Question

A hot dog vendor faces a daily demand curve of Q = 1800 – 15P, where P is the price of hot dogs in cents and Q is the number of hot dogs purchased each day. a. If the vendor has been selling 300 hot dogs each day, how much revenue has he been collecting? b. What is the price elasticity for hot dogs? c. The vendor decides that he wants to generate more revenue. Should he raise or lower the price of his hot dogs?

Answer 1

Answer

a)

Q=1800-15P

Q=300

300=1800-15P

15P=1500

P=100

total revenue =P*Q=300*100=30000

the total revenue is $30000

-------------

b)

price elasticity =(dQ/dP)*Q

dQ/dP=-15 .......... first differentiation of the demand curve

price elastcity=(-15)*(100/300)

=-5

The price elasticity is -5. The demand is elastic as the elasticity is below -1.

---------

c)

A revenue is maximum when demand is unit elastic, and the given demand is elastic so the vendor should decrease the price to increase revenue.

the price should be

price elasticity of demand =(dQ/dP)*(P/Q)

-1=(-15)*(P/(1800-15P))

1800-15P=15P

30P=1800

P=60

Q=1800-15*60=900

TR=P*Q=60*900=54000