Question

A firm sells​ 3,000 headphones at a price of​ $3 per unit. Even though this price is slightly higher than competing​ brands, the management is considering a further increase in price by 25 cents. The firm plans to focus advertising efforts on superior sound clarity.​ Rachel, the​ firm's marketing​ head, feels confident that a price increase by 25 cents will increase revenue. Industry analysts are of the opinion that even though the revenue is likely to​ increase, the firm must be careful of rivals who are actively competing for higher market share. a. Based on Rachel's assumption, would she think the price elasticity of demand for headphones is elastic, or inelastic? The firm increased the price of headphones to​ $3.25 and the firm was able to sell 2,775 headphones at this new price. b. What is the price elasticity of demand? Was Rachel's assumption correct?

Answer 1

a. Based on Rachel's assumption, would she think the price elasticity of demand for headphones is elastic, or inelastic?

Answer :

Inelastic.

Explanation :

When demand is inelastic price and total revenue moves into same direction. So when price increases, total revenue will increase. Here when price increases, total revenue is increase. Thus demand is inelastic.

b. What is the price elasticity of demand?

Answer :

Price elasticity of demand =[(Q2-Q1) /(Q2 +Q1) /2]÷[(P2-P1) /(P2+P1)/2]

=[(2775-3000)/(2775+3000)/2]÷[3.25-3)/(3.25+3)/2]

=[225/2887.5]÷[0.25/3.125]

=0.0779/0.08

=0.97

Was Rachel's assumption correct?

Yes.

Because when price elasticity of demand is less than 1 it is inelastic.

Total revenue =Price *quantity

When price is 3=3*3000

   =9000.

When price is 3.25=3.25*2775

=9018.75.

So total revenue increased.