The following information is for a public good.P_a and P_b are the prices that individuals A and B are willing to pay for the last unit of a public good, rather than do without it.These people are the only two members of society.Refer to the data below.If the marginal cost of this good at the optimal quantity is $4, the optimal quantity must be: A)1 unit. B)2 units. C)3 units. D)4 units.

Question

Quizplus · Accepted Answer

To determine the optimal quantity of a public good, we need to compare the marginal cost of providing the good to the sum of the marginal benefits for all individuals in the society. In this case, we only have two individuals, A and B, and their willingness to pay for the last unit of the public good, P_a and P_b, respectively. To find the optimal quantity, we need to add up the individuals' marginal benefits until they equal the marginal cost. Starting with the highest willingness to pay, which is from individual A, we have P_a = $10. Adding individual B's willingness to pay, P_a + P_b = $16. Since the marginal cost is $4, we can divide the sum of the individuals' willingness to pay by the marginal cost: ($10 + $6) / $4 = 4 units. However, we need to remember that we are looking for the last unit of the public good that individuals are willing to pay for before doing without it. That means we need to subtract one unit from the optimal quantity: 4 units - 1 unit = 3 units. Therefore, the optimal quantity of the public good is 3 units, and the best choice is C) 3 units.

The Following Information Is for a Public Good