Question

If Starbucks’s marketing department estimates the income elasticity of demand for its coffee to be $\mathbf{2}\mathbf{.}\mathbf{6}$, how will the prospect of an economic boom (expected to increase consumers’ incomes by$\mathbf{6}$percent over the next year) impact the quantity of coffee Starbucks expects to sell?

Short answer

The demand will increase by $15.6\%$.

Step-by-step solution

Find the elasticity of demand

The elasticity of demand is defined as the ratio of the percentage change in demand with the percentage change in price.

$\mathrm{E}=\frac{\mathrm{\%}{\mathrm{\Delta Q}}_{\mathrm{x}}^{\mathrm{d}}}{\mathrm{\%}{\mathrm{\Delta QP}}_{\mathrm{x}}}$

$\%\Delta Q_x^d$represents the change in the quantity demanded

$\%\Delta Q{P}_x$represents the change in price

$E$is own price of elasticity of demand

Calculation

According to the task we have,

$E=2.6$

$\%\Delta Q{P}_x=6$

By substituting the values, we will get,

$\begin{array}{c}E=\frac{\%\Delta Q_x^d}{\%\Delta Q{P}_x}\\ 2.6=\frac{\%\Delta Q_x^d}{6}\\ \%\Delta Q_x^d=15.6\%\end{array}$

Since it is expected for the consumer's income to increase by $6\%$ over the next year, the demand for coffee will also increase by $15.6\%$ .