\documentclass{standalone}
\usepackage{tikz}


\begin{document}
\begin{tikzpicture}\draw[thin,->] (0,0)--(3.2,0);
\draw[thin,->] (0,0)--(0,3);
\draw[blue,thick] plot[smooth,domain=0:3]  function {1+x/3};
\draw[red,thick] plot[smooth,domain=0:3]  function {(x+x**2/3)/2};
\draw[red,purple] plot[smooth,domain=0:3]  function {(1+2*x/3)};



\node[blue] at (1,1.6) {$c(\rho)$};
\node[red] at (2.1,2.5) {$c(\rho)\rho$};


\end{tikzpicture}
\end{document}