[math-fun] Re: Death Valley marathon
Joshua Zucker writes:
I don't see the 15:9 split making any kind of sense, since the people drank the original 8 units of water each too, so they GAVE 7:1 units of water. What is the sense behind it? It seems to me to be the solution you get if you just don't think through the problem completely enough.
Let's change the scenario: I invest $5,000,000 in a three-story office building and you invest $3,000,000. There are three tenants: Propp Enterprises, Zucker Enterprises, and Yoyodyne Incorporated, each of which occupies one floor. If the rent we charge Yoyodyne is $8,000 per month, how should you and I split it? Would you really settle for just $1,000 per month, even though you put up 3/8 of the money for the building? If this is different from the Death Valley marathon sccenario, what makes it different? (Maybe I'm being dense...) Jim
On 8/10/07, James Propp <jpropp@cs.uml.edu> wrote:
Joshua Zucker writes:
I don't see the 15:9 split making any kind of sense, since the people drank the original 8 units of water each too, so they GAVE 7:1 units of water. What is the sense behind it? It seems to me to be the solution you get if you just don't think through the problem completely enough.
Let's change the scenario: I invest $5,000,000 in a three-story office building and you invest $3,000,000. There are three tenants: Propp Enterprises, Zucker Enterprises, and Yoyodyne Incorporated, each of which occupies one floor. If the rent we charge Yoyodyne is $8,000 per month, how should you and I split it? Would you really settle for just $1,000 per month, even though you put up 3/8 of the money for the building?
Suppose the three tenants are A, B, and C. Clearly then I want to get 3/8 of the money from each tenant. But if I'm a tenant too, shouldn't I be paying you 5/8 of the rent on my part of the building, and you be paying me 3/8 of the rent on your part? So Yoyodyne pays $8000 per month, I take $3k and you take $5k. But also I owe you $5k for rent on my part of the building, and you owe me $3k, so net (including the differential ownership of the floors we occupy), it still ends up 1:7, not 3:5. In other words, you'd be awfully generous to let me have a whole floor when you also get only one floor, without some financial compensation! --Joshua
On Fri, 10 Aug 2007, James Propp wrote:
Let's change the scenario: I invest $5,000,000 in a three-story office building and you invest $3,000,000. There are three tenants: Propp Enterprises, Zucker Enterprises, and Yoyodyne Incorporated, each of which occupies one floor. If the rent we charge Yoyodyne is $8,000 per month, how should you and I split it? Would you really settle for just $1,000 per month, even though you put up 3/8 of the money for the building?
Good scenario, but let's make the numbers more extreme. You pay $1,000,000 and I pay $1 to build the building, and Yoyodine pays $1,000,000/month rent. Each of us gets one floor of the building. Do I get $1 per month plus free rent, or do I owe you something for my floor's rent?
On 8/10/07, James Propp <jpropp@cs.uml.edu> wrote:
Joshua Zucker writes:
I don't see the 15:9 split making any kind of sense, since the people drank the original 8 units of water each too, so they GAVE 7:1 units of water. What is the sense behind it? It seems to me to be the solution you get if you just don't think through the problem completely enough.
Let's change the scenario: I invest $5,000,000 in a three-story office building and you invest $3,000,000. There are three tenants: Propp Enterprises, Zucker Enterprises, and Yoyodyne Incorporated, each of which occupies one floor. If the rent we charge Yoyodyne is $8,000 per month, how should you and I split it? Would you really settle for just $1,000 per month, even though you put up 3/8 of the money for the building?
Well, Propp Enterprises and Zucker Enterprises should also pay $8,000 a month rent, so there's a total of $24,000 in rent. I think that this should be split with $15,000 going to Propp Realty and $9,000 going to Zucker Realty, in proportion to their investments. This happens to result in a net inflow to Propp Holding company (which owns both Propp Enterprises and Propp Realty) of $7,000, but I don't think the merger of those two enterprises should affect the rent or how it's divided. To look at it another way, let's triple the price of the office building, and reveal that it actually consists of 3 separate office buildings. You spent $15 million; almost enough to build 2 8-million-dollar buildings, and are using one and renting another. I spent $9 million, enough to build the 8-million building I'm using, and a little bit extra to help you finish the third building. So ignoring buildings that we each built for our own use, you spent $7 million on the rental property and I spent $1 million, and that's how we should divide the rent. If I spend a couple thousand more to connect the three buildings with walkways and call it one big one, that shouldn't change how we divide the rent. Or to take another extreme example, let's suppose that Zucker enterprises merges with Megacorp, A company that has never done rental before, but spends a trillion dollars on the office buildings it uses itself. Now Zucker-megacorp has spent 1.003 trillion on the office building project, and Propp has spent a paltry 5 million. How should they now divide the $8000/month rent they recieve? -- Andy.Latto@pobox.com
participants (4)
-
Andy Latto -
James Propp -
Jason Holt -
Joshua Zucker