\documentclass[tikz,border=5pt]{standalone}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[xscale=6,yscale=4.3,domain=0:1,samples=100]
\draw[ultra thick,->] (0,0)--(1.1,0) node[scale=1.2,above] {$m$};
\draw[ultra thick,->] (0,0)--(0,1) node[scale=1.2,above right] {$s$};
\node[scale=.8, below left] at (0, 0) {$0$};
\draw[dashed] (1,1)--(0,1) node[scale=.8,left] {$1$};
\draw[dashed] (1,1)--(1,0) node[scale=.8,below] {$1$};
\draw[dotted] (1,0.13)--(0,0.13) node[scale=.9,above left] {$s^*$};
\draw[dotted] (1,0.05)--(0,0.05) node[scale=.9,left] {$s_*$};
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\node[scale=.8, above,red] at (0.3770, 0.5) {$ m =\ell(s)$};
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\draw[thick,->,teal] (0.89,0.0049)--(0.89,0.1);
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\draw[thick,->,teal] (.8544,0.8804)--(.7806,.9854);
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\draw[thick,->,teal] (0.8710,0.5924)--(0.8488,0.6955);
\draw[thick,->,teal] (0.4372,0.7597)--(0.3561,0.7772);
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\end{tikzpicture}
\end{document}