So the reason why the time value of money works, and it makes sense to say that we can say that the utility of $1000 today and $1050 in a year are about the same, is because of the existence of the wider financial system. In other words, this isn’t necessarily true in a vacuum; however if I wanted $1050 in a year, I can invest the $1000 I have right now into 1 year treasuries. The converse is more complex; if I am guaranteed $1050 in a year I may not be able to get a loan for $1000 right now from a bank because I’m not the fed and loans to me have a higher interest rate, but perhaps I can play some tricks on the options market to do this? At any rate, I can get pretty close if I were getting an asset-backed loan, such as a mortgage.
Note that I’m not saying that actors are indifferent to which option they get, but that it is viewed with equal utility (when discounted by your cost of financing, basically).
This is a bit of a cop-out, but I would say modelling the utility of money without considering the wider world is a bit silly anyway, because money only has value due to its use as a medium of exchange and as a store of value, both of which depend on the existence of the rest of the world. The utility of money thus cannot be truly divorced from the influence of eg. finance.
Note that I’m not saying that actors are indifferent to which option they get, but that it is viewed with equal utility
I think this is precisely what “equal utility” means in context.
To be clear, in this post I’m trying to talk about expected utility maximizers, the simple mathematical abstraction of “agent who has a utility function (which satisfies certain technical conditions) and attempts to maximize its expected value”. And the reason I’m trying to talk about that type of agent is because I think the things I’m replying to are also trying to talk about that type of agent.
Possibly it would be clearer to simply leave “money” out of it, but reusing examples from prior art seems useful. Also I think it makes the post less dry. Perhaps I should have started with a big disclaimer that I’m trying to talk about expected utility maximizers and references to a thing labeled “money” are not intended to invoke concepts like “global economy” or “purchasing goods and services”. I’m talking about a hypothetical agent who values this thing labeled “money” for its own sake.
The reason I’m talking about that type of agent is because I think understanding that type of agent can be useful when we try to think about more-realistic agents, who more-realistically value a real-world thing called “money” that exists in a global economy and can be used to purchase goods and services. But those more-realistic agents, and that more-realistic money, are not what I’m talking about currently. And I’m not here trying to justify why I think that can be useful.
(Or maybe the things I’m replying to aren’t trying to talk about that type of agent, they just use words like “expected utility” without intending to point at their technical definition and that confuses things. But if that’s the case, then I’m probably not the only person who thinks that’s what they’re trying to talk about; and so it still seems good for me to clarify what happens with that type of agent, in the sort of situation in question.)
(Probably it would be good for me to find some examples of the things I’m responding to, but that would be a different type of effort than I feel like putting in currently.)
So the reason why the time value of money works, and it makes sense to say that we can say that the utility of $1000 today and $1050 in a year are about the same, is because of the existence of the wider financial system. In other words, this isn’t necessarily true in a vacuum; however if I wanted $1050 in a year, I can invest the $1000 I have right now into 1 year treasuries. The converse is more complex; if I am guaranteed $1050 in a year I may not be able to get a loan for $1000 right now from a bank because I’m not the fed and loans to me have a higher interest rate, but perhaps I can play some tricks on the options market to do this? At any rate, I can get pretty close if I were getting an asset-backed loan, such as a mortgage.
Note that I’m not saying that actors are indifferent to which option they get, but that it is viewed with equal utility (when discounted by your cost of financing, basically).
This is a bit of a cop-out, but I would say modelling the utility of money without considering the wider world is a bit silly anyway, because money only has value due to its use as a medium of exchange and as a store of value, both of which depend on the existence of the rest of the world. The utility of money thus cannot be truly divorced from the influence of eg. finance.
I think this is precisely what “equal utility” means in context.
To be clear, in this post I’m trying to talk about expected utility maximizers, the simple mathematical abstraction of “agent who has a utility function (which satisfies certain technical conditions) and attempts to maximize its expected value”. And the reason I’m trying to talk about that type of agent is because I think the things I’m replying to are also trying to talk about that type of agent.
Possibly it would be clearer to simply leave “money” out of it, but reusing examples from prior art seems useful. Also I think it makes the post less dry. Perhaps I should have started with a big disclaimer that I’m trying to talk about expected utility maximizers and references to a thing labeled “money” are not intended to invoke concepts like “global economy” or “purchasing goods and services”. I’m talking about a hypothetical agent who values this thing labeled “money” for its own sake.
The reason I’m talking about that type of agent is because I think understanding that type of agent can be useful when we try to think about more-realistic agents, who more-realistically value a real-world thing called “money” that exists in a global economy and can be used to purchase goods and services. But those more-realistic agents, and that more-realistic money, are not what I’m talking about currently. And I’m not here trying to justify why I think that can be useful.
(Or maybe the things I’m replying to aren’t trying to talk about that type of agent, they just use words like “expected utility” without intending to point at their technical definition and that confuses things. But if that’s the case, then I’m probably not the only person who thinks that’s what they’re trying to talk about; and so it still seems good for me to clarify what happens with that type of agent, in the sort of situation in question.)
(Probably it would be good for me to find some examples of the things I’m responding to, but that would be a different type of effort than I feel like putting in currently.)