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: Film Orson Alfred Woody Ingmar 1st. $7 $5 $3 $2 2nd. 6 4 2 1 3rd. 5 3 1 0 4th. 4 2 0 0 5th. 3 1 0 0 a. Within the dorm room, is the showing of a movie a public good? Why or why not? b. If it cost $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 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 Orson 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?

Transcript

00:01 Hello, let's use this table and answer all parts of this question.

00:10 Let's start with part a.

00:12 So within the dorm room is the showing of a movie is a public good.

00:17 Why or why not? and yes, the showing of a movie is a public good.

00:27 So yes, it is a public good.

00:42 None of the roommates can be excluded from viewing the movie.

00:49 Because one roommate's viewing does not affect the ability of another roommate to view the movie.

00:56 The good is also non -rival in consumption.

01:02 So this is a public good because known of roommates roommates can be excluded from viewing can be excluded from viewing this movie okay now part b the roommates should rent three movies three the answer is three because the value of the fourth film four plus two would be less than the cost but for third film the value is nine and it's greater than six for the third film the value which is nine and it's greater than six so they will watch but for the first third for the fourth film film the value is nine the value is 6, oh sorry, the cost is 8, yeah, i put mistaken 6, it's 8.

02:40 And for the 4th film, 6 is less than 8, so they will not buy the 4th film.

02:50 Okay, part c.

02:53 If they choose optimal number from part b and it's 3, and then split the cost of renting the videos equally, how much surplus does, each person obtained from watching the movies.

03:06 So the total cost is 24, we multiply 8 by 3 and we divide this equally evenly among four roommates and each would pay 6.

03:25 So the cost of each roommate will be equal to $8 multiplied by 3 fill divided by four roommates and it will be six dollars and now we can find the surplus of each roommate so orson he values three movies six seven plus six plus five it's it's eighteen minus cost and it's 12 dollars of surplus.

04:14 Alfred, his value is 5 plus 4 plus 3 or 12, his surplus is 6, woody, he values 3 plus 2 plus 1, it's 6 minus 6 which is the cost and his surplus is 0.

04:38 And finally ingmar he values 3, he values.

04:45 At 2 plus 1 plus 0 it's 3 minus the cost and he has negative surplus it's negative 3 and the total surplus total if we add all this numbers we'll see that the total surplus is 15 dollars okay, now part d.

05:20 Is there any way to split the cost to ensure that everyone benefits? the cost could be divided up by the roommates based on the benefits they receive.

05:35 So because orson values the move is the most, he would pay the greatest share.

05:41 And the problem is that that gives each roommate an incentive to understate the value of movies to him...

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