\usepackage{comment}

\includecomment{draft}  %  activate this line for draft printing of equation names under equations
\includecomment{derivation}  %  activate this line for extra material giving details of derivations
%\excludecomment{draft}  %  activate this line for non-draft
%\excludecomment{derivation}  %  activate this line for the shorter version of the paper

%  Anything in a draft environment is printed only when draft is set in an \inlcudecomment, as above.
% Use for equation, table, figure, theorem names and anything else handy to see while you are working on a paper

%  Example:

\begin{equation}\label{eq:w}
H_N  = \frac{\beta_U}{1-\beta_U}F_N .
\end{equation}
\begin{draft}
eq:w
\end{draft}

%  Same for derivation. Using separately enables the production of a finished paper with derivation details.

%  Example:

Then I equate the constants and the coefficients on $b_t$ and $n_t$ to find recursions for the household role valuations:
\begin{derivation}
Substitute \eqref{eqA:interior} into the equation above for the constant in the Bellman equation to get:
\end{derivation}
\begin{equation}\label{eqA:HS}
H_{S,t} = \frac{1}{1+r} (H_{S,t+1} + \phi_{S,t} H_{B,t+1})
\end{equation}
\begin{derivation}
Add the equations above for the constant and for $b$ to get:
\[
{H}_{B,t}+H_{S,t} =\alpha(\tilde{p}_t-p_t)+\frac{1}{1+r}((1-\sigma_B){H}_{B,t+1} -\phi_{U,t}{H}_{N,t+1} )
\]
\[+\frac{1}{1+r}({H}_{S,t+1} + \phi_{U,t}{H}_{N,t+1})
\]
Substitute \eqref{eq:HS} to get
\[
{H}_{B,t}=\alpha(\tilde{p}_t-p_t)+\frac{1}{1+r}({H}_{S,t+1}+ (1-\sigma_B){H}_{B,t+1}+(-\phi_{U,t}+\phi_{U,t}){H}_{N,t+1}-H_{S,t+1} - \phi_{S,t} H_{B,t+1})
\]
so,
\end{derivation}
\begin{equation}\label{eqA:HB}
H_{B,t} = \alpha (\tilde{p}_t - p_t) + \frac{1}{1+r}  (1 - \sigma_{B,t} - \phi_{S,t}) H_{B,t+1}
\end{equation}