I would like to draw the following figure (rotated 180 degrees--I do not know why it came out upside down) using TikZ:

It seems that this should be easy, and I have tried playing with ARC function but am coming up empty. Does someone have an idea on this?
This is what I've tried:
\def\R{\mathbb{R}}
\newcommand{\cvx}{convex}
% glossary
\begin{document}
\begin{figure}
\begin{tikzpicture}[scale=0.5]
\scriptsize
\draw (0,11.5) -- (0,0) node[below left]{$0$} -- (11,0) node[below right]{$Z$};
\node [above left] at (0,11){$\chi$};
\node [above] at (0,12){$$Consumption$$};
\node [below] at (5.5,0){$\Delta$ in $Z$};
\draw (0,0)arc(90:-90:11cm and 5.5cm);
\draw (0,5.5) node[below left]{$t^*$} -- (11,5.5);
\draw (11.2,11) -- (11.7,11) -- (11.7,5.5) -- (11.2,5.5);
\node[align=left, right] at (11.7,8.25) {Prohibitive\\Range};
\draw[fill=gray] (11,5.5)arc(0:90:11cm and 5.5cm);
\draw[fill=gray] (11,5.5) -- (0,5.5) -- (0,11);
\end{tikzpicture}
\caption{The Laffer curve}
\end{figure}
\end{document}

