Question

Barnacle Industries was awarded a patent over 15 years ago for a unique industrial-strength cleaner that removes barnacles and other particles from the hulls of ships. Thanks to its monopoly position, Barnacle has earned more than \(160 million over the past decade. Its customers-spanning the gamut from cruise lines to freighters-use the product because it reduces their fuel bills. The annual (inverse) demand function for Barnacle's product is given by P=400-.0005 Q, and Barnacle's cost function is given by C(Q)=250 Q. Thanks to subsidies stemming from an energy bill passed by Congress nearly two decades ago, Barnacle does not have any fixed costs: The federal government essentially pays for the plant and capital equipment required to make this energy-saving product. Absent this subsidy, Barnacle's fixed costs would be about \)4 million annually. Knowing that the company's patent will soon expire, Marge, Barnacle's manager, is concerned that entrants will qualify for the subsidy, enter the market, and produce a perfect substitute at an identical cost. With interest rates at 7 percent, Marge is considering a limit-pricing strategy. If you were Marge, what strategy would you pursue? Explain.

Short answer

The strategy to earn higher profit is deciding to establish a pricing strategy that limits the entry of new competitors.

Step-by-step solution

To find the annual inverse demand function for barnacles’ product

Barnacle Industries, a company that owns a subsidy to make a product that removes barnacles and other particles from the hulls of ships, has had a monopoly profit of $160 million. However, without this subsidy your fixed costs will increase from $0 to $4 million and therefore your profits will decrease.

The annual (inverse) demand function for Barnacles product is given by:

$\text{P}=400-0.0005Q$

And Barnacles cost function is given by:

$C\left(Q\right)=250Q$

To be able to determine the determined level of production in the monopoly market, Bernacle's condition is given in which the marginal costs$\left(MC\right)$are equal to the marginal revenue $\left(MR\right)$, leaving: $MC=MR$

To find the marginal costs

To obtain the income and marginal costs, the demand and cost functions, equations (l) and (2) must be derived respectiv

$\begin{array}{c}MR=\frac{\text{dP}}{\text{dQ}}=400-0.0005Q^2\\ =400-\left(2\right)0.0005Q\\ =400-0.001Q\\ \text{MC}=\frac{\text{dP}}{\text{dQ}}=250Q\\ =250\end{array}$

To find the maximum profits

Equating the MR and MR as equation (3) the level of production that maximizes profits can be obtained:

$\begin{array}{l}\text{MC}=\text{MR}\\ 250=400-0.001Q\\ Q=\frac{400-250}{0.001}\\ Q=150,000\end{array}$

To find the profits

As the production level Q is obtained, the company's profits can be maximized by substituting the value obtained (150,000) in the inverse function demand in the monopoly scenario. Therefore, substituting Q in equation (l)

$\begin{array}{c}P=400-0.0005\times (150,000)\\ =400-75\\ =325\end{array}$

To find the level of production and that maximize profit benefits

Taking the level of production and the prices that maximize profit, the benefits of the monopolistic company with subsidy can be obtained with the following equation:

$\begin{array}{c}\mathrm{Benefit}=\mathrm{Total}\mathrm{revenue}-\mathrm{Total}\mathrm{cost}\\ =\left(\mathrm{PQ}\right)-\left(\mathrm{MC}\times \mathrm{Q}\right)\\ =\left(325\times 150,000\right)-\left(250\times 150,000\right)\\ =\left(48,750,000-37,500,000\right)\\ =11,250.000\end{array}$

Barnacle Industries will generate a profit of $11,250,000 in a monopoly scenario with subsidies from the government. However, when the patent is removed and new competitors enter, the company can adopt a limit pricing strategy for the entry of new competitors in which it can establish a price equal to its marginal cost, that is, $250. Substituting this price in the Benefit equation, the company's earnings would be $0.

$\begin{array}{c}\text{Benefit}=\left(250\times 150,000\right)-\left(250\times 150,000\right)\\ =0\end{array}$

Therefore, the best option for the company is to seek to eliminate the subsidy from the government for the $4 million, which substituting in the benefit equation will reduce to:

$\begin{array}{c}\mathrm{Benefit}=\left(48,750,000-37,500,000-4,000,000\right)\\ =7250000\end{array}$

Therefore, eliminating the subsidies will allow the company to have a lower profit than the previous one from its monopolistic situation, but it will be much higher if it decides to establish a pricing strategy that limits the entry of new competitors where its profit will be $0.