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I am looking to reproduce the figure below using tikz:

enter image description here

The codes that I have aren't producing this figure exactly.

   \begin{tikzpicture}[nodes={text height=0.7em,text depth=0.25ex},
my arc/.style={insert path={(4,0)  arc[start angle=0,end angle=180,radius=2]}},
my curve/.style={insert path={(0,0) to[out=-90,in=-135] (1,0) -- ++ (66:4)}}]
\begin{scope}
\clip[my curve] -| cycle;
\fill[red!20,my arc] -- ++ (0,-1) -- ++ (4,0);
\end{scope}
\draw (0,4) node[above left] {$x$} |- (5,0) node[below left] {$y$};
\draw[my arc] node[pos=0.1,above right]{$\alpha\, W(y)$};
\draw[my curve] node[right] {$P(y)$};
\draw (0,2) node[left]{$x^{*}$} -| (2,0) node[below] {$y^*$}
\draw (0,1.8) node[left]{$x_{0}$} -| (1.8,0) node[below] {$y_{0}$}
(0,1) node[left]{$a$} -- (2,1) node[above left]{Incentive-feasible set}; 
\end{tikzpicture}

The $P(y)$ curve is too straight and the bottom is kind of flat. Also I cannot add $x_{0}$ and $y_{0}$ for some reason. My Texstudio editor would just collapse with it. Any help would be appreciated.

EDIT: With Schrodinger's cat's help:

    \begin{tikzpicture}[nodes={text height=0.7em,text depth=0.25ex},
my arc/.style={insert path={(4,0)  arc[start angle=0,end angle=180,radius=2]}},
my curve/.style={insert path={(0,0) to[out=-90,in=-114,looseness=1.5] (1,0) -- ++ (70:4)}}]
\begin{scope}
\clip[my curve] -| cycle;
\fill[red!20,my arc] |- ++ (4,-1);
\end{scope}
\draw (0,4) node[above left] {$x$} |- (5,0) node[below left] {$y$};
\draw[my arc,name path=arc] node[pos=0.1,above right]{$\alpha\, W(y)$};
\draw[my curve,name path=curve] node[right] {$P(y)$};
% \draw  (0,2) node[left]{$x^{*}$} -| (2,0) node[below] {$y^*$};
\draw[name intersections={of=arc and curve,by={i0,i1}}] 
(i1-|0,0) node[left]{$x_{0}$} -| (i1|-0,0) node[below] {$y_{0}$}
-| (2.1,0) node[below] {$y^*$} node[anchor=east,yshift=6ex,align=left]{Incentive-\\ feasible set} ; 
\end{tikzpicture}

enter image description here

OGC
  • 809

1 Answers1

1

This computes the intersection. The first code in this answer also does.

\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{intersections}
\begin{document}
\begin{tikzpicture}[nodes={text height=0.7em,text depth=0.25ex},
my arc/.style={insert path={(4,0)  arc[start angle=0,end angle=180,radius=2]}},
my curve/.style={insert path={(0,0) to[out=-90,in=-114,looseness=1.5] (1,0) -- ++ (66:4)}}]
 \begin{scope}
  \clip[my curve] -| cycle;
  \fill[red!20,my arc] |- ++ (4,-1);
 \end{scope}
 \draw (0,4) node[above left] {$x$} |- (5,0) node[below left] {$y$};
 \draw[my arc,name path=arc] node[pos=0.1,above right]{$\alpha\, W(y)$};
 \draw[my curve,name path=curve] node[right] {$P(y)$};
% \draw  (0,2) node[left]{$x^{*}$} -| (2,0) node[below] {$y^*$};
 \draw[name intersections={of=arc and curve,by={i0,i1}}] 
 (i1-|0,0) node[left]{$x_{0}$} -| (i1|-0,0) node[below] {$y_{0}$}
 (0,1) node[left]{$a$} node[anchor=west,yshift=-1.4ex,align=left]{Incentive-\\
 feasible set}
 -- (i1|-0,1) ; 
\end{tikzpicture}
\end{document}

enter image description here

  • Thanks but how do I get the bottom part to be more round and the P(y) curve is to be a bit curvy? – OGC May 14 '20 at 05:42
  • 1
    @OGC In order to have a smooth result you need to adjust the in and out angles such that the in and the subsequent out differ by 180. I did that now. –  May 14 '20 at 05:47
  • @Schrondinger's cat Any suggestion on how I can get rid of the horizontal line with the label a? – OGC May 14 '20 at 06:09
  • 1
    @OGC Remove (0,1) node[left]{$a$} node[anchor=west,yshift=-1.4ex,align=left]{Incentive-\\ feasible set} -- (i1|-0,1) (but keep the ; in the end!). –  May 14 '20 at 06:09
  • Thanks a lot. I've made an edit as well. – OGC May 14 '20 at 06:12
  • I want to be still able to have the label of Incentive-feasible set though. – OGC May 14 '20 at 06:17
  • 2
    @OGC Then use \draw[name intersections={of=arc and curve,by={i0,i1}}] (i1-|0,0) node[left]{$x_{0}$} -| (i1|-0,0) node[below] {$y_{0}$} (0,1) node[left]{$a$} node[anchor=west,yshift=-1.4ex,align=left]{Incentive-\\ feasible set} ;. –  May 14 '20 at 06:19
  • Thanks a lot! I've made an edit to get close to the figure I wanted. – OGC May 14 '20 at 06:25