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 = 500 -0.001Q, and Barnacle’s cost function is given by C(Q) = 300Q. 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 $5 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 6 percent, Marge is considering a limit-pricing strategy.

Instructions: Enter your responses to the nearest penny (two decimal places).

What would Barnacle's profits be if Marge convinces the government to eliminate the subsidy?


$ ___________________


What would be the profit of a new entrant if the subsidy is eliminated and Barnacle continues to produce the monopoly level of output?


$ __________________

Answer 1

Solution:

Given

Barnacle has earned more than $160 million over the past decade

P = 500 -0.001Q

C(Q) = 300Q.

Barnacle's profits be if Marge convinces the government to eliminate the subsidy is:

calculation:

Barnacle's product is given by P = 500 -0.001Q

As marginal revenue curve will have twice the slope of the demand curve thus

MR = 500 -0.002Q

Barnacle's cost function is given by C(Q) = 300Q. Thus, the slope of TC = 300, hence MC equals 300

Setting MR = MC

500 -0.002Q = 300

200 = 0.002Q

Q = 1,00,000

Substituting the profit-maximizing quantity into the inverse demand function to determine the price:

P = 500 - 0.001Q = 500 - 0.001 * 100,000 = 400

Profit = Total revenue - Total cost = (400 * 1,00,000) - (300 * 100,000) = 10,000,000

Hence

Barnacle's profits = 10,000,000 - 8,000,000

= 2,000,000

profit of a new entrant if the subsidy is eliminated and Barnacle continues to produce the monopoly level of output is:

calculation:

The (inverse) residual demand curve for entrants would be 400 - 0.001Q

400 -0.002Q = 300

100 / 0.002 = Q

Q = 50,000

P = 400 - 0.001Q = 400 - 0.001 * 50,000 = 350

Profit = Total revenue - Total cost = (350-300) * 50,000 = 2,500,000

Barnacle's profits  = 2,500,000 - 8,000,000

= -5,500,000