Elasticity, Total Revenue, and Pricing
Seller total revenue is price times quantity sold: . A price change creates opposing price and quantity effects; demand elasticity determines which dominates.
With elastic demand, a price cut produces a larger percentage quantity increase, raising revenue. With inelastic demand, the price loss dominates and revenue falls. At unit elasticity, revenue is approximately unchanged.
Decompose the revenue change
Ticket price falls from 40 and attendance rises from 800 to 1,100. Revenue moves from 44,000. The seller loses $10 on each old sale but gains 300 sales; the quantity effect dominates.
| Demand | Raise price | Cut price |
|---|---|---|
| elastic | revenue falls | revenue rises |
| unit elastic | roughly unchanged | roughly unchanged |
| inelastic | revenue rises | revenue falls |
This test works only for movement along stable demand. Revenue is not profit: cleaning, staffing, licensing, and capacity costs remain. The profit-maximizing price may differ from the revenue-maximizing price, and elasticity can vary across intervals and customer groups.
Tonight's little theatre
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Revenue is not profit: costs remain to be deducted, and volume changes can affect marginal cost or capacity. Elasticity may also vary by price interval, time, and customer group, so real pricing cannot rely on one fixed coefficient.
KNOWLEDGE QUIZ
Should the theatre cut ticket prices?
A theatre with 1,200 seats considers a price cut. Forecast attendance is below capacity. Fixed cost is 10,000 and each attendee costs another 10. Assume audience composition and show quality are unchanged.
Current: price 50, attendance 800. Proposal: price 40, attendance 1,100.
- Compute midpoint elasticity and the change in revenue.
- Separate the revenue change into lost revenue on old customers and revenue from extra customers.
- Compute profits and the attendance needed at price 40 to match old profit. Would revenue alone justify the decision?