Coursework Sample: Price Elasticity and Pricing Decisions: A Worked Analysis

Model Answer

Introduction

Price elasticity of demand (PED) measures the responsiveness of quantity demanded to a change in price, and it is one of the most practically important concepts a pricing manager can use (Sloman et al., 2018). This report analyses two products sold by a UK supermarket chain following separate price changes: an own-label breakfast cereal, whose price was reduced, and a branded ground coffee, whose price was increased. Using sales data recorded before and after each change, the arc elasticity formula is applied to calculate PED for both products. The findings are then used to explain why the two products behave so differently, to test the relationship between elasticity and total revenue, and to recommend a pricing strategy appropriate to each category. The report closes by evaluating the limitations of the method used and by considering how the results generalise to UK grocery retail more widely.

Price Elasticity of Demand: Concept and Determinants

PED is defined as the percentage change in quantity demanded divided by the percentage change in price (Begg et al., 2014). Because demand curves slope downwards, the coefficient is normally negative; economists typically report its absolute value when classifying goods. A PED greater than one indicates elastic demand, where quantity demanded changes proportionately more than price. A PED less than one indicates inelastic demand, where quantity demanded is relatively unresponsive. A coefficient of exactly one describes unit elasticity, while the extreme cases of perfectly elastic and perfectly inelastic demand are represented by horizontal and vertical demand curves respectively (Parkin, Powell and Matthews, 2014), as illustrated schematically in Figure 1.

Several factors determine where a product sits on this spectrum. The availability of close substitutes is the most significant: own-label cereal has many near-identical rivals on the same shelf, so a small price change causes shoppers to switch brands readily (Pindyck and Rubinfeld, 2018). Branded goods with strong loyalty, by contrast, face fewer effective substitutes because consumers perceive them as distinct even where objective quality differences are small. The proportion of income spent on the good also matters: cheap, frequently purchased items absorb a smaller share of the household budget, which dampens the incentive to search for alternatives when the price moves modestly (Krugman and Wells, 2018). Finally, the time horizon affects elasticity, since consumers have more scope to adjust habits, seek out substitutes and switch suppliers the longer a price change persists, meaning long-run elasticity is generally higher than short-run elasticity for the same good (Mankiw and Taylor, 2020).

Worked Calculation of PED

Sales data recorded for four weeks before and four weeks after each price change are summarised in Table 1. Because both changes are relatively large, the arc (midpoint) elasticity formula is used, which divides the change in quantity or price by the average of the two values rather than the original value alone; this avoids the asymmetry that arises when a rise and an equivalent fall in price produce different PED estimates under the simple point elasticity method (Sloman et al., 2018).

For the own-label cereal, the price was cut from £1.60 to £1.40 and weekly sales rose from 2,400 to 3,000 units. The percentage change in quantity is (3,000 − 2,400) ÷ [(3,000 + 2,400) ÷ 2] = 600 ÷ 2,700 = 22.22%. The percentage change in price is (£1.40 − £1.60) ÷ [(£1.40 + £1.60) ÷ 2] = −£0.20 ÷ £1.50 = −13.33%. Dividing gives PED = 22.22% ÷ −13.33% = −1.67. As the absolute value exceeds one, demand for the cereal is elastic.

For the branded coffee, the price was raised from £3.20 to £3.50 and weekly sales fell from 1,200 to 1,140 units. The percentage change in quantity is (1,140 − 1,200) ÷ [(1,140 + 1,200) ÷ 2] = −60 ÷ 1,170 = −5.13%. The percentage change in price is (£3.50 − £3.20) ÷ [(£3.50 + £3.20) ÷ 2] = £0.30 ÷ £3.35 = 8.96%. Dividing gives PED = −5.13% ÷ 8.96% = −0.57. As the absolute value is below one, demand for the coffee is inelastic.

Table 1: Arc elasticity and total revenue calculations for the two products.

Implications for Pricing and Total Revenue

The total revenue test states that when demand is elastic, a price cut raises total revenue because the proportionate rise in quantity outweighs the proportionate fall in price; when demand is inelastic, a price rise raises total revenue because the proportionate fall in quantity is smaller than the proportionate rise in price (Baumol and Blinder, 2016). The data in Table 1 confirm this rule for both products. Cereal revenue rose from £3,840 to £4,200 per week, a gain of £360, after the price cut — consistent with elastic demand. Coffee revenue rose from £3,840 to £3,990 per week, a smaller gain of £150, after the price rise — consistent with inelastic demand.

These results carry a clear pricing implication. Where demand is elastic, as with the cereal, further price cuts are likely to keep raising revenue until the coefficient approaches unity, after which additional cuts would start to erode revenue; the retailer should therefore monitor the elasticity coefficient rather than assuming the relationship holds indefinitely (Frank, 2015). Where demand is inelastic, as with the coffee, the retailer has scope to raise price further without a proportionate loss of volume, though this must be balanced against the risk of reputational damage if customers perceive the increase as opportunistic, particularly during a period of high grocery price inflation (Competition and Markets Authority, 2021).

Application to a UK Retail Case

These findings map onto a wider pattern observed across UK grocery retail. Own-label ranges typically face PED coefficients well above one because supermarkets stock them alongside near-identical rivals and actively use price as the main point of differentiation (Sloman et al., 2018). Retailers such as the major UK grocery chains have consequently used aggressive own-label price cuts to defend market share against discounters, on the logic that lower margins per unit are more than offset by higher volumes. Branded lines with strong equity, by contrast, retain more pricing power because loyal customers accept moderate increases rather than switch, which is one reason manufacturers of established brands were able to pass on a meaningful share of input-cost inflation during the recent cost-of-living period without a proportionate loss of volume (Office for National Statistics, 2023).

Cross-price elasticity is also relevant here: a price cut on own-label cereal may draw customers away from the branded coffee aisle if shoppers reallocate a fixed grocery budget, so pricing decisions cannot be made in isolation product by product (Pindyck and Rubinfeld, 2018). Any pricing strategy therefore needs to be evaluated at category level rather than line by line, and retailers are expected by the Competition and Markets Authority to ensure that headline discounts on elastic lines are genuine reductions rather than achieved by first raising the reference price (Competition and Markets Authority, 2021).

Cross-Elasticity and Competitor Response

The analysis so far has treated each product’s elasticity as if it depended only on its own price, but cross-price elasticity of demand (XED) — the responsiveness of quantity demanded for one good to a change in the price of another — adds a further layer of complexity that a pricing manager cannot ignore (Begg et al., 2014). If a discount supermarket cuts the price of its own equivalent cereal in response to the retailer’s move, some of the 22.22% quantity gain calculated above would be eroded, because part of the increase reflects switching from the discounter’s line rather than genuinely new demand. Similarly, a positive cross-price elasticity would exist between the branded coffee and cheaper own-label alternatives sitting on an adjacent shelf: if the branded price rise pushes some customers toward the own-label coffee, the retailer still captures the sale, but at a lower margin per cup than if the branded line had been chosen (Krugman and Wells, 2018). This suggests that PED calculated in isolation, as in Table 1, should be read as a starting point for pricing strategy rather than a complete forecast, since competitor reactions and within-category substitution can both amplify and dampen the initial estimate over subsequent trading periods.

Evaluation of Limitations

The arc elasticity method assumes that all other factors influencing demand remained constant over the two four-week periods, yet in practice promotions, seasonality, weather and competitor pricing could all have contributed to the change in quantity sold, which would bias the PED estimate (Krugman and Wells, 2018). The four-week sample is also short: consumer habits may continue adjusting beyond this window, meaning the true long-run elasticity could differ from the short-run figure calculated here (Mankiw and Taylor, 2020). Finally, elasticity is not fixed; it can shift with income levels, the entry of new substitutes, or changes in consumer preferences, so the coefficients reported should be treated as indicative rather than as permanent parameters for future pricing decisions.

A further limitation concerns data quality. Weekly till data record what was sold at the shelf price actually charged, but they cannot separate the effect of the headline price change from any simultaneous in-store promotion, loyalty-card discount or end-of-aisle display that a retailer may have run alongside it; without a controlled experiment or a comparison store where price was held constant, some of the estimated quantity response may be attributable to these confounding factors rather than to price alone (Pindyck and Rubinfeld, 2018). A more rigorous approach would use panel data across many stores and time periods, or a natural experiment design, to isolate the pure price effect before committing to a chain-wide pricing decision based on a single four-week comparison.

Conclusion

The evidence supports a differentiated pricing strategy. Because demand for the own-label cereal is elastic, competitive price cuts are an effective lever for growing both volume and revenue, provided the retailer tracks the coefficient to avoid cutting price beyond the point of unit elasticity. Because demand for the branded coffee is inelastic, moderate price increases are unlikely to trigger a proportionate fall in volume and can improve revenue, though this pricing power should be used cautiously given regulatory scrutiny of pricing practices and the risk of long-run brand damage. More broadly, the analysis illustrates why a single, uniform pricing rule across a retailer’s range is unlikely to be optimal: elasticity, and therefore the correct pricing response, varies systematically with the availability of substitutes, the proportion of income spent on the good, and the strength of brand loyalty.

Figure 1: Illustrative elastic and inelastic demand curves. A given price fall along the flatter (elastic) curve produces a proportionately larger rise in quantity demanded than an equivalent price fall along the steeper (inelastic) curve.

References

Baumol, W.J. and Blinder, A.S. (2016) Economics: Principles and Policy. 13th edn. Boston: Cengage Learning.

Begg, D., Vernasca, G., Fischer, S. and Dornbusch, R. (2014) Economics. 11th edn. Maidenhead: McGraw-Hill Education.

Competition and Markets Authority (2021) Pricing Practices: Guidance for Businesses. London: CMA.

Frank, R.H. (2015) Microeconomics and Behaviour. 9th edn. New York: McGraw-Hill.

Krugman, P. and Wells, R. (2018) Microeconomics. 5th edn. New York: Worth Publishers.

Mankiw, N.G. and Taylor, M.P. (2020) Economics. 5th edn. Andover: Cengage Learning.

Office for National Statistics (2023) Consumer Price Inflation, UK: Methodology and Data. London: ONS.

Parkin, M., Powell, M. and Matthews, K. (2014) Economics. 9th edn. Harlow: Pearson.

Pindyck, R.S. and Rubinfeld, D.L. (2018) Microeconomics. 9th edn. Harlow: Pearson.

Sloman, J., Garratt, D., Guest, J. and Jones, E. (2018) Economics. 10th edn. Harlow: Pearson.