TikZ/Pgf - I can't get "node" to work

Question

I'm having trouble with some work and I would appreciate any help. I would like to add this kind of text into my project:

And here's my code, I don't know why node[left]{$P^*=50$} and node[below]{$Q^*=500$} don't display
begin{tikzpicture} 
begin{axis} [axis lines = left, xlabel = $Q$, ylabel = {$P$}]

addplot [domain=0:960, samples=100, color=green] {0.1*x} node [left] {$CMg$};
addlegendentry{$0,1cdot Q$};

addplot [domain=0:1000, samples=100, color=red] {100-1/10*x} node [above right] {$IMg$};
addlegendentry{$100-0,1cdot Q$}

draw [dashed] (0,50) node[left]{$P^*=50$} -- (500,50) -- (500,0) node[below]{$Q^*=500$};

end{axis}
end{tikzpicture}

Thanks in advance!

Zarko · Answer

Let mi spell out my comment ... and add some small modification of your diagram code. You may liked it:
documentclass[margin=3mm]{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.17}

begin{document}
    begin{tikzpicture}
begin{axis}[
    axis lines = center, 
    xmax=1150, ymax=110,
    xlabel = $Q$, 
    ylabel = $P$,
    label style=right,
    legend style={at={(0.5,1)},legend columns=-1,
                  font=scriptsize, anchor=north},
    legend cell align=left,
    samples=2, no marks,
    clip=false  % <---
            ]

addplot +[domain=0:960] {0.1*x} node [right] {$CMg$};
addplot +[domain=0:1000] {100-1/10*x} node [above right] {$IMg$};
legend{${100-0,1{cdot}Q}$,  ${0,1{cdot}Q}$};

draw[dashed]   (-2pt,   50) node[left, font=footnotesize]{$P^*{=}50$} -| 
                (500,-2.5ex) node[below,font=footnotesize]{$Q^*=500$};
end{axis}
    end{tikzpicture}
end{document}

TikZ/Pgf - I can't get "node" to work

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