Question

At​ Roy's Music​ Shack, when the price of CDs is ​$15​, 700 are demanded. When the price of CDs is ​$16​, 600 are demanded. Using the averages of the two prices and​ quantities, the price elasticity of demand for CD is __ Round your answer to one decimal​ place, and express your answer in absolute value.​)

Answer 1

Answer

Price of CD	Quantity demand for CD
$15	700
$16	600

Let us denote the old price and the new price as P₁, and P₂ respectively. Let the quantity demanded at P₁ is Q_{1 ,} and the quantity demanded at P₂ is Q₂.

So, when P₁ = $15 , Q₁ = 700

when P₂ = $16 , Q₂ = 600

The price elasticity of demand (E_d) is the responsiveness of the quantity demanded for the change in price. It is the percentage change in quantity demanded due to the percentage change in price.

The E_d using averages of the two prices and quantities is as follows:

E_d =[(Q₂ -  Q₁)/{(Q₂ + Q₁)/2}] / [(P₂ - P₁)/{(P₂ + P₁)/2}]

Putting the respective values, we get,

E_d = [(600-700)/{(600+700)/2}] / [(16-15)/{(16+15)/2}]

Or, E_d = {(- 100)/(1300/2)} / {(1)/(31/2))

Or, E_d = - (100/650) / (1/15.5)

Or, E_d = - 0.1538 / 0.0645

Or, E_d = - 2.38

Or, E_d = - 2.4

Taking modulus,

| E_d | = 2.4

Or, E_d = 2.4 (approx.)

So, here the price elasticity of demand (E_d ) is 2.4 approximately , i.e. E_d >1. It means, the percentage change in quantity demand is greater than the percentage change in price.The price elasticity of demand is elastic here.

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