<p>I believe $n_{t-1}$ is a quantity from the past, so you should be able to treat it as an exogenous variable</p>

CC BY-SA 3.0
2017-12-04T21:11:15.670Z
2017-12-04T21:17:30.683Z
2017-12-04T21:17:30.683Z
fabriceulysse
<p>$n_{t-1}$ is exogenous at time $t$. Since you must be working in a dynamic setting, $n_t$ will also show up in the utility function at time $t+1$.</p>

CC BY-SA 3.0
2017-12-04T21:17:09.743Z
2017-12-04T21:17:09.743Z
N. X
<p>In the habit formation RBC model, the utility can be given as follows:</p>

<p>$U(c_{t},n_{t}) = \ln(c_{t}) - \frac{\theta}{1+\upsilon} \bigg(\frac{n_{t}}{n_{t-1}^{\phi}}\bigg)^{1+\upsilon}$</p>

<p>When I do FOC wrt $n_t$, I'm confused about how to treat the variable $n_{t-1}$. Is it exogenous or should I try to find $\frac{\partial n_{t-1}}{\partial n_t}$?</p>

<p>Many thanks.</p>

CC BY-SA 3.0
2017-12-05T11:30:26.370Z
Could you tell us a bit more about your model? Is this infinite horizon or are there finitely many periods? What are yo trying to maxmimize with the FOC? It looks like, if you were maximizing the lifetime utility, you would have to set this up as a dynamic programming problem rather than optimising a single period utility.
Ubiquitous
<macroeconomics><rbc>
Utility function of habit formation model
user68863
# Utility function of habit formation model

(Asked by: username_0 on 2017-12-02)

In the habit formation RBC model, the utility can be given as follows:

$U(c\_{t},n\_{t}) = \ln(c\_{t}) - \frac{\theta}{1+\upsilon} \bigg(\frac{n\_{t}}{n\_{t-1}^{\phi}}\bigg)^{1+\upsilon}$

When I do FOC wrt $n\_t$, I'm confused about how to treat the variable $n\_{t-1}$. Is it exogenous or should I try to find $\frac{\partial n\_{t-1}}{\partial n\_t}$?

Many thanks.

**Tags:** macroeconomics, rbc

> **Comments:**
> **username_1**: Could you tell us a bit more about your model? Is this infinite horizon or are there finitely many periods? What are yo trying to maxmimize with the FOC? It looks like, if you were maximizing the lifetime utility, you would have to set this up as a dynamic programming problem rather than optimising a single period utility.  

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## 2 answers

### Answer by username_2 on 2017-12-04. Score: 1 | Accepted answer

I believe $n\_{t-1}$ is a quantity from the past, so you should be able to treat it as an exogenous variable


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### Answer by username_3 on 2017-12-04. Score: 1

$n\_{t-1}$ is exogenous at time $t$. Since you must be working in a dynamic setting, $n\_t$ will also show up in the utility function at time $t+1$.


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