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:

Question

The following information is for a public good.P<sub>a</sub> and P<sub>b</sub> 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.

Quizplus · Accepted Answer

To find the optimal quantity of the public good, we need to compare the total benefit of the good to the marginal cost of producing it. In this case, the total benefit is the sum of the prices that individuals A and B are willing to pay for the last unit of the good:

Total Benefit = PS1U1B1aS1U1B0 + PS1U1B1bS1U1B0
Total Benefit = $10 + $8
Total Benefit = $18

Since the marginal cost of producing the good is $4, the optimal quantity is the one where the marginal benefit equals the marginal cost. At a quantity of 3 units, the marginal benefit is the sum of the prices that A and B are willing to pay for the last unit of the good:

Marginal Benefit = PS1U1B1aS1U1B0 + PS1U1B1bS1U1B0 - PS1U1B0S1U1B0
Marginal Benefit = $10 + $8 - $4
Marginal Benefit = $14

The marginal benefit of producing the third unit of the public good is greater than the marginal cost, so producing three units is the optimal quantity.

The Following Information Is for a Public Good