# Section 3.7: Elasticity of Demand

## Relative and Percentage Rates of Change

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).

#### Example:

Population = f(t) = 2.7t + 282

Percentage rate of change = p(t) = 270/(2.7t + 282)

## Elasticity of Demand

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)

#### Example:

x = f(p) = 1000(40 - p)

E(p) = -pf'(p)/f(p) = p/(40 - p)

E(p)DemandInterpretationRevenue
0 < E(p) < 1Inelastic

Demand is not sensitive to changes in price.

% price change → smaller % demand change.

Price increase → revenue increase
E(p) > 1Elastic

Demand is sensitive to changes in price.

% price change → larger % demand change.

Price increase → revenue decrease
E(p) = 1Unit% price change → same % demand change.

Drag the slider to see how the elasticity of demand changes with different values of p.

p = 8