CB2400 Chap.4 Elasticity and Revenue Decisions
Elasticity and Revenue Decisions
Elasticity measures proportional response
Own-price elasticity of demand divides the percentage change in quantity demanded by the percentage change in price. The ratio is unit-free, so responsiveness can be compared across products measured in different units.
Demand elasticity is negative because price and quantity move in opposite directions, but verbal classification conventionally uses the absolute value.
Midpoint and point methods answer different settings
The midpoint method uses each pair of endpoint averages and gives one arc elasticity regardless of the direction in which the movement is read.
Point elasticity combines a local slope with the current price-to-quantity ratio. It is appropriate for very small changes or a supplied demand function. A straight line has a constant slope but changing elasticity because P divided by Q changes along the curve.
Revenue supplies a directional audit
Total revenue equals price times quantity.
With elastic demand, a price rise produces a larger proportional quantity loss and revenue falls. With inelastic demand, the price effect dominates and revenue rises. Unit elasticity balances the percentage effects locally. If the computed magnitude and revenue direction disagree, inspect the percentage denominators and arithmetic.
What this chapter covers
- 01
unit-free responsiveness
- 02
elastic and inelastic ranges
- 03
midpoint elasticity
- 04
point elasticity
- 05
slope versus elasticity
- 06
price and total revenue
Worked example · free
Use midpoint elasticity and check revenue
- 3Compute the midpoint percentage quantity change.
- 3Compute the midpoint percentage price change and divide.
- 2Classify and compare total revenue.
Key terms
- Price Elasticity
- The percentage quantity response divided by the percentage own-price change.
- Arc Elasticity
- Responsiveness measured across an interval using midpoint percentage changes.
- Point Elasticity
- Responsiveness at one point using the local slope and price-to-quantity ratio.
- Elastic Demand
- Demand with an absolute own-price elasticity greater than one.
- Inelastic Demand
- Demand with an absolute own-price elasticity less than one.
Elasticity and Revenue Decisions FAQ
Why is elasticity different from slope?
Slope uses unit changes and depends on the measurement units. Elasticity uses percentage changes and is unit-free. Along a straight demand curve the slope remains constant, but the price-to-quantity ratio changes, so point elasticity changes from the high-price end to the low-price end.
Why use the midpoint formula?
An initial-value percentage gives different magnitudes when the same movement is read forward and backward. The midpoint method divides each change by the average of its two endpoints, producing one arc elasticity for the interval and avoiding that direction-dependent denominator problem.
How does elasticity predict total revenue?
When demand is elastic, quantity changes proportionally more than price, so a price increase lowers total revenue and a price cut raises it. When demand is inelastic, the price effect is larger, so a price increase raises revenue. Unit elasticity leaves revenue locally unchanged.
Exam move
Build a three-column table for elastic, unit elastic and inelastic demand. Add the price-rise and price-fall revenue directions. Then solve one midpoint example and one point-elasticity example from a linear function. Verify each result by calculating revenue or by checking whether the high-price, low-quantity point should be more elastic.
For every arc calculation, write the average price and average quantity before forming either percentage. This prevents a mixed-denominator answer. Retain the negative sign during computation, then use the absolute value only for the elasticity classification. When a demand function is supplied, calculate quantity at the named price, identify dQ/dP and multiply the slope by P/Q. Do not report the slope coefficient alone.
Audit the result through units: elasticity has none, while slope does. Next, test the revenue prediction numerically with price times quantity at both observations. Under elastic demand, price and revenue move in opposite directions; under inelastic demand, they move together. Practise explaining why a straight line changes elasticity despite its constant slope, focusing on the changing P/Q ratio.
End with determinant prompts covering substitutes, adjustment time and budget share, but treat them as reasons for responsiveness rather than replacements for a calculation when observations are available. Preserve unrounded values through the comparison with one, then round only the reported elasticity so a borderline classification is not changed by presentation.
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