<p>Perhaps <span class="math-container">$c_t = y_t - k_{t+1}$</span> and <span class="math-container">$k_{t+1}$</span> under steady state is <span class="math-container">$\alpha \beta y_{t+1}$</span>. You can think of the <span class="math-container">$c_{t}$</span> as coming from the accounting identity of C = Y - I in the long run.</p>

CC BY-SA 4.0
2023-01-08T20:01:46.297Z
I think utilizing the budget constraint makes sense, but I'm still a bit confused on the timing aspect. Since $z$ is still stochastic, why wouldn't the steady state for $k$ include an expectation over $z$?
qwerty
CC BY-SA 4.0
2023-01-09T21:35:12.497Z
This is independent of the stochastic process under the current functional forms. Also  you aren’t solving the expectations bit just yet. Only when you get the policy functions and think about the complete system do you need to think about expectations.
EndLoop
CC BY-SA 4.0
2023-01-04T20:06:36.037Z
2023-01-04T20:06:36.037Z
EndLoop
<p>I'm doing some self-studying using the publicly available preliminary exams from UC Davis and need help understanding a statement given in the solutions.</p>
<p><strong>This particular problem is from the 2015 August Macro Prelim</strong>:</p>
<p><a href="https://i.sstatic.net/9VlZj.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/9VlZj.png" alt="enter image description here" /></a></p>
<p><strong>The answer to this question is</strong>:</p>
<p><a href="https://i.sstatic.net/63C3f.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/63C3f.png" alt="enter image description here" /></a></p>
<p><strong>My question</strong>:
How does one get from the Euler Equation <span class="math-container">$$\frac{k_{t+1}}{c_t} = \alpha \beta E\left[ \frac{y_{t+1}}{c_{t+1}} \right]$$</span> that <span class="math-container">$c_t = (1-\alpha \beta)y_t$</span> and <span class="math-container">$k_{t+1} = \alpha \beta y_t$</span>? It's not obvious to me that rearranging that equation in any manner yields the provided result.</p>

CC BY-SA 4.0
2023-01-04T19:56:13.887Z
By typing up your question, rather than presenting it as an image, you make your question more accessible to vision impaired readers and make it a more discoverable resource through search.
BKay
CC BY-SA 4.0
2023-01-04T20:19:25.640Z
Thanks - I made an edit to include the Euler equation in question. I was not sure whether including the whole question was necessary since the solutions seemed to suggest not, but wanted to hedge against the chance other details were indeed relevant. If they turn out to be, I will further edit.
qwerty
<macroeconomics><policy>
Euler Equation and Policy Functions
qwerty
# Euler Equation and Policy Functions

(Asked by: username_0 on 2023-01-04)

I'm doing some self-studying using the publicly available preliminary exams from UC Davis and need help understanding a statement given in the solutions.

**This particular problem is from the 2015 August Macro Prelim**:

[![enter image description here](https://i.sstatic.net/9VlZj.png)](https://i.sstatic.net/9VlZj.png)

**The answer to this question is**:

[![enter image description here](https://i.sstatic.net/63C3f.png)](https://i.sstatic.net/63C3f.png)

**My question**:
How does one get from the Euler Equation $$\frac{k\_{t+1}}{c\_t} = \alpha \beta E\left[ \frac{y\_{t+1}}{c\_{t+1}} \right]$$ that $c\_t = (1-\alpha \beta)y\_t$ and $k\_{t+1} = \alpha \beta y\_t$? It's not obvious to me that rearranging that equation in any manner yields the provided result.

**Tags:** macroeconomics, policy

> **Comments:**
> **username_1**: By typing up your question, rather than presenting it as an image, you make your question more accessible to vision impaired readers and make it a more discoverable resource through search.  
> **username_0**: Thanks - I made an edit to include the Euler equation in question. I was not sure whether including the whole question was necessary since the solutions seemed to suggest not, but wanted to hedge against the chance other details were indeed relevant. If they turn out to be, I will further edit.  

---

## 1 answers

### Answer by username_2 on 2023-01-04. Score: 0 | Accepted answer

Perhaps $c\_t = y\_t - k\_{t+1}$ and $k\_{t+1}$ under steady state is $\alpha \beta y\_{t+1}$. You can think of the $c\_{t}$ as coming from the accounting identity of C = Y - I in the long run.

> **Comments:**
> **username_0**: I think utilizing the budget constraint makes sense, but I'm still a bit confused on the timing aspect. Since $z$ is still stochastic, why wouldn't the steady state for $k$ include an expectation over $z$?  
> **username_2**: This is independent of the stochastic process under the current functional forms. Also  you aren’t solving the expectations bit just yet. Only when you get the policy functions and think about the complete system do you need to think about expectations.  

---

