\( \newcommand{\colvec}[2]{\begin{bmatrix}#1 \\ \vdots\\ #2 \end{bmatrix}} \)
\( \newcommand{\rfirmsset}[1][R]{\mathbf{F}^{#1}} \)
\( %\newcommand{\mdefentry}[8][f]{\IfValueTF{#2}{(#1_{#3#5}( #2 )^{#7#8})_{\substack{#3 \in #4\\#5 \in #6}}}}{ (#1_{#3#5}^{#7#8})_{\substack{#3 \in #4\\#5 \in #6}}} \)
\( \newcommand{\irowsum}{    \begin{bmatrix}      1 \\      \vdots \\      1    \end{bmatrix}  } \)
\( \newcommand{\isum}{    \underset{s \times p}{      \begin{bmatrix}        1 & \hdots & 0 & & 1 & \hdots & 0\\        \vdots & \ddots & \vdots & \hdots &\vdots & \ddots & \vdots\\        0 & \hdots & 1 & & 0 & \hdots & 1      \end{bmatrix}    }  } \)
\( \newcommand{\colvecid}[2][1]{ \ifnum #1>1     \underbrace{ \begin{bmatrix} #2\\ \vdots\\                                #2         \end{bmatrix}       }_{\substack{#2                                \\#1 \textrm{ times}}}     }   \else                                 \begin{bmatrix}         #2\\                                               \vdots\\                                               #2       \end{bmatrix}        \fi \)
\( \newcommand{\ioorders}{\mathbf{O}} \)
\( \newcommand{\sectorsset}{\mathbb{S}} \)
\( \newcommand{\sectorssetsize}{n} \)
\( \newcommand{\regionsset}{\mathbb{R}} \)
\( \newcommand{\regionssetsize}{m} \)
\( \newcommand{\firmsset}{\mathbb{F}} \)

\( \newcommand{\firmssetsize}{p} \)
\( \newcommand{\catfdset}{\mathbb{C}^{\textrm{fd}}} \)
\( \newcommand{\catfdsetsize}{r} \)
\( \newcommand{\catvaset}{\mathbb{C}^{\textrm{va}}} \)
\( \newcommand{\catvasetsize}{q} \)
\( \newcommand{\ioz}{\mathbf{Z}} \)
\( \newcommand{\ioy}{\mathbf{Y}} \)
\( \newcommand{\iov}{\mathbf{V}} \)
\( \newcommand{\iox}{\mathbf{x}} \)
\( \newcommand{\ioa}{\mathbf{A}} \)
\( \newcommand{\iok}{\mathbf{K}} \)
\( \newcommand{\ioava}{\mathbf{A}_{\textrm{va}}} \)
\( \newcommand{\ioinv}{\mathbf{\Omega}} \)
\( \newcommand{\Damage}{\mathbf{\Gamma}} \)
\( \newcommand{\damage}{\gamma} \)
