Consider the demand curve Q^d = 500P^-². If the price is 1, the elasticity of demand is A) -0.50 B) -2 C) 500 D) -500

Question

Quizplus · Accepted Answer

The formula for elasticity of demand is (% change in quantity demanded)/(% change in price).
At a price of 1, the quantity demanded can be found by setting P=1 in the demand equation:
QS1U1P1dS1S1P0 = 500PS1U1P1 S1S1P0S1U1P1-S1S1P0S1U1P12S1S1P0
QS1U1dS1S1P0 = 500S1U1P1 S1S1P0S1U1-1S1S1P0S1U1P1
QS1U1dS1S1P0 = 500S1U1P1 S1S1P0(2S1U1-1)
At P=1, S1S1P0=2 and S1U1=2:
QS1U1dS1S1P0 = 500(2)(2(2)-1)
QS1U1dS1S1P0 = 3000
Now, if the price were to increase to 2, the quantity demanded can be found by setting P=2:
QS1U1dS1S1P0 = 500(2)(2(2)-2) = 2000
The percentage change in quantity demanded is:
[(3000-2000)/3000] x 100% = 33.33%
The percentage change in price is:
[(2-1)/1] x 100% = 100%
So, the elasticity of demand is:
(% change in quantity demanded)/(% change in price) = (-33.33%)/(100%) = -0.333 = -2/6 = -2. Therefore, the answer is B.

Consider the Demand Curve Qd = 500P -2

Consider the Demand Curve Q^d = 500P^-²