Question

Recently, Pacific Cellular ran a pricing trial in order to estimate the elasticity of demand for its services. The manager selected three states that were representative of its entire service area and increased prices by $\mathbf{5}$percent to customers in those areas. One week later, the number of customers enrolled in Pacific’s cellular plans declined $\mathbf{4}$percent in those states, while enrolments in states where prices were not increased remained flat. The manager used this information to estimate the own price elasticity of demand and, based on her findings, immediately increased prices in all market areas by $\mathbf{5}$percent in an attempt to boost the company’s $\mathbf{2012}$annual revenues. One year later, the manager was perplexed because Pacific Cellular $\mathbf{2012}$annual revenues were $\mathbf{10}$percent lower than those in $\mathbf{2011}$—the price increase apparently led to a reduction in the company’s revenues. Did the manager make an error? Explain.

Short answer

The manager made an error in decision-making.

Step-by-step solution

Find the elasticity

$4\%$Given, the number of customers enrolled in Pacific's cellular plans declined by .

In this case, we use the following equation:

$E_{Q_x·l_x}=\frac{\%\Delta Q_x^d}{\%\Delta P_x}$

It immediately increased prices in all market areas by $5\%$in an attempt to boost the company's $2012$annual revenues.

Calculating the elasticity as follows:

$$\begin{gathered} E_{Q_x·l_x}=\frac{\%\Delta Q_x^d}{\%\Delta P_x} \\ =\frac{-4}{5} \\ {E}_{Q_x·p_x}=-0.8 \end{gathered}$$

Therefore, the elasticity is localid="1658333784859" $\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{8}$

Find the elasticity when revenue gets reduced

Now, the prices increased in all market areas by $5\%$, so the price increase apparently led to a reduction in the company's revenues by $10\%$.

Now we calculate the elasticity as follows:

$$\begin{gathered} E_{Q_x·p_x}=\frac{\%\Delta Q_x^d}{\%\Delta P_x} \\ =\frac{-10}{5} \\ {E}_{Q_x·p_x}=-2 \end{gathered}$$

Therefore, the elasticity islocalid="1658333817094" $\mathbf{-}\mathbf{2}$

As per the calculations, therefore it can be concluded that the manager made an error in decision-making.

The changes in the demand shows that it is elastic, which means that there will be a decrease in the company's revenue due to the price increase.