8 thoughts on “1-3 Carlos Raposo. What if we valued time instead of money?”
Gabriel J P Pinto
Hi!
This approach reminded me of the one used by Blatt in Dynamic Economic Systems to justify risk-taking behavior by firms. He develops a (simplified) translation from wealth-space to time-space based on time to recover an initial investment under uncertainty (payback time). Given two investments with prices P_0, and P_1, you would take the one that had the smaller payback time.
Very nice! We have also started to teach EE without stochasticity, which is similar to what you’re doing here. I like your proposal to think of risk neutrality as being indifferent to going back a year or zooming forward a year with equal chance. Or at least your pointing out that the dominant definition of risk neutrality often implies that one is indifferent between losing 3 years and gaining 1 year with equal chance (which of course makes little sense).
The argument which connects wealth dynamics and the utility functions of mainstream theory is linearization of the dynamic, and that doesn’t actually require stochasticity.
In the textbook we’re writing, we now begin with a fully deterministic discussion of growth rates to motivate this connection. No stochastic calculus is needed, which is didactically better. Once the role of non-linearity is clear, and that of a growth rate as a scale factor of time, it’s easy to throw in randomness and recover the exact equations of EUT in the relevant setup.
Question: is this written up in citable form somewhere?
Thank you for your comment. I am looking forward to reading your deterministic discussion. I think it is the key that will open EE to the general public.
Regarding a citable paper, we do not have one yet. If you want to mention us somehow, feel free to do it in an informal way. And if you need any input from our side, we’ll be happy to help.
Good luck with your textbook! For sure one of the most interesting the world of economics will see this year 🙂
Really enjoyed this. I like its application to one-shot gambles which I have always thought should be solvable via an ergodicity framework.
You prompted me to play around with negative growth versions of your exponential growth example. I realised something I found counterintuitive.
My intuition was that preferences should change in a negative exponential growth environment. However it seems that preferences should remain the same, that is you should avoid the fair gamble in both the positive and negative growth case. In the positive case, the fair gamble moves you backward in time on average, which you shouldn’t want. In the negative case, the fair gamble moves you forward in time on average, which again you shouldn’t want.
This makes sense from the EE framework whereby it is the dynamic that determines the “utility-function”, and in both cases it is the same underlying dynamic.
Thank you very much! Glad you liked it. I think Pablo and me came up with all this because we were missing as well a way of handling one-shot gambles within wealth dynamics.
As I tried to explain during the Q&A, if you think about it, only growing or decaying dynamics are acceptable. We cannot deal with flat dynamics in our model, because time lapses become infinite. From this point of view, in the case of a decaying dynamic what we “want” is to avoid “advancing” in time. What this means, is that instead of having du=dt, for decaying wealth dynamics we might need to say that du=-dt. This makes sense if what you value is to “go back” in time. By doing this, you get the usual logarithm as a utility function for a decaying multiplicative dynamic.
I do not know if there is a better or cleaner way to handle this. Maybe you have some ideas!
I think there is something deep in what you are pursuing, but I suspect that there is something deeper once you solve the negative/positive/flat problem. I will keep thinking about it. 🙂
Hi!
This approach reminded me of the one used by Blatt in Dynamic Economic Systems to justify risk-taking behavior by firms. He develops a (simplified) translation from wealth-space to time-space based on time to recover an initial investment under uncertainty (payback time). Given two investments with prices P_0, and P_1, you would take the one that had the smaller payback time.
Nice talk, thank you!
John Blatt book
https://books.google.de/books?hl=de&lr=&id=jzz3DwAAQBAJ&oi=fnd&pg=PP1&dq=blatt+Dynamic+Economic+Systems&ots=mUEQv5H-mn&sig=vXo2xk8_o2nxjP9bwuKH2QZMbMI&redir_esc=y#v=onepage&q=blatt%20Dynamic%20Economic%20Systems&f=false
Hi Gabriel,
Thank you for your feedback. I’ll try to look more into this, a mapping from wealth to time is exactly what we are doing. Looks promising.
Thank you,
Carlos
Very nice! We have also started to teach EE without stochasticity, which is similar to what you’re doing here. I like your proposal to think of risk neutrality as being indifferent to going back a year or zooming forward a year with equal chance. Or at least your pointing out that the dominant definition of risk neutrality often implies that one is indifferent between losing 3 years and gaining 1 year with equal chance (which of course makes little sense).
The argument which connects wealth dynamics and the utility functions of mainstream theory is linearization of the dynamic, and that doesn’t actually require stochasticity.
In the textbook we’re writing, we now begin with a fully deterministic discussion of growth rates to motivate this connection. No stochastic calculus is needed, which is didactically better. Once the role of non-linearity is clear, and that of a growth rate as a scale factor of time, it’s easy to throw in randomness and recover the exact equations of EUT in the relevant setup.
Question: is this written up in citable form somewhere?
Hi Ole,
Thank you for your comment. I am looking forward to reading your deterministic discussion. I think it is the key that will open EE to the general public.
Regarding a citable paper, we do not have one yet. If you want to mention us somehow, feel free to do it in an informal way. And if you need any input from our side, we’ll be happy to help.
Good luck with your textbook! For sure one of the most interesting the world of economics will see this year 🙂
Really enjoyed this. I like its application to one-shot gambles which I have always thought should be solvable via an ergodicity framework.
You prompted me to play around with negative growth versions of your exponential growth example. I realised something I found counterintuitive.
My intuition was that preferences should change in a negative exponential growth environment. However it seems that preferences should remain the same, that is you should avoid the fair gamble in both the positive and negative growth case. In the positive case, the fair gamble moves you backward in time on average, which you shouldn’t want. In the negative case, the fair gamble moves you forward in time on average, which again you shouldn’t want.
This makes sense from the EE framework whereby it is the dynamic that determines the “utility-function”, and in both cases it is the same underlying dynamic.
Hi Ollie,
Thank you very much! Glad you liked it. I think Pablo and me came up with all this because we were missing as well a way of handling one-shot gambles within wealth dynamics.
As I tried to explain during the Q&A, if you think about it, only growing or decaying dynamics are acceptable. We cannot deal with flat dynamics in our model, because time lapses become infinite. From this point of view, in the case of a decaying dynamic what we “want” is to avoid “advancing” in time. What this means, is that instead of having du=dt, for decaying wealth dynamics we might need to say that du=-dt. This makes sense if what you value is to “go back” in time. By doing this, you get the usual logarithm as a utility function for a decaying multiplicative dynamic.
I do not know if there is a better or cleaner way to handle this. Maybe you have some ideas!
Thanks again!
I think there is something deep in what you are pursuing, but I suspect that there is something deeper once you solve the negative/positive/flat problem. I will keep thinking about it. 🙂