Question

The demand for a product is Q_d = 2446 – 95P. Calculate the price elasticity of demand at a price of $18 and explain the meaning of this particular numerical value.

Answer 1

Q_d = 2446 – 95P

Put P = $18

Qd = 2446 - (95 * 18)

Qd = 2446 - 1710

Qd = 736

So, Q = 736

As we know that, Q_d = 2446 – 95P

Also, P = $18, Q = 736

The slope dQ/dP of the demand curve is −95

As per formula

Elasticity of Demand , E = dQ / dP * P / Q

Plugging values in above formula, we get

Elasticity of Demand, E = 95 * 18 / 736 = 2.32

( Minus Sign is ignored and only absolute value is taken. So, dQ / dP = 95)

Elasticity of Demand is 2.32. This means that Elasticity is greater than 1. This means that demand is Elastic. Elastic Demand means that a given percentage change in price will result in even large percentage change in quantity demanded. If demand is elastic at a particular price level, then percentage drop in price will result in an even larger percentage increase in the quantity sold resulting in increase in total revenue. The vice versa also holds true.