Answer to Question #262885 in Economics of Enterprise for Mohamed

Question

The Teenager Company makes and sells skateboards at an average price of $70 each. During the past year, they sold 4,000 of these skateboards. The company believes that the price elasticity for this product is about −2.5. If it decreases the price to $63, what should be the quantity sold? Will revenue increase? Why

 

Answer 1

P1 = $70 per unit

P2 = $63 per unit

Q1 = 4,000 units

Q2 = ?

E_d = -2.5

Formula for price elasticity is written as:

$E_d=\frac{(Q_2-Q_1)}{(P_2-P_1)}\times\frac{(P_2++P_1)}{(Q_2+Q_1)}$

$-2.5=\frac{(Q_2-4000)}{(63-70)}\times\frac{(63+70)}{(Q_2+4000)}$

$-2.5=\frac{(Q_2-4000)}{(-7)}\times\frac{(133)}{(Q_2+4000)}$

$2.5=\frac{19\times(Q_2-4000)}{(Q_2+4000)}$

$2.5\times(Q_2+4000)=19\times(Q_2-4000)$

$2.5Q_2+10000=19Q_2-76000$

$16.5Q_2=86000$

$Q_2=\frac{86000}{16.5}=5212$

Revenue at Q1 = $70 * 4000 = $280,000

Revenue at Q2 = $63 * 5212= $328,356

Revenue will increase in case of price decreases from $70 to $63 per unit because it will increases quantity sold from 4,000 to 5,212 skateboards.