Final answer:
To determine the number of traps set and lobsters harvested in a competitive market with open access, you would maximize profit, defined as total revenue from lobsters sold minus total cost of traps. The lack of ownership of the ocean contributes to overharvesting, which can be mitigated by regulatory measures like fishing licenses and harvest limits, addressing the 'Tragedy of the Commons'.
Step-by-step explanation:
Australian lobster fishers are concerned about the potential for a collapse in the lobster industry due to overharvesting. To analyze their choices for regulation, we can illustrate using the given profit function derived from the harvest rate of lobsters, L = 330X – X2, where L is the number of lobsters harvested and X is the number of traps set. Given the cost of $280 per trap and a selling price of $20.14 per lobster, the profit will be the total revenue from selling the lobsters minus the total cost of the traps. To maximize profit in a competitive market with open access, lobster fishers will continue to set traps until the marginal cost equals marginal revenue.
To find this point, we first need to calculate the total revenue (TR) which is the selling price of lobsters multiplied by the harvest rate, and the total cost (TC), which is the cost per trap multiplied by the number of traps. The profit function (π) can then be defined as:
π(X) = TR(X) – TC(X) = (20.14 × (330X – X2)) – (280 × X)
The number of traps set and lobsters harvested will be the values of X and L that maximize the profit function. Without restrictions, this is generally where the derivative of the profit function with respect to X (marginal profit) is zero, but additional analysis is needed to consider the biological sustainability and regulatory approaches to prevent overharvesting, as described in Garret Hardin's concept of the 'Tragedy of the Commons'.