Q.The demand function is $x = 40 - 5p$, where $x$ is the quantity demanded at price $p$ (in ₹). Find the elasticity of demand at $p = 6$ and interpret your result.

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

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

Substituting $R_A = 50$ and $\eta = 5$:

$R_M = 50\left(1 - \frac{1}{5}\right) = 50\cdot\frac{4}{5} = 40.$

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;
• $0 < \eta < 1$: demand is inelastic (demand responds less than proportionally to a price change).

Since the given condition is $0 < \eta < 1$, the demand falls in the inelastic category.

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.
• $|\eta_d| < 1$: inelastic — quantity changes less than proportionally.

So an elastic demand function has $|\eta_d| > 1$.