How to draw these (indifference) curves in TikZ
With tikz
First plot
\documentclass[margin=10pt]{standalone} \usepackage{tikz} \usetikzlibrary{arrows.meta} \begin{document} \begin{tikzpicture}[>=Triangle,thick] \draw[->](0,0)node[below]{$0$}--(6,0)node[below left]{Dimention1}; \draw[->](0,0)--(0,6)node[below left]{Dimention2}; \draw (1.2,5.3) to [bend right=30] coordinate[pos=0.2] (l_i)(5,0.5); \fill (l_i)circle(2.2pt)node[above right]{$\ell_i$}; \draw (5.5,2) to [bend left=10] coordinate[pos=0.2] (l'_j)(0.5,3.5); \fill (l'_j)circle(2.2pt)node[above right]{$\ell'_j$}; \fill (1,3.5)circle(2.2pt)coordinate(l_j)node[above right]{$\ell_j$}; \fill (3.6,1.5)circle(2.2pt)coordinate(l'_i)node[above right]{$\ell'_i$}; \end{tikzpicture} \end{document}
Second plot
\documentclass[margin=10pt]{standalone} \usepackage{tikz} \usetikzlibrary{arrows.meta} \begin{document} \begin{tikzpicture}[>=Triangle,thick] \draw[->](0,0)node[below]{$0$}--(6,0)node[below left]{income}; \draw[->](0,0)--(0,6)node[below left]{heath}; \draw(0,5)node [left,text width=1cm]{normal health}--(5.5,5); \draw (0.8,5)coordinate(A') to [bend right=20] coordinate[pos=0.85] (A) (5.5,2); \draw (2,5)coordinate(B') to [bend right=20] coordinate[pos=0.2] (B) coordinate[pos=0.7] (B'') (5.5,1); \foreach \i in{A,B,A',B'}{\fill (\i)circle (2.2pt)node[above right]{$\i$};} \fill (B'')circle (2.2pt)node[below left]{$B''$}; \foreach \i/\j in{A'/y_1^*,B'/y_2^*}{\draw[dashed](\i)--+(0,-5)node[below]{$\j$};} \end{tikzpicture} \end{document}
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={$\text{y}_\text{A}^*$,$\text{y}_\text{B}^*$},
]
\addplot[solid, domain=0:9.5] {8};
\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}