The table below shows the quantity of coal per ton, the extraction cost per ton,

Question

The table below shows the quantity of coal per ton, the extraction cost per ton, and user cost per ton for the BTU Coal Company in the current year. 5. Extraction User QuantityCost Cos $50 50 50 50 50 50 $ 100 150 250 350 If the current price of a ton of coal is $200, how many tons of coal should BTU extract and sell this year to maximize profits? (5 points) a) b) If the current price of a ton of coal is $300, how many tons of coal should BTU extract and sell this year to maximize profits? (5 points) c) BTU has been told by government regulators that it must cease operations in a year. If the current price of a ton of coal is $250, how many tons of coal should BTU extract and sell this year to maximize profits? (s poins d) If user costs increase by $50 at each level of output and if the current price of a ton of coal is $300, how many tons of coal should BTU extract and sell this year to maximize profits? (s points)

Explanation / Answer

a) Note that optimal conditions require the utility to charge a price that is equal to the sum of the marginal external cost and marginal user cost. When P = 200, sum of EC and UC is 200 when Q is 1 unit and this is the optimal quantity

b) When P = 300, sum of EC and UC is 300 when Q is 3 unit and this is the optimal quantity

c) It will charge 250 so it can maximum extract 300 units and avoid the user cost

d) When user cost is now increased by 50, and price is P = 300, sum of EC and UC is 300 when Q is 2 unit and this is the optimal quantity

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