Question

You are an assistant to a senator who chairs an ad hoc committee on reforming taxes on telecommunication services. Based on your research, AT&T has spent over $\mathbf{\$}\mathbf{15}$million on related paperwork and compliance costs. Moreover, depending on the locale, telecom taxes can amount to as much as$\mathbf{25}$percent of a consumer’s phone bill. These high tax rates on telecom services have become quite controversial, due to the fact that the deregulation of the telecom industry has led to a highly competitive market. Your best estimates indicate that, based on current tax rates, the monthly market demand for telecommunication services is given by${\mathbf{Q}}^{\mathbf{d}}\mathbf{=}\mathbf{300}\mathbf{-}\mathbf{4}\mathbf{P}$and the market supply (including taxes) is${\mathbf{Q}}^{\mathbf{s}}\mathbf{=}\mathbf{3}\mathbf{P}\mathbf{-}\mathbf{120}$(both in millions), where P is the monthly price of telecommunication services. The senator is considering tax reform that would dramatically cut tax rates, leading to a supply function under the new tax policy of${\mathbf{Q}}^{\mathbf{s}}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{2}\mathbf{P}\mathbf{-}\mathbf{120}$. How much money per unit would a typical consumer save each month as a result of the proposed legislation?1

Short answer

After the proposed legislation, a typical consumer will save$\mathrm{\$}1.67(60-58.33)$ each month.

Step-by-step solution

Given Information:

Market for telecommunication devices is ${\mathrm{Q}}^{\mathrm{d}}=300-4\mathrm{P}$and the market supply is ${\mathrm{Q}}^{\mathrm{s}}=3\mathrm{P}-120$.

Equilibrium price in the market, demand and supply function:

By equating the supply and demand function and substituting the given values, we get the equilibrium price. The calculations are shown as follows-

$\begin{array}{c}{\mathrm{Q}}^{\mathrm{s}}={\mathrm{Q}}^{\mathrm{d}}\\ 3\mathrm{P}-120=300-4\mathrm{P}\\ 4\mathrm{P}+3\mathrm{P}=300+120\\ 7\mathrm{P}=420\\ \mathrm{P}=\frac{420}{7}\\ \mathrm{P}=60\end{array}$

Thus the equilibrium price in the market is $60.

To determine the equilibrium quantity, we will substitute the price in demand function as follows-

$\begin{array}{c}{\mathrm{Q}}^{\mathrm{d}}=300-4\mathrm{P}\\ =300-4\left(60\right)\\ =300-240\\ =60\end{array}$

Thus the equilibrium quantity in the market is 60 units.

After the new tax law, the supply function will be${\mathrm{Q}}^{\mathrm{s}}=3.2\mathrm{P}-120$ . The new situation will occur in the market , as a result.

$\begin{array}{c}{\mathrm{Q}}^{\mathrm{s}}={\mathrm{Q}}^{\mathrm{d}}\\ 3.2\mathrm{P}-120=300-4\mathrm{P}\\ 120+300=4\mathrm{P}+3.2\mathrm{P}\\ 420=7.2\mathrm{P}\\ \mathrm{P}=\frac{420}{7.2}\\ \mathrm{P}=58.33\end{array}$

The new equilibrium price will be $58.33.

After the proposed legislation, the price has decreased by $1.67.Thus, every typical consumer will save $\mathrm{\$}1.67(60-58.33)$ in a month.