When the price of spicy sauce was $10dollar sign, 10, people bought 100 jars. When the price increased to $12dollar sign, 12, people only bought 40 jars. What is the price elasticity of demand for spicy sauce?

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%