Four roommates are planning to spend the weekend in their...

Four roommates are planning to spend the weekend in their dorm room watching old movies, and they are debating how many to watch. Here is their willingness to pay for each film: a. Within the dorm room, is the showing of a movie a public good? Why or why not? b. If it costs $8 to rent a movie, how many movies should the roommates rent to maximize total surplus? c. If they choose the optimal number from part (b) and then split the cost of renting the movies equally, how much surplus does each person obtain from watching the movies? d. Is there any way to split the cost to ensure that everyone benefits? What practical problems does this solution raise? e. Suppose they agree in advance to choose the efficient number and to split the cost of the movies equally. When Steven is asked his willingness to pay, will he have an incentive to tell the truth? If so, why? If not, what will he be tempted to say? f. What does this example teach you about the optimal provision of public goods?

Four roommates are planning to spend the weekend in their dorm room watching old movies, and they are debating how many to watch. Here is their willingness to pay for each film:

a. Within the dorm room, is the showing of a movie a public good? Why or why not?
b. If it costs $8 to rent a movie, how many movies should the roommates rent to maximize total surplus?
c. If they choose the optimal number from part (b) and then split the cost of renting the movies equally, how much surplus does each person obtain from watching the movies?
d. Is there any way to split the cost to ensure that everyone benefits? What practical problems does
this solution raise?
e. Suppose they agree in advance to choose the efficient number and to split the cost of the movies equally. When Steven is asked his willingness to pay, will he have an incentive to tell the truth? If so, why? If not, what will he be tempted to say?
f. What does this example teach you about the optimal provision of public goods?

Key Concepts

Incentive Compatibility in Mechanism Design

In the context of public goods, incentive compatibility refers to designing mechanisms where individuals are encouraged to reveal their true valuations. Without proper incentives, participants might misrepresent their willingness to pay to lower their own expense share, which can distort the decision-making process regarding the efficient provision of the public good.

Free Rider Problem

The free rider problem arises in the provision of public goods because individuals may understate their true willingness to pay, hoping to benefit from the good without contributing to its cost. This strategic behavior can lead to under-provision of the good, as the sum of declared valuations may fall short of covering the cost even when the true aggregate benefit is high.

Public Goods

Public goods are characterized by non-excludability and non-rivalry. This means that once the good is provided, no one can be prevented from using it, and one person’s consumption does not reduce its availability to others. In contexts like a shared movie screening in a dorm, the viewing experience is available to all roommates simultaneously without diminishing the benefits to any individual.

Marginal Analysis for Public Goods Provision

Efficient provision of public goods involves comparing the aggregate marginal benefit— the sum of all individuals’ willingness to pay for one more unit of the good—with the marginal cost of providing that unit. The optimal level of provision is achieved when the total benefit equals or exceeds the cost, ensuring that the resource is allocated where it creates net positive value.

Cost Sharing and Surplus Distribution

When costs are shared among individuals, total surplus is determined by subtracting the cost from the total benefit received by everyone. How the cost is split affects individual surplus; an equal split might result in some individuals not realizing a personal gain even if the overall surplus is positive. This concept highlights the challenges of asymmetrical benefits in shared consumption scenarios.

Transcript

00:05 So this question is related to public doing indeed.

00:10 So question a is asking whether the film is a public goal it is.

00:15 For two reasons, the first one is it is non -excutable.

00:18 So one person watching the movie can't approve any other in the dorm to watch.

00:24 And the second one is a non -reveillance, which is basically one person watching and doesn't diminish other people watching as well.

00:32 So question a is asking, the number of moving to to maximize the to maximize the public to total surplus so let's start by putting here the benefit and then the cost and then total surplus so for the first move it benefit the willingness for to pay for all four then is 17 the cost is eight so the total surplus is nine do the same think cumulatively when you get to the third movie you'll see that the total benefit is 39 because it's 24 and then the total surplus is then is 15 this is the maximum the maximum total surplus so choosing three will maximum the total surplus for all of that now let's see here question c if we divide actually the course which is basically 24 by 4 we got 6 and then calculating the total surplus based on that we'll have stephen tutorial plus will be 18 minus 6 which is 12 18 is the cumulative benefit for watching a movie and then it costs for peter is now six for james it is pretty much zero he doesn't benefit or he doesn't lose either and uh christoph is basically losing money losing uh he doesn't benefit from from this so that's is uh that is uh also for questions question the question question question question question question question so the question is, is there any way to spread it across with? yes, there is such a way which is basically as a public provision of the movies, which will be, for example, the head of the dome, decide to collect the willingness of pay for each of them, and then rain the movie, the number of movie that will make sure that everyone benefit from that.

03:11 That number will make sure that on the total benefit is kind of greater to the cost.

03:15 As long as that kind of condition is satisfied, the head of the dome, can basically try to grab...

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