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

Answer:

C) $2

Explanation:

Q = 2000 - 500P => $\frac{dQ}{dP} = -500$

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 = $\frac{P}{Q}\frac{dQ}{dP} = \frac{P}{2000-500P} \times (-500)$

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

=> $\frac{P}{2000-500P} = \frac{1}{500}$

=> 500P = 2000 - 500P

=> P = 2