Question

3. Anthony and Betty are deciding whether to contribute $100 each for the improvement of the local public library. If they do not contribute, they can make use of those $100 on their own leisure. This can be understood as the measure of their private benefit under a non-contribution scenario. In addition, Anthony and Betty benefit from all contributions made, no matter who makes them. More precisely, a $1 contribution from any of them brings each of them a $0.90 benefit. a) There are four possible outcomes: both individuals contribute, none of them contribute, Anthony contributes, but not Betty, or Betty contributes, but not Anthony. What is the scenario that maximizes the social surplus in this case? Explain. b) Suppose that Anthony makes a contribution. What will Betty choose to do? What if Anthony does not contribute? What will Betty now do? Will Anthony and Betty's decisions lead us to a socially efficient outcome? What kind of economic problem is illustrated here?

3. Anthony and Betty are deciding whether to contribute $100 each for the improvement of the local public library. If they do not contribute, they can make use of those $100 on their own leisure. This can be understood as the measure of their private benefit under a non-contribution scenario. In addition, Anthony and Betty benefit from all contributions made, no matter who makes them. More precisely, a $1 contribution from any of them brings each of them a $0.90 benefit.

   1. a) There are four possible outcomes: both individuals contribute, none of them contribute, Anthony contributes, but not Betty, or Betty contributes, but not Anthony. What is the scenario that maximizes the social surplus in this case? Explain.

   2. b) SupposethatAnthonymakesacontribution.WhatwillBettychoosetodo?What if Anthony does not contribute? What will Betty now do? Will Anthony and Betty's decisions lead us to a socially efficient outcome? What kind of economic problem is illustrated here?

Answer 1

Given that:

Benefit from contributing is $0.90 for each dollar contributed. Cost of contributing is $100.

Let's start by assuming a case where both of them contributes:

Cost = $100 + $100 = $200

Benefit = ($0.90 x 100) + ($0.90 x 100)

Net benefit = 200-180 = $20

Case 2 where only one of them contributes:

Cost = $100

Benefit = ($0.90 x 100) + 100 = 190

Net benefit = 190-100 = $90

Case 3 where no one contributes:

Cost = 0

Benefit = $100 + $100

Net benefit = 200

Thus, a scenario where no one contributes will be the one that maximizes social surplus.

B) If one of them say Anthony makes a contribution, betty will choose not to contribute. This is because her benefit from contributing is less than the cost.

If Anthony does not contribute, Betty will also not contribute, This is because of dominant strategy of both the players being not to contribute.

Economic problem here illustrated is free rider problem.