<p>Suppose we are given an instantaneous utility function and discounted rate with budget constraint. Using the exponentially discounted utility function, we can find the optimal consumption stream of a person. Now we know the instantaneous utility and also the total utility of different time(period). But what if we are asked to compare which one is better off given change of utility function?</p>
<p>I think it is time to calculate total utility. For instance, the utility of having one burger is 1, with discounted rate 0.5. In this case, if I choose to eat one burger today and one burger tomorrow, for current point of view, I will get utility = 1+0.5*1=1.5. But what is the total utility of these two days? Is it simply 1+1=2?</p>

CC BY-SA 4.0
2023-08-27T09:33:19.597Z
What is "total utility?"
Michael Greinecker
CC BY-SA 4.0
2023-08-27T12:16:47.283Z
Well, it doesn't ask for total utility. It asks to find out which type of the person (HDU, EDU) is better off. So I think I should calculate U(c0)+U(c1)+U(c2) and take the larger one. This sum is what I mean by total utility in the context
Nonenicht
CC BY-SA 4.0
2023-08-27T13:13:02.700Z
I don't think it makes much sense to ask whether someone would be better off with a different utility function.
Michael Greinecker
CC BY-SA 4.0
2023-08-27T13:17:08.840Z
Then what if we want to compare the difference between a person who decide consumption or saving, with another plan of comsumption/buying annuity? Using same utility function and exponential discounted utility, we will get different consumption streams. How do I figure out which plan is better by using utility
Nonenicht
CC BY-SA 4.0
2023-08-27T13:18:53.600Z
I don't know if I should include the discount factor, consider the EDU from period 0 point of view, or simply add utility gains from different periods together
Nonenicht
CC BY-SA 4.0
2023-08-27T16:19:16.910Z
If you have a discounted utility model, you sum up all discounted instantaneous utilities along the stream.
Michael Greinecker
<microeconomics><utility><behavioral-economics>
How do I calculate total utility under discounted utility framework
Nonenicht
# How do I calculate total utility under discounted utility framework

(Asked by: username_0 on 2023-08-27)

Suppose we are given an instantaneous utility function and discounted rate with budget constraint. Using the exponentially discounted utility function, we can find the optimal consumption stream of a person. Now we know the instantaneous utility and also the total utility of different time(period). But what if we are asked to compare which one is better off given change of utility function?

I think it is time to calculate total utility. For instance, the utility of having one burger is 1, with discounted rate 0.5. In this case, if I choose to eat one burger today and one burger tomorrow, for current point of view, I will get utility = 1+0.5\*1=1.5. But what is the total utility of these two days? Is it simply 1+1=2?

**Tags:** microeconomics, utility, behavioral-economics

> **Comments:**
> **username_1**: What is "total utility?"  
> **username_0**: Well, it doesn't ask for total utility. It asks to find out which type of the person (HDU, EDU) is better off. So I think I should calculate U(c0)+U(c1)+U(c2) and take the larger one. This sum is what I mean by total utility in the context  
> **username_1**: I don't think it makes much sense to ask whether someone would be better off with a different utility function.  
> **username_0**: Then what if we want to compare the difference between a person who decide consumption or saving, with another plan of comsumption/buying annuity? Using same utility function and exponential discounted utility, we will get different consumption streams. How do I figure out which plan is better by using utility  
> **username_0**: I don't know if I should include the discount factor, consider the EDU from period 0 point of view, or simply add utility gains from different periods together  
> **username_1**: If you have a discounted utility model, you sum up all discounted instantaneous utilities along the stream.  

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## 0 answers

