# [Tex/LaTex] How to draw these (indifference) curves in TikZ

pgfplotstikz-pgf

I would like to reproduce the following plots but I have no idea how to do this. Does anyone of you know how to draw these curves in PGF/TikZ (or in any other suited way)?  Here is a pgfplots solution. Based on salim bou's answer.

# Plot 1 \documentclass[margin=10pt]{standalone}
\usepackage{pgfplots}

\begin{document}
\begin{tikzpicture}
\begin{axis}[
axis x line=bottom,
axis y line=left,
xmin=0, xmax=10,
ymin=0, ymax=10,
xlabel={Dimension 1},
ylabel={Dimension 2},
ytick=\empty,
xtick={0},
]
\draw (axis cs:2.2,9.5) to [bend right=30] coordinate[pos=0.2] (l_i) (axis cs:8,.5);
\fill (l_i) circle (2.2pt) node[above right] {$\ell_i$};

\draw (axis cs:.5,6) to [bend right=10] coordinate[pos=0.8] (dl_j) (axis cs:9,3.5);
\fill (dl_j) circle (2.2pt) node[above right] {$\ell_j'$};

\fill (axis cs:1.5,6) circle (2.2pt) node[above right] {$\ell_j$};
\fill (axis cs:6,2.5) circle (2.2pt) node[above right] {$\ell_i'$};
\end{axis}
\end{tikzpicture}

\end{document}


# Plot 2 \documentclass[margin=10pt]{standalone}
\usepackage{pgfplots}
\usepackage{amsmath}

\begin{document}
\begin{tikzpicture}
\begin{axis}[
axis x line=bottom,
axis y line=left,
xmin=0, xmax=10,
ymin=0, ymax=10,
xlabel={income},
ylabel={health},
ytick=\empty,
extra y ticks={8},
extra y tick style={align=center, font=\scriptsize},
extra y tick labels={normal\\health},
xtick={0},
extra x ticks={1,3},
extra x tick labels={$\text{y}_\text{A}^*$,$\text{y}_\text{B}^*$},
]

\draw (axis cs:1,8) to [bend right=10]
coordinate[pos=0] (A') coordinate[pos=0.7] (A) (axis cs:8,3.5);
\fill (A') circle (2.2pt) node[above right] {A'};
\fill (A) circle (2.2pt) node[above right] {A};

\draw (axis cs:3,8) to [bend right=30]
coordinate[pos=0] (B') coordinate[pos=0.17] (B) coordinate[pos=0.6] (B'') (axis cs:8,1.5);
\fill (B') circle (2.2pt) node[above right] {B'};
\fill (B) circle (2.2pt) node[above right] {B};
\fill (B'') circle (2.2pt) node[above right] {B''};

\draw[dashed, thin] (axis cs:1,8) -- (axis cs:1,0);
\draw[dashed, thin] (axis cs:3,8) -- (axis cs:3,0);
\end{axis}
\end{tikzpicture}

\end{document}