<p><strong>Edit:</strong> Roel Beetsma replied! He says he got the same derivation we basically got. So the solutions seem to be mistaken and we win! Also I'm removing the strikeout below.</p>

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

<p>Note that
$$+ e\frac{\lambda - \theta}{[-1-\lambda]}$$</p>

<p>actually simplifies to</p>

<p>$$ - e\frac{\lambda - \theta}{[1 + \lambda]} $$</p>

<p>rather than with $\lambda + \theta$ in the numerator like you had.</p>

<p>So the solutions has</p>

<p>$$- e \frac{1 + \theta}{1 + \lambda}$$</p>

<p>instead of what we have above. The difference between the two is:</p>

<p>$$-e\frac{-1 - \lambda}{1 + \lambda} = e$$</p>

CC BY-SA 3.0
2016-06-01T03:23:20.713Z
Mods, feel free to delete this if you feel it is a non-answer. I did email the original people who did the derivation (Beetsma and Jensen) that Walsh got from their paper, and linked them back here though.
Kitsune Cavalry
CC BY-SA 3.0
2016-06-01T16:15:12.533Z
Scorreeeeeeeeee
Kitsune Cavalry
CC BY-SA 3.0
2016-06-01T23:29:09.157Z
Do I get points for finding the error? Lol
123
CC BY-SA 3.0
2016-06-02T02:33:51.543Z
I can only give you the 5 with my upvote lol.
Kitsune Cavalry
CC BY-SA 3.0
2016-06-02T15:43:22.830Z
Sorry 123 but your math were wrong so points go to Kitsune ! (However I had risen the minus sign before so technically I should attribute points to me lol)
Alexis L.
CC BY-SA 3.0
2016-06-03T14:58:10.360Z
Hah. Fair enough.
123
CC BY-SA 3.0
2016-06-01T02:37:23.410Z
2016-06-01T16:14:35.313Z
2016-06-01T16:14:35.313Z
Kitsune Cavalry
<p>I am solving questions from Walsh and then verifying with a solutions manual. However, I keep solving a question and arriving at a slightly different answer than that suggested by the solution manual. </p>

<p>The solution given by the manual: </p>

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

<p>However, when I take the optimal $\pi^e$ and substitute into (121) I get </p>

<p>$$\pi^* = \frac{\pi^T[-1-\lambda]}{[-1-\lambda]} + \frac{\lambda k [ -1-\lambda]}{[-1-\lambda]} + \frac{\theta k [1+ \lambda]}{[-1-\lambda]} +e\frac{\lambda - \theta}{[-1-\lambda]}$$ </p>

<p>and this simplifies to: </p>

<p>$$\pi^*= \pi^T + k(\lambda - \theta) - e\frac{\lambda + \theta}{[1 + \lambda]}$$</p>

<p>And so my issue is that I don't see how there is no $\lambda$ in the numerator of the fraction multiplying e at the end of the simplification. </p>

<p>Can anyone see my error? I must be missing something simple. </p>

CC BY-SA 3.0
2016-05-25T20:34:44.827Z
Found almost like you with a $\lambda - \theta$ for the last numerator. No sign of the $1+\theta$ . The solution seems weird as the factor on the "e" is $\lambda - \theta$ in equation (121) and I don't see how it can turn in what is here given as a solution ...
Alexis L.
CC BY-SA 3.0
2016-05-26T02:49:29.997Z
Which problem in Walsh is it? Maybe there's an errata somewhere for it. I got the same derivation as you.
Kitsune Cavalry
CC BY-SA 3.0
2016-05-26T03:41:41.380Z
#14, chapter 7. It is page 328 of 3rd edition. I think it is #11 of chapter 8 for the second edition.
123
CC BY-SA 3.0
2016-05-31T17:42:34.647Z
123, please share the knowledge (solution manual) ;)
An old man in the sea.
CC BY-SA 3.0
2016-05-31T21:35:18.210Z
Sure. Is there a way I can send you the file?
123
CC BY-SA 3.0
2016-06-01T12:12:48.523Z
@123 just send the link to anoldmaninthesea@gmail.com . Thanks ;)
An old man in the sea.
CC BY-SA 3.0
2016-06-01T16:17:08.127Z
The mystery is over folks. The original people who made the question that Walsh got it from emailed me back.
Kitsune Cavalry
<macroeconomics>
Finding optimal Inflation - Walsh
123
# Finding optimal Inflation - Walsh

(Asked by: username_0 on 2016-05-25)

I am solving questions from Walsh and then verifying with a solutions manual. However, I keep solving a question and arriving at a slightly different answer than that suggested by the solution manual.

The solution given by the manual:

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

However, when I take the optimal $\pi^e$ and substitute into (121) I get

$$\pi^\* = \frac{\pi^T[-1-\lambda]}{[-1-\lambda]} + \frac{\lambda k [ -1-\lambda]}{[-1-\lambda]} + \frac{\theta k [1+ \lambda]}{[-1-\lambda]} +e\frac{\lambda - \theta}{[-1-\lambda]}$$

and this simplifies to:

$$\pi^\*= \pi^T + k(\lambda - \theta) - e\frac{\lambda + \theta}{[1 + \lambda]}$$

And so my issue is that I don't see how there is no $\lambda$ in the numerator of the fraction multiplying e at the end of the simplification.

Can anyone see my error? I must be missing something simple.

**Tags:** macroeconomics
> **Comments:**
> **username_1**: Found almost like you with a $\lambda - \theta$ for the last numerator. No sign of the $1+\theta$ . The solution seems weird as the factor on the "e" is $\lambda - \theta$ in equation (121) and I don't see how it can turn in what is here given as a solution ...  
> **username_2**: Which problem in Walsh is it? Maybe there's an errata somewhere for it. I got the same derivation as you.  
> **username_0**: #14, chapter 7. It is page 328 of 3rd edition. I think it is #11 of chapter 8 for the second edition.  
> **username_3**: 123, please share the knowledge (solution manual) ;)  
> **username_0**: Sure. Is there a way I can send you the file?  
> **username_3**: @123 just send the link to anoldmaninthesea@gmail.com . Thanks ;)  
> **username_2**: The mystery is over folks. The original people who made the question that Walsh got it from emailed me back.  

---

## 1 answers

### Answer by username_2 on 2016-06-01. Score: 4 | Accepted answer

**Edit:** Roel Beetsma replied! He says he got the same derivation we basically got. So the solutions seem to be mistaken and we win! Also I'm removing the strikeout below.

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

Note that
$$+ e\frac{\lambda - \theta}{[-1-\lambda]}$$

actually simplifies to

$$ - e\frac{\lambda - \theta}{[1 + \lambda]} $$

rather than with $\lambda + \theta$ in the numerator like you had.

So the solutions has

$$- e \frac{1 + \theta}{1 + \lambda}$$

instead of what we have above. The difference between the two is:

$$-e\frac{-1 - \lambda}{1 + \lambda} = e$$

> **Comments:**
> **username_2**: Mods, feel free to delete this if you feel it is a non-answer. I did email the original people who did the derivation (Beetsma and Jensen) that Walsh got from their paper, and linked them back here though.  
> **username_2**: Scorreeeeeeeeee  
> **username_0**: Do I get points for finding the error? Lol  
> **username_2**: I can only give you the 5 with my upvote lol.  
> **username_1**: Sorry 123 but your math were wrong so points go to Kitsune ! (However I had risen the minus sign before so technically I should attribute points to me lol)  
> **username_0**: Hah. Fair enough.  

---

