\documentclass{scrartcl}
\usepackage{color}
\usepackage{multicol}
\usepackage[final]{graphicx}
\usepackage{pst-plot,pstricks}
	\input{pstplot-logarithmic-axes}
\begin{document}
	\psset{xunit=2cm,yunit=2cm}
	\begin{pspicture}(-0.5,-1.5)(2.5,1.5)
		\psgrid[xunit=1,yunit=1,subgriddiv=2,griddots=5,gridlabels=0](0,-1)(2,1)
		\psaxes[Dx=1,Dy=0.5]{->}(0,0)(-0.5,-1.2)(2.5,1.2)
		\psplot[linestyle=dashed]{0}{1}{1 x -1 mul add}
		\psplot{0}{2}{1 2.71828 x exp div}
		\psplot{0}{2}{1 2.71828 x 0.5 mul exp div -0.5 mul}
		\psplot[linecolor=red]{-0.2}{0}{0}
		\psline[linecolor=red](0,0)(0,0.5)
		\psplot[linecolor=red]{0}{2}{1 2.71828 x exp div 1 2.71828 x 0.5 mul exp div -0.5 mul add}
	\end{pspicture}
\end{document}
