Question

A monopolist earns 30\( million annually and will maintain that level of profit indefinitely, provided that no other firm enters the market. However, if another firm enters the market, the monopolist will earn 30\) million in the current period and 15\( million annually thereafter. The opportunity cost of funds is 10 percent, and profits in each period are realized at the beginning of each period.

a. What is the present value of the monopolist's current and future earnings if entry occurs?

b. If the monopolist can earn 16\) million indefinitely by limit pricing, should it do so? Explain.

Short answer

1. ${\mathrm{\pi }}^{\mathrm{L}}=\left(\frac{1+0.1}{0.1}\right)\mathrm{\$}16$
2. ${\mathrm{\pi }}^{\mathrm{L}}=11\times 16=\mathrm{\$}176$

Therefore, ${\mathrm{\pi }}^{\mathrm{MD}}>{\mathrm{\pi }}^{\mathrm{L}}$. So, the monopolistic company it will be convenient to allow the entry of the new company.

Step-by-step solution

To find the present value of the monopolist

a.

The present value of the monopolist's current and future earnings if entry occurs can be determinate with the following equation:

${\pi }^{MD}={\pi }^M+\left(\frac{1}{1+i}\right){\pi }^D+{\left(\frac{1}{1+i}\right)}^2{\pi }^D+{\left(\frac{1}{1+i}\right)}^3{\pi }^D+\dots$

${\pi }^{MD}={\pi }^M+\frac{{\pi }^D}{i}$

In particular, the incumbent earns the monopoly profit during the first period. This induces the entry of new companies which will reduces profits to ${\mathrm{\pi }}^{\mathrm{D}}$in all remaining periods. The term ${\mathrm{\pi }}^{\mathrm{D}}$I reflects the present value of the perpetuity of duopoly profits.

To find the monopoly profit value

By substituting the monopoly profit values on equation (1), the annually benefit thereafter the entry of the new competitor and the opportunity cost the present value will be:

$\begin{array}{c}{\pi }^{MD}=\$30+\frac{\$15}{10\%}\\ =30+\frac{15}{0.10}\\ =\$180\end{array}$

To find the limit price strategy

b.

Through a limit price strategy, the monopolistic company that limits the entry of new competitors can be defined through the following formula:

${\mathrm{\pi }}^{\mathrm{L}}={\mathrm{\pi }}^{\mathrm{L}}+\left(\frac{1}{1+\mathrm{i}}\right){\mathrm{\pi }}^{\mathrm{L}}+{\left(\frac{1}{1+\mathrm{i}}\right)}^2{\mathrm{\pi }}^{\mathrm{L}}+{\left(\frac{1}{1+\mathrm{i}}\right)}^3{\mathrm{\pi }}^{\mathrm{L}}+\dots$

${\pi }^L=\left(\frac{1+i}{i}\right){\pi }^L$

To find the monopolist value

By substituting the values assuming that the monopolist can earn million indefinitely by limit pricing the present value will be:

$\begin{array}{c}{\mathrm{\pi }}^{\mathrm{L}}=\left(\frac{1+0.1}{0.1}\right)\mathrm{\$}16\\ =\mathrm{\$}176\end{array}$

Therefore, ${\pi }^{MD}>{\pi }^L$so the monopolistic company it will be convenient to allow the entry of the new company.