The relative rate of change of a function f(x) is f'(x)/f(x), or equivalently, d/dx ln f(x)
The percentage rate of change is 100 × f'(x)/f(x), or equivalently, 100 × d/dx ln f(x).
Population = f(t) = 2.7t + 282
Percentage rate of change = p(t) = 270/(2.7t + 282)
The elasticity of demand at price p, denoted by E(p), is:
E(p) = -(relative rate of change of demand)/(relative rate of change of price)
x = f(p) = 1000(40 - p)
E(p) = -pf'(p)/f(p) = p/(40 - p)
| E(p) | Demand | Interpretation | Revenue |
|---|---|---|---|
| 0 < E(p) < 1 | Inelastic | Demand is not sensitive to changes in price. % price change → smaller % demand change. | Price increase → revenue increase |
| E(p) > 1 | Elastic | Demand is sensitive to changes in price. % price change → larger % demand change. | Price increase → revenue decrease |
| E(p) = 1 | Unit | % price change → same % demand change. |
Drag the slider to see how the elasticity of demand changes with different values of p.