<p>I guess you already know that <span class="math-container">$\exp(-\rho t)$</span> is the the discount factor. In particular, it is obtained by continuously compounding the discount factor</p>

<p><span class="math-container">$$\exp(-\rho t)=\lim_{m \to \infty} \left(1+ \frac{\rho}{m}\right)^{mt}$$</span></p>

CC BY-SA 4.0
2018-12-02T19:10:05.957Z
2018-12-02T19:10:05.957Z
Patricio
<p>Currently I'm studying the RCK model at my Advanced Macroeconomics I classes. 
A question arose almost immediately when I saw the utility function of a household in this model. </p>

<p><a href="https://i.sstatic.net/UCFv5.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/UCFv5.png" alt="enter image description here"></a></p>

<p>The question is: why are we using exp(-ρt) inside this integral? I mean: why this functional form in particular? I love mastering every single aspect of every model I study, that's why I'm asking so. 
Thank you really much in advance for your kind responses.</p>

CC BY-SA 4.0
2018-12-02T22:47:15.037Z
It's just there for bringing future utility to present value in continuous time. $\rho$ is the discount factor.
Pedro Cavalcante
<macroeconomics><economic-growth><balanced-growth>
Why are we using exp(.) as the functional form in the household maximization problem inside the RCK model?
shannontesla
# Why are we using exp(.) as the functional form in the household maximization problem inside the RCK model?

(Asked by: username_0 on 2018-12-02)

Currently I'm studying the RCK model at my Advanced Macroeconomics I classes.
A question arose almost immediately when I saw the utility function of a household in this model.

[![enter image description here](https://i.sstatic.net/UCFv5.png)](https://i.sstatic.net/UCFv5.png)

The question is: why are we using exp(-ρt) inside this integral? I mean: why this functional form in particular? I love mastering every single aspect of every model I study, that's why I'm asking so.
Thank you really much in advance for your kind responses.

**Tags:** macroeconomics, economic-growth, balanced-growth

> **Comments:**
> **username_1**: It's just there for bringing future utility to present value in continuous time. $\rho$ is the discount factor.  

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## 1 answers

### Answer by username_2 on 2018-12-02. Score: 3 | Accepted answer

I guess you already know that $\exp(-\rho t)$ is the the discount factor. In particular, it is obtained by continuously compounding the discount factor

$$\exp(-\rho t)=\lim\_{m \to \infty} \left(1+ \frac{\rho}{m}\right)^{mt}$$


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