Question

2. A price change causes the quantity demanded of a good to decrease by 30 percent, while the total revenue of that good increases by 15 percent. Is the demand curve elastic or inelastic? Explain.

Answer 1

Let,

Initial Price = P

Initial Quantity = Q

So Revenue = PQ

Now, After a fall in Quantity by 30% due to price rise and also the total revenue increases by 15%

So, New quantity = Q - 30% of Q = 0.7Q

New Revenue = PQ + 15% of (PQ) = 1.15PQ

Let new price = P'

So, P' * 0.7Q = 1.15PQ

P' = 1.15PQ/0.7Q = 1.642 P

P' = P + 0.642P

So, Percentage Increase in P = 64.2% = 0.642

We know,

$Elasticity = \frac{Percentage\; change\; in\; Q}{Percentage \;change \;in\; P}$

So, Elasticity = - 0.3/0.642 = - 0.467

As, |Elasticity| = |-0.467| = 0.467 < 1 so demand is inelastic.

Hence, The demand is inelastic