# Tikz: wrong intersection with axis

In the following code the dashed line that intersects with the y-axis is out of place and I don't know where I'm making the mistake (if there is any):

\documentclass{article}
\usepackage{pgfplots}
\usetikzlibrary{intersections,calc}

\begin{document}

\begin{tikzpicture}
\draw [<->] (0,5) node (ejey) [left]{$\omega$} |- (5.5,0)  node (ejex)
[right]{$l$};
\draw [name path = ls] (0.5,0.5) coordinate (a) -- (4.5,4.5) node
(b) [right] {$l^{s}(\omega, r)$};
\draw [name path = ld] (0.5,4.5) coordinate (c) -- (4.5,0.5) node
(d) [right] {$l^{d}(\omega)$};
\path [name intersections={of=ls and ld, by=i}];
\draw [dashed] (ejey |- i) node [left] {$\omega_{0}^{*}$} -| (i |- ejex)
node [below] {$l_{0}^{*}$};
\end{tikzpicture}

\end{document}

-

The problem appears because your dashed line starts at the x-coordinate of the centre of the ejey node, that is at the centre of the omega. To make the line start flush with the axis, you can use

(ejey.east |- i)

(ejey |- i)

\documentclass{article}
\usepackage{pgfplots}
\usetikzlibrary{intersections,calc}

\begin{document}

\begin{tikzpicture}
\draw [<->] (0,5) node (ejey) [left]{$\omega$} |- (5.5,0)  node (ejex) [right]{$l$};
\draw [name path = ls] (0.5,0.5) coordinate (a) -- (4.5,4.5) node (b) [right] {$l^{s}(\omega, r)$};
\draw [name path = ld] (0.5,4.5) coordinate (c) -- (4.5,0.5) node (d) [right] {$l^{d}(\omega)$};
\path [name intersections={of=ls and ld, by=i}];
\draw [dashed] (ejey.east |- i) node [left] {$\omega_{0}^{*}$} -| (i |- ejex) node [below] {$l_{0}^{*}$};
\end{tikzpicture}

\end{document}
-
\documentclass{standalone}
\usepackage{pgfplots}
\usetikzlibrary{intersections,calc}

\begin{document}

\begin{tikzpicture}
\draw [<->] (0,5) coordinate (ejey) |- (5.5,0) coordinate (ejex);
\node [left] at (ejey) {$\omega$};
\node [right] at (ejex)  {$l$};
\draw [name path = ls] (0.5,0.5) coordinate (a) -- (4.5,4.5) node    (b) [right] {$l^{s}(\omega, r)$};
\draw [name path = ld] (0.5,4.5) coordinate (c) -- (4.5,0.5) node    (d) [right] {$l^{d}(\omega)$};
\path [name intersections={of=ls and ld, by=i}];
\draw [dashed] (ejey |- i) node [left] {$\omega_{0}^{*}$} -| (i |- ejex)    node [below] {$l_{0}^{*}$};
\end{tikzpicture}

\end{document}

-