Your price curve, on one page

1Elasticity

How far your units move, in percent, when your price moves 1%. Always negative; the size is the whole question.

• 0 to −1: inelastic. Profit rises with the price: walk up, and measure each step.
• Below −1: one price where profit peaks (lesson 4).
• Near −1: the best price could be anywhere; the data may not say (lesson 3).

2Your history

One row per period (half-months work): the days, the units and the average price, which is sales ÷ units. Fit units a day, never units a period.

At least 5 periods, and a price that moved: at least 2% variation (standard deviation ÷ mean). Leave out stockouts, big event deals, launches and listing changes.

3The fit, and how sure

elasticity = the slope of log(units a day) on log(price)

95% interval = elasticity ± t × standard error (HC3)

t is 2.23 on 12 periods, 3.18 on five. No best price when the interval includes −1, the estimate is within two standard errors of −1, or one standard error moves the best price by more than 50%. The direction is then up.

4The price that makes the most

best price = (landed cost + fixed fees a unit) ÷ (1 − referral rate) × ε ÷ (1 + ε)

For ε below −1. The referral fee is a share of the price; fulfilment and storage are fixed a unit. Keep them apart. A move across $10 or $50 changes the fulfilment fee: price both sides with The Fee Staircase.

5The raise

units can fall by = 1 − contribution a unit today ÷ contribution a unit at the new price

Needs no elasticity. Compare it with what the elasticity says the units will do. A raise has to be badly wrong to lose; a cut has to be right to break even.

6The discount

extra units it must sell = contribution a unit today ÷ contribution a unit on the discount − 1

A deal's own fee comes off the contribution. What a sale buys beyond that (rank afterwards, stock cleared before the cliff) is a separate bet: make it knowing what the sale cost.

7Move it, and measure it

• Never more than 5% a step.
• Before: write down the new price, the units a day you expect and the change a month.
• While live: watch Buy Box share or conversion; if either drops, reverse the step.
• After two weeks: add the period to your history and fit again.

8Every SKU, in order

1. Fit each SKU with the history for it; put elasticity, standard error and interval in one table with its price, units and costs.
2. Start at the top of what the next step is worth. Then the SKUs too close to −1: a 5% step up is the cheapest way to learn.
3. A SKU without five periods, or whose price never moved, is unread, not wrong: move it on purpose.

Every two weeks: one step for each SKU at the top, one new period into each history.