Finding optimal Inflation - Walsh
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.



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:

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