# Your firm sells a product facing a Price Elasticity of Demand = -1.55. What change in price would...

## Question:

Your firm sells a product facing a Price Elasticity of Demand = -1.55. What change in price would lead to a 12% rise in Quantity Demanded?

a. -2.64%

b. -7.74%

c. -13.7%

d. 31.4%

## Price Elasticity of Demand:

The price elasticity of demand is a measure of how elastic or sensitive the quantity demanded of a commodity in response to changes in the price of that commodity. The formula for the price elasticity of demand is {eq}\eta = \frac{\%\triangle Q_d}{\%\triangle P} {/eq}.

A list of information given in the problem is shown below.

Given:

{eq}\text{price elasticity of demand: }\eta = -1.55 \\\text{percentage change in quantity demanded: } \%\triangle Q_d = 12\% {/eq}

To solve for the change in price that would lead to a 12% rise in quantity demanded, we use the following formula for the price elasticity of demand.

{eq}\eta = \frac{\%\triangle Q_d}{\%\triangle P} {/eq}

Since {eq}\eta = -1.55 {/eq} and {eq}\%\triangle Q_d = 12\% {/eq}, then the above equation becomes:

{eq}-1.55 = \frac{12\%}{\%\triangle P} \\\%\triangle P= \frac{12\%}{-1.55 } \\\%\triangle P= -7.74 \% {/eq}

The change in price that would lead to a 12% rise in quantity demanded is -7.74%. The price of the product has to fall by 7.74% so that the quantity demanded increases by 12%.

The answer is letter b. -7.74%. 