Answer to Question #314803 in Microeconomics for Fawaz

Question

Sailright Inc. manufactures and sell sailboards. Management believes that the price elasticity of demand is -3.0. Currently, boards are priced at $500 and the quantity demanded is 10000 per year. If the price is increased to $600, how many sailboards will the company be able to sell each year? How much will total revenue change as a result of the price increase?

Answer 1

E_d=$\frac{ change of quantity demanded}{ change in price}$

% change in Quantity

$\frac{Q1-Q}{Q}$ =$\frac{Q1-10000}{10000}$

=0.0001Q₁-1

% change in price

$\frac{P1-P}{P}$ =$\frac{600-500}{500}$

=$\frac{100}{500}$ =0.2

E_d= $\frac{0.0001Q1-1}{0.2}$ ,Where E_d=-3,then

-3=$\frac{0.0001Q1-1}{0.2}$

-0.6=0.0001Q₁-1

0.4=0.0001Q₁

Q₁=4000

change in revenue ;

=(P₁$\times$ Q₁)-(P$\times$Q)

=(600$\times$4000)-(500$\times$10000)

=2,400,000-5,000,000

=-2,600,000

therefore by increasing prices the total revenues reduced by $2,600,000