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 -0.0005Q, and Barnacle’s cost function is given by C(Q) = 250Q. 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 $6 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?

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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?


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


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Answer 1

Part a) Profits with subsidy in place

First let us calculate cost function in the form Q = a - bP

Here, P = 400 - 0.0005Q

0.0005Q = 400 - P

Q = 800,000 - 2000P

This is of the form Q = a - bp where a=800,000 and b=2000

Now let us calculate the marginal cost

The cost function is given by C(Q) = 250Q

Marginal cost = dC(Q) / dQ (derivative of cost function with respect to Q)

Marginal cost =d/dQ ( 250Q) = 250 X d/dQ(Q)

Marginal cost = 250

Call this c. Thus, c = 250.

Now, if the cost function is given by Q = a - bP and the constant marginal cost is given by c, the profit maximizing price in a monopoly is given by :

p^M = a + cb / 2b

pM = 800,000 + (250 X 2000) / 2 X 2000

= 1,300,000/ 4000

p^M = 325

This is the limit price with subsidy in place

Now let us find quantity for maximum profit

Q = 800,000 - 2,000 X P

Q = 800,000 - 2,000 X 325

Q = 150,000

Now, the revenue generated from this quantity is R = P X Q

Revenue = 325 X 150,000 = 48,750,000

The cost is given by C = 250 X Q

cost = 250 X 150,000 = 37,500,000

Profit = Revenue - Cost = 48,750,000 - 37,500,000

Profit = 11,250,000

Thus, the profit at limit pricing with the subsidy in place is $11,250,000.00 per year

part b) Profit if the subsidy is eliminated

In this case, fixed cost of 6000,000 is to be added in the cost function to calculate total cost

C(Q) = 6,000,000 + 250Q

However, the marginal cost will not change and will be 250

Thus, the values of a, b and c will not change and the price will still be P = $325 and quantity will still be Q= 150,000

Now, the revenue generated from this quantity is R = P X Q

Revenue = 325 X 150,000 = 48,750,000

The cost is given by C = 250 X Q + 6,000,000

cost = 250 X 150,000 + 6,000,000= 43,500,000

Profit = Revenue - Cost = 48,750,000 - 43,500,000

Profit = 5,250,000

Thus, the profit at limit pricing if the subsidy is eliminated is $5,250,000.00 per year

Note that the profit has reduced due to the elimination of subsidy but the company has managed to create entry barrier for new players who would enter the market.. Any company which would like to compete after expiry of the patent will have to bear an extra annual cost of $6,000,000 + 7% (interest rate).

Note that interest rates are not considered in profit calculations, because the company is assumed to be debt free and hence has not cost of interest.