Question

Horsehead, Massachusetts lies on a bay inhabited by lobsters. The town council issues permits for trapping lobsters and is trying to determine how many permits to issue. Assume that is costs $3,000 to operate a lobster boat and that if there are x boats in the bay, total revenue per month will be TR(x) = 1000(10x − x²).

(a) Graph the marginal revenue and marginal cost curves for operating a boat.

Answer 1

To graph the marginal revenue and marginal cost curves for operating a boat, we need to understand the revenue and cost functions. The marginal revenue curve will be a decreasing line with a negative slope, starting from the y-intercept of $10,000 and moving downwards. The marginal cost curve will be a horizontal line at $3,000.

Step-by-step explanation:

To graph the marginal revenue and marginal cost curves for operating a boat, we need to understand the revenue and cost functions.

The total revenue function TR(x) = 1000(10x − x²) represents the amount of money earned from operating x boats.

The marginal revenue function MR(x) represents the additional revenue earned from operating one more boat, given by the derivative of the total revenue function, MR(x) = 1000(10 − 2x).

The marginal cost function MC(x) represents the additional cost incurred from operating one more boat, which is a constant value of $3,000.

To graph the marginal revenue and marginal cost curves, we plot them on a graph with the number of boats (x) on the x-axis and the revenue or cost on the y-axis.

The marginal revenue curve will be a decreasing line with a negative slope, starting from the y-intercept of $10,000 and moving downwards. The marginal cost curve will be a horizontal line at $3,000.