduce the associated negative externalities (crime, healthcare costs). Evidence from countries that have introduced minimum unit pricing suggests measurable falls in alcohol sales.

The case that it is limited / ineffective. The core problem is that demand for alcohol is price-inelastic, especially for dependent drinkers and addicts, so a higher price causes only a small fall in quantity — the very people the policy targets may barely cut back. Because demand is inelastic, most of the effect is to raise producer/retailer revenue rather than to reduce drinking, and it makes low-income drinkers worse off (a regressive effect) without changing their behaviour much. Consumers may switch to other sources — cross-border or online purchases, home-brewing, or illegal supply — undermining the policy. There is also a risk of government failure: setting the price too low achieves little, while setting it too high fuels black markets.

Evaluation and judgement. The effectiveness of the minimum price hinges on PED and on which drinkers are targeted. For moderate and price-sensitive drinkers (more elastic demand), it can meaningfully reduce consumption; for addicted drinkers (highly inelastic demand), its impact on quantity is small, so it works more as a revenue-raiser and a regressive tax than as a behaviour-change tool. It is therefore partially effective — best judged as one part of a wider strategy alongside measures that shift the demand curve itself, such as education, treatment and advertising restrictions, which tackle the underlying preferences rather than just the price. On balance, a minimum price can reduce total and harmful consumption, but its effectiveness is modest and uneven, and it should not be relied on alone.

Income elasticity of demand (YED) measures how demand responds to a change 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 economic cycle. A firm selling an income-elastic luxury (e.g. foreign holidays, premium cars) can expect demand to grow strongly in a boom but fall sharply in a recession, so it can plan capacity, stock, staffing and marketing accordingly, and perhaps diversify to reduce risk. A firm selling an inferior good may expect demand to rise in a downturn — useful for counter-cyclical planning. Over the long run, as economies grow and incomes rise, demand for income-elastic goods expands, signalling where to invest and which markets to enter (e.g. selling luxuries in fast-growing emerging economies).

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 higher incomes. YED tells the firm nothing about the effect of price (PED) or competitors' actions, which also drive demand. Forecasts of future income growth are themselves uncertain, so even an accurate YED gives an uncertain demand forecast. Other factors — advertising, innovation, fashion — can swamp the income effect entirely.

Judgement. YED is a useful planning tool, particularly for anticipating how demand moves over the cycle and as incomes grow, helping a firm manage risk and target investment. However, it is not sufficient on its own: it must be combined with knowledge of PED, rivals and reliable income forecasts, and treated with caution because the coefficient can shift. YED is most useful for firms whose products are strongly income-sensitive 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.