The cost of hiring a secuirty guard to patrol the neighborhood of a community is 300 per week
Assuming that the marginal benefit of the first secuirty guard is 100 for each of the ten (n=10) individuals living in the community what is the optimal outcome in a private market? is that efficient?
To determine the optimal outcome in a private market and assess if it is efficient, we need to compare the marginal benefit and the marginal cost.
Given that there are ten individuals living in the community, and each individual benefits 100 from the first security guard, the total marginal benefit can be calculated by multiplying the individual marginal benefit (100) by the number of individuals (10), resulting in a total marginal benefit of 1000.
The cost of hiring one security guard is $300 per week. Therefore, the marginal cost is $300.
In a private market, the optimal outcome occurs where the marginal benefit is equal to the marginal cost. Thus, we need to determine if the marginal benefit is equal to the marginal cost.
Marginal benefit = $1000
Marginal cost = $300
Since the marginal benefit ($1000) is greater than the marginal cost ($300), the optimal outcome would be to hire the first security guard in the private market. This means that the community should hire the security guard.
However, to determine if this outcome is efficient, we need to consider if any additional security guards would provide greater benefits to the community. If the marginal benefit of hiring an additional security guard is less than the marginal cost, it would not be efficient.
Unfortunately, the information provided does not include the marginal benefit of additional security guards, so we cannot definitively determine if the outcome is efficient or not. Additional information would be needed to make that assessment.