Question

I need step by step solution to the following this question asap .I have limited time so please do it quickly with detailed explanation

thanks in advance/Ha

40 Consider an island with exclusive fishing rights to their own waters. The fishing industry is unregulated and the production function, representing the yearly catch, is given by f(x)=22x-* where x is the number of boats launched. Yearly industry profit is split equally among fishing boats and the cost of launching a boat equals 80. Fish is sold at a world market price of p=40. A market failure is likely to occur in this market. Explain why and analyze the problem by comparing the profit maximizing solution for the fishing industry with "sustainable" fishing (revenue maximizing solution) and the free entry solution. Suggest a policy that leads to an efficient outcome.

Answer 1

This question is an example of the Tragedy of the Commons problem.

Since the island is a public good and anyone can freely enter to fish, every agent is looking to maximize their income. But this will lead to market failure, as the number of fishes is limited and entry for fishing is unrestricted.

The profit function is given by , where c is the cost of launching the boat.
$\prod$(X) = 40[22x - x^2/40] - 80x

Entry in the fishing waters will continue, since nobody owns it, until the economic profit of having another boat is zero,i.e.
until $\prod$(X)/x = 0.
=> {40[22x - x^2/40] - 80x}/x = 880 -x - 80 = 0
=> x = 800
It means that the maximum number of boats that can maximize profit is 800.

The 'sustainable' solution for the profit maximizing solution is given by
$\prod$^'(X) = pf'(x) - c = 0 (First order condition)
40[22 - x/20] - 80 = 0
=> x* = 400

It means that the optimal solution for the number of boats is 400, but due to unregulated access to the water body, the number of boats is 800.

The policy suggestion to get an efficient outcome would be to either get the water body regulated by the government that will limit the access to the water body or privatize the water body so that individuals who can pay a 'fee' can enter it to fish.