Question

If the demand function for orange juice is expressed as Q = 2000 - 500p, where Q is quantity in gallons and p is price per gallon measured in dollars, then the demand for orange juice has a unitary elasticity when price equals

A) $0.
B) $1.
C) $2.
D) $4.

Answer 1

C) $2

Step-by-step explanation:

Q = 2000 - 500P =>
`(dQ)/(dP) = -500`

The price elasticity of demand is is defined to be the percentage change in quantity demanded divided by the percentage change in price. The formula is:

Elasticity =
`(P)/(Q)(dQ)/(dP) = (P)/(2000-500P) * (-500)`

Unitary elasticity (change in price leads to equal change in quantity demanded) means absolute value of elasticity = 1 => elasticity = -1

=>
`(P)/(2000-500P)  = (1)/(500)`

=> 500P = 2000 - 500P

=> P = 2