Answer:
(B) 40%
Explanation:
↓Q / ΔPrice = Price-elasicity
The price elasticity is the relationship between a change in price with the quantity demanded of a certain good assuming, other factor remains constant.
ΔPrice = (P0 - P1)/((P0 + P1)/2) = (2 - 6)/((2+6)/2) = 4/4 = 1
We know that price elasticity is 0.4
Now we can solve for the change in the quantity demanded:
↓Q/ 1 = 0.4
↓Q = 0.4 x 1 = 0.40 = 40%
The price elasticity of demand is 0.4, the reduction in demand will be 40%.
Price-elasticity of demand refers to the change in quantity demanded of a good with respect to change in its price. The price- elasticity of demand can be calculated as:
[tex]\rm Price-elasticity \:of \:demand = \dfrac{Change\:in\:demand}{Change\:in\:price}[/tex]
When using the mid-point method, the value of change in price will be:
[tex]\rm Change\: in\: price = \dfrac{P2 - P1}{\dfrac{P2+P1}{2}}[/tex]
Where P1 is the initial price, and P2 is the changed price.
Given:
P1 is $2
P2 is $6
Price elasticity of demand is 0.40
Change in price will be calculated as:
[tex]\rm Change\: in\: price = \dfrac{P2 - P1}{\dfrac{P2+P1}{2}}\\\\\rm Change\: in\: price = \dfrac{\$6 - \$2}{\dfrac{\$6 + \$2}{2}}\\\\\rm Change\: in\: price = \dfrac{\$4}{\$4}\\\\\rm Change\: in\: price = 1[/tex]
Therefore, change in quantity demanded will be:
[tex]\begin{aligned} \rm Price-elasticity \:of \:demand &=\rm \dfrac{Change\:in\:demand}{Change\:in\:price}\\\\\rm 0.40 &=\rm \dfrac{Change\:in\:demand}{1}\\\\\rm Change\:in\:demand &= 0.40\times1\\\\\rm Change\:in\:demand &= 0.40\end[/tex]
The reduction in smoking is therefore 40%.
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