Australian lobstermen fear a collapse of the lobster industry from over-harvesting. They are comparing various policy options

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Question:

Australian lobstermen fear a collapse of the lobster industry from over-harvesting.

They are comparing various policy options for regulation. Use the following information to analyze their choice.

Suppose it costs $36 for each lobster trap set. Lobsters sell for $12. If X traps are set, the harvest rate of lobsters, L, as a function of the number of traps, is given by:

L = 42X –X2.

a. With no restrictions (competitive markets exist) on the number of traps, and open access to the waters, how many traps will be set? How many lobsters will be harvested? How much profit will be realized from lobstering?

b. Suppose lobstermen could limit the number of traps permitted. How many traps should be permitted, if Australia wanted to maximize overall profits from lobstering? How many lobsters would be harvested? What would total profits be from lobstering? Note– prices are fixed at $12.