Typically one would include the space as part of your \text, insert a manual control space \ , or use a \quad:

\documentclass{article}
\usepackage{mathtools}
\newcommand{\pdi}[2]{\partial #1 / \partial #2}
\newcommand{\eqs}{\overset{s}{=}}
\begin{document}
Lastly, the comparative static of $x^*$ w.r.t.\ $\bar{P}$,
\[
\pdi{x^*}{\bar{P}} = -\frac{-1 - \frac{-a}{2(x^*-1)}}{\underbrace{\pdi{U^c}{x}-\pdi{U^h}{x}}_{\mathclap{\text{($-$) by stability condition}}}}
\eqs{-1 - \frac{-a}{2(x^{*}-1)}} < 0 \text{ for $x^{*} \neq 1$}.
\]
Lastly, the comparative static of $x^*$ w.r.t.\ $\bar{P}$,
\[
\pdi{x^*}{\bar{P}} = -\frac{-1 - \frac{-a}{2(x^*-1)}}{\underbrace{\pdi{U^c}{x}-\pdi{U^h}{x}}_{\mathclap{\text{($-$) by stability condition}}}}
\eqs{-1 - \frac{-a}{2(x^{*}-1)}} < 0 \ \text{for $x^{*} \neq 1$}.
\]
Lastly, the comparative static of $x^*$ w.r.t.\ $\bar{P}$,
\[
\pdi{x^*}{\bar{P}} = -\frac{-1 - \frac{-a}{2(x^*-1)}}{\underbrace{\pdi{U^c}{x}-\pdi{U^h}{x}}_{\mathclap{\text{($-$) by stability condition}}}}
\eqs{-1 - \frac{-a}{2(x^{*}-1)}} < 0 \quad \text{for $x^{*} \neq 1$}.
\]
\end{document}
Above I loaded mathtools (which automatically loads amsmath). It allowed me to use \mathclap for the \underbrace text - avoiding possible overflow of the denominator in the fraction.
Note the use of \[...\] rather than $$...$$.
\text{...}. often\qquadis used (works in either math or text). – barbara beeton Jan 20 '15 at 20:47