Q.If the demand function is $x = 50 - p$, find the price elasticity of demand when $p = 20$, and state whether demand is elastic, inelastic, or of unit elasticity at this price.

Use the relation $R_M = R_A\left(1 - \frac{1}{\eta}\right)$ with $R_A = 50$ and $\eta = 5$.

The relationship between marginal revenue $R_M$, average revenue $R_A$ and the elasticity of demand $\eta$ is

$R_M = R_A\left(1 - \frac{1}{\eta}\right).$

…

When $0 < \eta < 1$, the percentage change in demand is smaller than the percentage change in price, so demand is inelastic.

The (numerical value of the) price elasticity of demand $\eta$ compares the proportional change in quantity demanded with the proportional change in price. The standard classification is:

• $\eta > 1$: demand is elastic (demand is highly responsive to price);
• $\eta = 1$: demand is unitary elastic; …

Elastic demand corresponds to $|\eta_d|>1$ (quantity responds more than proportionally to price).

The price elasticity of demand $\eta_d$ compares the proportional change in quantity demanded to the proportional change in price. Its magnitude classifies demand:

• $|\eta_d| > 1$: elastic — quantity changes more than proportionally.
• $|\eta_d| = 1$: unit elastic. …