Consider an economy with three consumers, each with a marginal benefit for a public good of MB = 10 - q.If the marginal cost of providing the good is $0 per unit, what is the DWL arising in the market outcome?
A)DWL = $150
B)DWL = $75
C)DWL = $50
D)DWL = $300
E)DWL = $200

Question

Quizplus · Accepted Answer

The Deadweight Loss (DWL) in this scenario can be calculated by considering the total benefit to the consumers and the cost of providing the public good. Since the marginal cost (MC) of providing the good is $0, the efficient quantity (q*) is where the sum of the marginal benefits (MB) of all consumers equals the MC. Each consumer has an MB = 10 - q, so for three consumers, the total MB = 3(10 - q) = 30 - 3q. Setting this equal to the MC (which is 0) and solving for q gives q = 10. The total benefit at this quantity is the area under the MB curve, which is a triangle with a base and height of 10, so (1/2)*10*10 = 50. However, since there's no cost to provide the good, the entire area under the MB curve represents consumer surplus in the efficient outcome. Without any external intervention, the market might not provide any of the public good due to its non-excludability and non-rivalry nature, leading to a DWL equal to the total potential benefit, which is $150 (since each consumer would get a benefit of 50, and there are three consumers).

Consider an Economy with Three Consumers, Each with a Marginal