Question

Barney owns a bagel business in New York City and he wants to increase his total revenue. He knows that, when bagels are $1, he sells 250 an hour, and when he lowers the price to $0.75, he sells 275 an hour. A) Using the midpoint method, compute the price elasticity of demand for Barney’s bagels. (show formula and all your calculations) B) Based on your answer to section A, is demand for Barney’s bagels elastic or inelastic? How do you know? Explain C) Based on your answer to section B, explain whether he should raise or lower the price to generate more revenue.

Answer 1

Initial price= P1= 1

Initial quantity= Q1= 250

New price= P2= 0.75

New quantity= Q2=275

A)

Midpoint method: Price elasticity of demand= % change in Quantity / % change in price

% change in Quantity= (Change in Quantity/Average of quantity) x 100

Change in quantity= Q2-Q1= 275-250= 25

Average of quantity= (Q2+Q1)/2= 525/2= 262.5

% change in Quantity= (25/262.5) x 100= 9.52

% change in price= (Change in price/Average of price) x 100

Change in price= P2-P1= 0.75-1= -0.25

Average of quantity= (P2+P1)/2= 1.75/2= 0.875

% change in Price= (-0.25/0.875) x 100= -28.57

Price elasticity of demand= 9.52/(-28.57)= -0.33

B)

Demand is elastic when % change in quantity demand > % change in price which cause price elasticity of demand to be greater than 1 while on the other hand demand is inelastic when % change in quantity demand < % change in price which cause price elasticity of demand to be less than 1.

Here absolute value of price elasticity of demand is 0.33 which is less than 1 so demand is inelastic.

C)

If demand is inelastic then there will be positive relationship between price and total revenue that is if price increases then total revenue will also increase.

If demand is elastic then there will be negative relationship between price and total revenue that is if price increases then total revenue will decrease.

Here demand is inelastic so to generate more revenue he should raise the price.