Cross-elasticity reveals where demand goes after a price change.
Key distinctions
Three conditions before calculating.
Non-symmetric direction
The effect of price A on demand B does not necessarily equal the effect of price B on demand A. Market shares, loyalty, availability and positioning create asymmetries. Each direction must be estimated separately.
Identifiable variation
Simultaneous promotions, seasonality and stockouts can create a misleading correlation. An experiment, a staggered rollout or a conditionally exogenous variation gives a more credible interpretation than a simple historical regression.
Portfolio contribution
Volumes gained and lost are multiplied by unit contributions, costs to serve and retention probabilities. The best price for an isolated reference can reduce the value of the portfolio.
Method
Estimating and using a cross-elasticity matrix
- 01Define the relevant portfolio
Include internal offers, competitors, non-consumption and complements liable to change; set segment, channel and period, since an elasticity averaged across heterogeneous contexts is rarely transportable.
- 02Prepare the variations
Build real net prices, availability, promotion, season, distribution and exposure; check that the changes are large enough, not perfectly synchronised and observed over a range close to the decision.
- 03Estimate with uncertainty
Compute the log change in demand B divided by that of price A, with an interval; test lags, up-down asymmetry and stability by segment, and reserve zero for effects that cannot be distinguished.
- 04Simulate the contribution
Apply the responses to reference volumes, then recompute net price, unit margin, transfers and costs; compare central, prudent and adverse scenarios before the pilot.
The directional matrix of demand transfers
Each cell shows the response of the offer in the row to the price change of the offer in the column.
| Demand ↓ / price → | Premium | Standard | Essential |
|---|---|---|---|
| Premium | -1.40 | +0.18 | +0.05 |
| Standard | +0.35 | -1.85 | +0.22 |
| Essential | +0.08 | +0.41 | -2.10 |
The premium price rise increases standard volume but reduces total margin
A range sells 10,000 Premium units at €120 and 18,000 Standard at €80. Unit contributions are €62 and €34. A 5% rise on Premium has an own elasticity of −1.4 and a Standard/Premium cross-elasticity of +0.35.
Premium loses 10,000 × 7% = 700 units. Its new unit contribution is €68, so contribution 9,300 × 68 = €632.4k, against €620k before. Standard gains 18,000 × 1.75% = 315 units, that is €10.7k of contribution. Gross portfolio gain: €23.1k. But 240 new Standard buyers would have bought Premium later; their lost future value of €120 represents €28.8k.
The immediate gain of €23.1k becomes −€5.7k after future value. The rise is limited to 2% on a pilot segment and accompanied by a service fence.
Acceptance conditions
What must be true to act.
- 01
The matrix is directional and segmented by relevant context.
- 02
The price variation is identifiable and close to the range decided.
- 03
Transfers are converted into contribution and future value.
- 04
The adverse intervals remain compatible with the risk accepted.
Limits
What this analysis does not prove.
- Elasticities change with the amplitude, the direction and the duration of the price.
- Unobserved competitors can absorb part of the transfers.
- An aggregate model describes heterogeneous individual substitutions poorly.
References
Works cited.
- Deaton, A. & Muellbauer, J. (1980), Economics and Consumer Behavior.
- Berry, S., Levinsohn, J. & Pakes, A. (1995), “Automobile Prices in Market Equilibrium”, Econometrica.
- Bijmolt, T. H. A., Van Heerde, H. J. & Pieters, R. G. M. (2005), “New Empirical Generalizations on the Determinants of Price Elasticity”, Journal of Marketing Research.