Newfoundland codfish sells at a competitively determined price of $10 per kilo. It costs a fisherman $1000 to operate his boat for one season. The total (province wide) catch of codfish (in kilos) is given by Q = 500N - N^2 where N is the number of fisherman. This means that each fisherman catches q = Q/N = 500 - N.
In absence of central planning, how many fishermen will operate in this industry? If the government were to control the fishing industry, and harvest the fishing grounds at a socially optimal rate so as to maximize the number of fish caught, how many fishermen would be employed? If the government were to charge a lump sum, annual license fee (in dollars) which sought to discourage over fishing how high should this fee be set in order to maximize the number of fish caught?