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Answer:
Price elasticity of demand = 0.33%
Explanation:
A price elasticity of demand can be defined as a measure of the responsiveness of the quantity of a product demanded with respect to a change in price of the product, all things being equal.
Mathematically, the price elasticity of demand is given by the formula;
[tex] Price \; elasticity \; of \; demand = \frac {Percentage \; change \; in \; price}{Percentage \; change \; in \; demand} [/tex]
Given the following data;
Old price = $10
New price = $12
Old quantity demanded = 100
New quantity demanded = 40
To find the price elasticity of demand, we would determine the percentage change in price and demand.
[tex] Percentage \; change \; in \; price = \frac {12 - 10}{10} * 100 [/tex]
[tex] Percentage \; change \; in \; price = \frac {2}{10} * 100 [/tex]
[tex] Percentage \; change \; in \; price = \frac {200}{10} [/tex]
Percentage change in price = 20%
[tex] Percentage \; change \; in \; demand = \frac {100 - 40}{100} * 100 [/tex]
[tex] Percentage \; change \; in \; demand = \frac {60}{100} * 100 [/tex]
[tex] Percentage \; change \; in \; demand = \frac {6000}{100} [/tex]
Percentage change in demand = 60%
Now, we can find the price elasticity of demand;
Substituting into the equation, we have;
[tex] Price \; elasticity \; of \; demand = \frac {20}{60} [/tex]
Price elasticity of demand = 0.33%