Question

Suppose that, prior to other firms entering the market, the maker of a new smartphone (Way Cool, Inc.) earns million per year. By reducing its price by 60 percent, Way Cool could discourage entry into "its" market, but doing so would cause its profits to sink to million. By pricing such that other firms would be able to enter the market, Way Cool's profits would drop to million for the indefinite future. In light of these estimates, do you think it is profitable for Way Cool to engage in limit pricing? Is any additional information needed to formulate an answer to this question? Explain.

Short answer

Decision not to adopt limit pricing technique is rational.

${\mathrm{\Pi }}_{\mathrm{L}}=\left(\frac{1+\mathrm{i}}{\mathrm{i}}\right){\mathrm{\pi }}_{\mathrm{L}}$

${\mathrm{\Pi }}_{\mathrm{MD}}={\mathrm{\pi }}_{\mathrm{M}}+\frac{{\mathrm{\pi }}_{\mathrm{d}}}{\mathrm{i}}$

Step-by-step solution

Limit pricing strategy

For the limit pricing strategy of the monopoly smartphone company Way Cool, Inc to be optimal, the present value of profits under limit pricing need to be greater than the present value if new competitors are allowed to enter in which:

${\mathrm{\Pi }}_{\mathrm{L}}>{\mathrm{\Pi }}_{\mathrm{MD}}$ Where,

${\mathrm{\Pi }}_{\mathrm{L}}$:are the expected benefit of the limit pricing strategy.

${\mathrm{\Pi }}_{\mathrm{MD}}$:are the expected benefit with the entry of new rivals.

To find the limit pricing strategy

To determine which decision combines, the equations for ${\mathrm{\Pi }}_{\mathrm{L}}$ and ${\text{Π}}_{\mathrm{MD}}$ must be reorganized, which are the following -

${\mathrm{\Pi }}_{\mathrm{L}}=\left(\frac{1+\mathrm{i}}{\mathrm{i}}\right){\mathrm{\pi }}_{\mathrm{L}}$

${\mathrm{\Pi }}_{\mathrm{MD}}={\mathrm{\pi }}_{\mathrm{M}}+\frac{{\mathrm{\pi }}_{\mathrm{d}}}{\mathrm{i}}$

Rearranging the above equations

$\frac{{\mathrm{\pi }}_{\mathrm{L}}-{\mathrm{\pi }}_{\mathrm{D}}}{\mathrm{i}}>{\mathrm{\pi }}_{\mathrm{M}}-{\mathrm{\pi }}_{\mathrm{L}}$

By substituting the data, we get

$\frac{\left(-2-30\right)}{\mathrm{i}}>80-(-2)$

Finding the limit pricing and entry

The equations for limit pricing and entry indicate the current profit as a monopolistic profit ($80million). In this case, the loss that would be obtained if the limit price is established as a strategy (- $2 million). The indefinite reduction in the company's profits would be seen if they decided to maintain their prices and let new competitors enter.

As the interest rate (i) is not available to determine which of the two options would suit the company, it should decide not to establish a limit price.