**Answer the following question.**

When the price of X doubles, its quantity demanded falls by 60 percent. Calculate its price elasticity of demand. What should be the percentage change in price so that its quantity demanded doubles?

#### Solution

We are given, that when the price of X doubles, its quantity demanded falls by 60 percent.

Percentage fall in demand = 60

Initial Price = x

New Price = 2x

`% "Increase in Price" = (2"x" - "x")/"x" xx 100 = 100%`

We know,

e_{d} = `- (% "Change in Demand")/(% "Change in Price") = -(60)/(100) = -0.6`

So, price elasticity of demand is -0.6

Now, if the demand ( say, y units ) is to double ( to 2y units),

`% "Change in Demand" = (2"y"-"y")/"y" xx 100 = 100%`

So,

`% "Change in Price" = -(% "Change in Demand")/("e"_"d") = -(100)/(0.6) = -166.6`

So, we can say that if the demand is to rise by double, then the price should fall by 166.66%.