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Question
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,
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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