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 = 480 -0.00006Q, and Barnacle’s cost function is given by C(Q) = 390Q. 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 $9 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.

What would Barnacle's profits be if Marge pursues a limit-pricing strategy if the subsidy is in place?

$ _______ What would Barnacle's profits be if Marge convinces the government to eliminate the subsidy? Enter your responses to the nearest penny (two decimal places). $ _______ 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

Cost function of the Company Bernacle is C(Q) = 390Q

So Marginal cost will be d/dQ9390Q) = 390

Price of good is 480-0.00006Q

Total Revenue will be 480Q-0.00006Q^2

Marginal Revenue will be d/dQ(480Q-0.00006Q^2) = 480 -0.00012Q

So for profit maximizing MR = MC

Or 480-0.00012Q= 390 Or, Q =(480-390)/0.00012 = 750,000

So Profit maximizing price is 480-0.00006*750000= $435

For 750,000 units which is the profit maximizing unit, total profit

Hence, Bernacle will set price lower than $435 under limit price strategy

If subsidy is intact, to generate profit, price of the product should be higher than $390, which is per unit cost as per cost function.

So limitng price will be between $390 and $435

Based on 75,000 units which is monopoly level output, profit of bernacle should be in range of $0 (when price =$390) and (435-390)*750000 = $33,750,000.

If the subsidy is removed, total cost of Bernacle is 390Q +9,000,000

Maximum profit Bernacle could generate is 33,750,000-9,000,000= $24,750,000

So Company will generate profit between $0 and $24,750,000

Monopoly level of output is 750,000

If both produce monopoly level of outpout total units will be 750,000*2 =1,500,000

Market Price will be 480-0.00006*1,500,000= $390.

At this market price loss of new company will be 390X750,000-390X750,000-9,000,0000

=-9,000,0000

The new company will not be able to recover it fixed cost.