Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $2,000 per month.Suppose that if x lobster boats operate in the bay, the total monthly revenue from lobster boats in the bay is $1,000(26x - x²).If there are no restrictions on entry and new boats come into the bay until there is no profit to be made by a new entrant, then the number of boats who enter will be X₁.If the number of boats that operate in the bay is regulated to maximize total profits, the number of boats in the bay will be X₂. A)X₁ = 24 and X₂ = 12. B)X₁ = 24 and X₂ = 24. C)X₁ = 12 and X₂ = 10. D)X₁ = 28 and X₂ = 16. E)None of the above.

Question

Quizplus · Accepted Answer

X₁ is found by setting the profit to zero: $1,000(26x - x^2) = 2,000x$. Solving gives x = 24. X₂ is found by maximizing profit: differentiate $1,000(26x - x^2) - 2,000x$ and set to zero, solving gives x = 12.

Suppose That in Horsehead, Massachusetts, the Cost of Operating a Lobster