%\NewDocumentCommand{\mentry}{m O{f} O{f'} O{} O{}}{\ensuremath{#1_{#2#3}^{#4#5}}}
%\NewDocumentCommand{\colvec}{m m}{  \ensuremath{    \begin{bmatrix}      #1\\      \vdots\\      #2    \end{bmatrix}  }}
%\NewDocumentCommand{\rfirmsset}{O{R}}{\ensuremath{\mathbf{F}^{#1}}}
%\NewDocumentCommand{\mdefentry}{m o O{f} O{\firmsset} O{f'} O{\firmsset} O{}  O{}}{  \IfValueTF{#2}{    \ensuremath{(#1_{#3#5}( #2 )^{#7#8})_{\substack{#3 \in #4\\#5 \in #6}}}  }{    \ensuremath{(#1_{#3#5}^{#7#8})_{\substack{#3 \in #4\\#5 \in #6}}}  }}
\newcommand{\irowsum}{\ensuremath{    \begin{bmatrix}      1 \\      \vdots \\      1    \end{bmatrix}  }}
\newcommand{\isum}{\ensuremath{    \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}    }  }}\NewDocumentCommand{\colvecid}{m o}{  \IfValueTF{#2}{    \ensuremath{      \underbrace{        \begin{bmatrix}          #1\\          \vdots\\          #1        \end{bmatrix}      }_{\substack{#1 \\#2 \textrm{times}}}    }    }    {      \ensuremath{        \begin{bmatrix}          #1\\          \vdots\\          #1        \end{bmatrix}      }    }  }
\newcommand{\ioorders}{\ensuremath{\mathbf{O}}}
\newcommand{\sectorsset}{\ensuremath{\mathbb{S}}}
\newcommand{\sectorssetsize}{\ensuremath{n}}
\newcommand{\regionsset}{\ensuremath{\mathbb{R}}}
\newcommand{\regionssetsize}{\ensuremath{m}}
\newcommand{\firmsset}{\ensuremath{\mathbb{F}}}

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