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

Five roommates are planning to spend the weekend in their dorm room watching movies, and they are debating how many movies to watch. Here is their willingness to pay: Buying a DVD costs \$15, which the roommates split equally, so each pays \$3 per movie. a. What is the efficient number of movies to watch (that is, the number that maximizes total surplus)? b. From the standpoint of each roommate, what is the preferred number of movies? c. What is the preference of the median roommate? d. If the roommates held a vote on the efficient outcome versus the median voter's preference, how would each person vote? Which outcome would get a majority? e. If one of the roommates proposed a different number of movies, could his proposal beat the winner from part (d) in a vote? f. Can majority rule be counted on to reach efficient outcomes in the provision of public goods?

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

Buying a DVD costs \$15, which the roommates split equally, so each pays \$3 per movie.
a. What is the efficient number of movies to watch (that is, the number that maximizes total surplus)?
b. From the standpoint of each roommate, what is the preferred number of movies?
c. What is the preference of the median roommate?
d. If the roommates held a vote on the efficient outcome versus the median voter's preference, how would each person vote? Which outcome would get a majority?
e. If one of the roommates proposed a different number of movies, could his proposal beat the winner from part (d) in a vote?
f. Can majority rule be counted on to reach efficient outcomes in the provision of public goods?

Key Concepts

Voting Mechanisms and Agenda Setting

The process by which proposals are put forward and voted on can significantly influence outcomes in public goods provision. Individuals may strategically propose alternatives or manipulate the agenda to achieve preferred outcomes, highlighting the potential divergence between outcomes reached through simple majority voting and those that would be efficient from a total surplus perspective.

Public Goods

A public good is characterized by non?excludability and non?rivalrous consumption, meaning that one person's consumption does not diminish another's and it is difficult to restrict access to the good. This concept is central when goods or services are provided collectively, as the benefits are shared by all participants regardless of individual contribution.

Efficient Provision of Public Goods

Efficiency in the provision of public goods is achieved when the total or aggregate marginal benefit across all individuals equals the marginal cost of providing the good. This concept focuses on maximizing total surplus or social welfare, ensuring that resources are allocated in a way that the overall benefit to society is as high as possible.

Individual Versus Collective Decision?Making

There is often a discrepancy between what is socially optimal and what individuals prefer, due to the way benefits and costs are distributed among individuals. Each participant may have a private optimum that does not account for the full benefit (or cost) experienced by the group, leading to decisions that deviate from the efficient outcome when aggregated.

Majority Rule and the Median Voter Theorem

Majority rule is a common decision mechanism where the outcome reflects the preference of the majority. The median voter theorem states that in a majority vote, the preferred outcome of the median voter will win, which may not coincide with the efficient or socially optimal level of provision, particularly in the context of public goods.

Transcript

00:01 Okay, guys, so this is chapter 22, problem 8.

00:05 In this question, we're given this table that is the value of watching a movie to each of these five roommates.

00:21 And it's saying buying a dvd then costs $15, but it's split evenly, so it's $3 per movie.

00:28 And this first part's asking us which number of movies maximize.

00:33 Is total surplus.

00:36 And again, our surplus is just the benefit one gets out of an item minus the cost of that item.

00:44 So for the first film, we see that quentin values at a $14 that only cost in three.

00:51 So he gets 11.

00:53 Similarly, spike.

00:54 It's worth seven.

00:56 We're at least surplus of five, surplus of one, and a surplus of minus one.

01:01 And that equals 23.

01:04 And so basically we're going to maximize surplus when the marginal surplus is zero.

01:10 So continuing down, second is worth the surplus is going to be nine for quentin.

01:17 It's going to be five for spike.

01:19 It's one for martin.

01:21 It's minus one.

01:22 Sorry, one for ridley, minus one for martin and minus three for stephen.

01:27 And that is still a total surplus for the second of 11.

01:30 The third is 7 plus 3 minus 1, minus 3, minus 3, still results in surplus of 3.

01:42 And so then for the fourth, we have 3 minus 1, minus 3, minus 3, which we now see is minus 7, which is negative, and so surplus is going to be maximized at the third movie, which means that is the efficient number of movies to watch...

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