Barnacle Industries was awarded a patent over 15 years ago for a unique industri

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 = 220 -0.000006Q, and Barnacle’s cost function is given by C(Q) = 200Q. 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 5 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? $ Instruction: Round all answers 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? $ Which strategy is more beneficial to Barnacle? Eliminating the subsidy and continuing to produce the monopoly output Limit pricing

Explanation / Answer

The annual (inverse) demand function for Barnacle’s product is given by P = 220 -0.000006Q, and Barnacle’s cost function is given by C(Q) = 200Q.

Barnacle’s fixed costs would be about $9 million annually without subsidies

Thus, the equilibrium profit maximizing price and quantity would be at the point where MC=MR

Here, TR= PQ= 220Q-0.000006Q2

MR= dTR/dQ= 220-0.000012Q……………………..(1)

TC=9+200Q without subsidies……………………..(2)

And

TC=200Q with subsidies……………………………..(3)

MC= 200………………………………………………………(4)

At the profit maximizing eq.

MR=MC or eqn (1) = eqn(4)

So 220-0.000012Q=200

Solving for Q we get Q= 1666666.67

And P= $210(Rounded off)

The total profit of the firm would be eq P X eqQ= 1666666.67X210=$350,000,000 or $350million

Limit Pricing is a pricing strategy a monopolist may use to discourage entry. If a monopolist set its profit maximising price (where MR=MC) the level of supernormal profit would attract new firms into the market.

Therefore, the monopolist may decide to set a price below this profit maximising level, but still enable it to make higher profits than in a competitive market.

In the long run a competitive firm operates at the minimum AC

Given the same Cost structure the minimum AC would be @

$200. So if the firm operates at the minimum price its Profits would be $666million( At P=200 in the inverse demand function)

So if the firm continues to get the subsidy and follows the limit price strategy it can earn a near double profit of 666$million

If however, the subsidy if eliminated the profits of Barnacle would be TP= PX Q its minimum AC continues to be the same but profit margin goes down due to the fixed cost component of $9 million annually

So, $666-9= $657

If the subsidy is eliminated and barnacle continues to produce the output at the monopoly level, the latter’s market would be washed off and the new entrant produces the complete output at the minimum AC price of $200 and earns the profits of Barnacle of $657 having adjusted for the subsidy amount.

It is thus better for Barnacle to pursue the limit pricing startegy and prevent the firm from enetering the market.

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