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# 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? - Economics

Short Note

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?

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#### 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,

ed = - (% "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%.

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