Learn · 08 / 10

8 · Elasticity vs λ — two dials that people conflate

A recurring confusion: "isn't λ just modelling demand sensitivity?" No — and keeping the two dials apart is what makes the empirical programme honest.

Elasticity lives in the payoffs. How much demand a firm loses when it raises price is a property of consumers, estimated in the demand stage. It reshapes the payoff surface U(p) itself: crossing elasticities change which prices are good ideas at all.

λ lives in the response. Given whatever payoff surface demand implies, λ says how sharply the firm converts payoff differences into choice probabilities. It never changes which price is best; it changes how decisively best is chosen.

In the Lab this is one experiment: change elasticity and the payoff bars themselves move (and with them the QRE); change λ with payoffs frozen and only the sharpness of the distribution moves. Two dials, visibly orthogonal.

Why it matters: when λ is estimated from data, everything mis-specified in the demand stage tries to leak into it ("λ absorbs unmodelled heterogeneity" — stated once, here). That is why the programme leads with the reciprocity test, which is λ-free as a symmetry statement (explainer 7): an asymmetric cross-response cannot be absorbed by any value of a noise parameter. Payoff facts and response facts are separated by construction, and the instruments are built to respect the separation.

So what would you do differently?

A demand elasticity and a rival's decisiveness look the same in a regression and mean opposite things for what you should do. Separate them before you set a price on either.

Change one, then the other, and compare →
▶ try it · elasticity moves the payoffs; λ moves the sharpness
in-browser · goldens-checked
demand elasticity ε (consumers) = 18.0
expected profit — the payoff surface itself best: £1.70
£1.70
10.0
£1.72
8.4
£1.74
6.8
£1.76
5.4
£1.78
4.3
response precision λ (the firm) = 0.500
0.02 · noise8 · sharp
choice probabilities — only the sharpness
£1.70
0.554
£1.72
0.245
£1.74
0.113
£1.76
0.056
£1.78
0.031

Turn ε: the payoff bars move, the best price can change, and the probabilities follow — that is a fact about consumers. Turn λ with ε frozen: the bars never move; only how decisively the best is chosen changes — a fact about the firm. Two dials, orthogonal by construction; conflating them is how mis-specified demand leaks into λ.