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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?
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Look, you guys, that this is Chapter 22 problem eight. In this stripping this question we're given on this table, that is three ah, value of watching a movie to each of these five roommates, a saying buying DVD than costs $15 but it's split evenly. Cem. It's $3 per movie in this first part's asking us which number of movies maximizes Total Star plus on again, her surplus is just the benefit. One gets out of an item minus the cost of that item. So for the first room way, see that Quinton Value's $14 they only cost him 37 gets 11. Similarly, Spike, it's work. Seven released. There was a five circles of one and a surplus of minus one in that equals 23. And so basically, we're gonna mask Meister Plast when the marginal so plaice is zero Still continuing down. Second is where the surplus give me nine, for Clinton is going to be five for Spike. It's one for Martin That's minus one by one for really minus one from Martin and minus three for Stephen and I still a Tolstoyan. Plus for the second of loving the third is seven last three minus one minus three minus three. Still, results of surplus of three and sent in for the fourth. We have three minus one minus three minus two minus three, which we now see is minus seven, which is negative. And so surpluses going be maximized on it. The third movie, which means that is the efficient number of movies to watch the second part of the question and asked us what each roommates preferred number of movies is. And so that's just going to be decreasing. You can see from the first table. Quinton conferred for bank preferred three Really preferred Tio Martin Barton. I prefer wine, and then Stephen prefered zero. The third part is then saying, What's the preference of the median roommates of the median, right? The mean is the average, the median is the middle, and the mod is the most often. And so the median roommate is going to be the one that if you lined all of them up in, around like adjusted in the previous question, it's going to be the one in the middle. And so the middle one is Ridley. He preferred to the movies the next part, then asked us what will be the result of majority rule on the efficient outcome? Or of the median Malcolm? And then who would each of the remains of a rebel force that Quinton, when those he prefers for movies over to movies to human, go for the efficient? Because that's the closest to what he would want. Doctor. The efficient three he wants for what? Also pretty efficient. Because, like once three and the efficient in history, Ridley would vote for the media because he is the median and two is less than three. Marchin would vote for the medium because he preferred one. The meeting is threesome to his closer to what he wants. And again, Stephen would not for the media because he prefers zero, and the meeting of two is closer to what he would prefer them. The efficient outcome is, and so then the median vote ah would win the next part, Then asked by the roommates if if any of the room has proposed a different voting strategy with the results of different from the previous question, the answer is no. And this is because we can see this in the median voters here, Um, which basically just says that in any majority rule you're going to get the results of the medium's odor. And then the very last part of the question asked US Will majority will result in the efficient or the surplus maximizing outcome. And the answer again is no. We saw about and Parts A and Diego's question where the efficient and the circles maximizing outcome was three. But our voting results in an outcome of you, so this wass Chapter 20.
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