Question

A company sells q ribbon winders per year at $p per\ribbon winder. The demand function for ribbon winders is given by P=300−0.02Q. Find the elasticity of demand when the price is $70 apiece. Will an increase in price lead to an increase in revenue

Answer 1

Answer:

0.30

Demand is inelastic and an increase in price would lead to an increase in total revenue

Explanation:

P=300−0.02Q

Make q the subject of the formula by dividing through by 0.02

50P = 15,000 - Q

Q = 15,000 - 50P

Differentiate the above equation

$\frac{dp}{dq} = -50$

Determine the value of q when p is 70

Q = 15,000 - 50(70) = 11,500

Elasticity = $[\frac{p}{q} . \frac{dp}{dq} ]$

[$\frac{70}{11500} . -50]$ = 0.30

Demand is inelastic and an increase in price would lead to an increase in total revenue

Price elasticity of demand measures the responsiveness of quantity demanded to changes in price of the good.

Price elasticity of demand = percentage change in quantity demanded / percentage change in price  

If the absolute value of price elasticity is greater than one, it means demand is elastic. Elastic demand means that quantity demanded is sensitive to price changes.  

Demand is inelastic if a small change in price has little or no effect on quantity demanded. The absolute value of elasticity would be less than one

Demand is unit elastic if a small change in price has an equal and proportionate effect on quantity demanded.  

Infinitely elastic demand is perfectly elastic demand. Demand falls to zero when price increases  

Perfectly inelastic demand is demand where there is no change in the quantity demanded regardless of changes in price.