<p>It is safe to assume that if the consumer passes away, his creditors get his endowment. This actually happens in real life. <span class="math-container">$B$</span> should obviously be zero. As far as the second period is concerned you can represent it as a von Neuman-Morgenstern utility from the lottery:</p>

<p><span class="math-container">$\beta u(c_2)$</span> with probability <span class="math-container">$p$</span> and <span class="math-container">$0$</span> with probability <span class="math-container">$1-p$</span>.</p>

<p>I.e. <span class="math-container">$U(c_1, c_2) = log(c_1) + p\beta log(c_2).$</span></p>

CC BY-SA 4.0
2019-12-07T23:50:01.533Z
2019-12-07T23:50:01.533Z
Grada Gukovic
<p>Here is the setup: 
Suppose that there is an individual who lives up to two periods. He lives with absolute certainty during period <span class="math-container">$1$</span>, and during this period his sub-utility function is given by:
<span class="math-container">$$u(c_1) = \log c_1.$$</span>
The individual is alive in period <span class="math-container">$2$</span> with probability <span class="math-container">$p$</span>, and if he is alive, his state sub-utility function is given by
<span class="math-container">$$u(c_2) =\log c_2$$</span>
and if he dies, he receives the fixed utility level <span class="math-container">$B$</span>. Suppose he has access to a perfect capital market and discounts the future at rate <span class="math-container">$\beta$</span>. His endowment is given by <span class="math-container">$(\omega_1, \omega_2)$</span>.</p>

<p>I have a few questions about how to approach this problem. The first question is: do we assume he can die with debt/excess savings at the end of period <span class="math-container">$1$</span>? If I assume that <span class="math-container">$p=0$</span> (dies with certainty), I get that he takes out a loan <span class="math-container">$s= \frac{\omega_2}{1+r}$</span> in the first period. Does this make sense, i.e., do we assume that even if he dies he gets an endowment of <span class="math-container">$\omega_2$</span> to pay off his debts? This result would correspond to <span class="math-container">$c_2 =0$</span>. </p>

<p>The second question is about the fixed utility level. Should this be interpreted as, if he dies, he gets utility <span class="math-container">$u(c_1) + B$</span>? Or <span class="math-container">$u(c_1) + \beta B$</span>? Or that we assume his total lifetime utility from consumption is <span class="math-container">$u(c_1) = B$</span>? </p>

<p>Thanks!</p>

CC BY-SA 4.0
2019-12-01T03:46:19.493Z
There is a lot of information missing from the problem. In terms of $\beta B$ vs $B$, it doesn't make much of a difference, just change the interpretation based on how you set up the problem.
lunar_props
CC BY-SA 4.0
2019-12-01T16:43:07.190Z
Yeah I agree I'm not sure why I asked that. So I guess we should assume that his person receives the endowment or something to pay off any debt
David Bowman
CC BY-SA 4.0
2019-12-01T20:24:42.463Z
You model an agent receiving utility from dying? Seems dumb.
123
<microeconomics><utility><expected-utility><probability><uncertainty>
Intertemporal choice with possibility of death
David Bowman
# Intertemporal choice with possibility of death

(Asked by: username_0 on 2019-11-30)

Here is the setup:
Suppose that there is an individual who lives up to two periods. He lives with absolute certainty during period $1$, and during this period his sub-utility function is given by:
$$u(c\_1) = \log c\_1.$$
The individual is alive in period $2$ with probability $p$, and if he is alive, his state sub-utility function is given by
$$u(c\_2) =\log c\_2$$
and if he dies, he receives the fixed utility level $B$. Suppose he has access to a perfect capital market and discounts the future at rate $\beta$. His endowment is given by $(\omega\_1, \omega\_2)$.

I have a few questions about how to approach this problem. The first question is: do we assume he can die with debt/excess savings at the end of period $1$? If I assume that $p=0$ (dies with certainty), I get that he takes out a loan $s= \frac{\omega\_2}{1+r}$ in the first period. Does this make sense, i.e., do we assume that even if he dies he gets an endowment of $\omega\_2$ to pay off his debts? This result would correspond to $c\_2 =0$.

The second question is about the fixed utility level. Should this be interpreted as, if he dies, he gets utility $u(c\_1) + B$? Or $u(c\_1) + \beta B$? Or that we assume his total lifetime utility from consumption is $u(c\_1) = B$?

Thanks!

**Tags:** microeconomics, utility, expected-utility, probability, uncertainty

> **Comments:**
> **username_1**: There is a lot of information missing from the problem. In terms of $\beta B$ vs $B$, it doesn't make much of a difference, just change the interpretation based on how you set up the problem.  
> **username_0**: Yeah I agree I'm not sure why I asked that. So I guess we should assume that his person receives the endowment or something to pay off any debt  
> **username_2**: You model an agent receiving utility from dying? Seems dumb.  

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## 1 answers

### Answer by username_3 on 2019-12-07. Score: 1

It is safe to assume that if the consumer passes away, his creditors get his endowment. This actually happens in real life. $B$ should obviously be zero. As far as the second period is concerned you can represent it as a von Neuman-Morgenstern utility from the lottery:

$\beta u(c\_2)$ with probability $p$ and $0$ with probability $1-p$.

I.e. $U(c\_1, c\_2) = log(c\_1) + p\beta log(c\_2).$


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