Multiple graphs in TikZ with intersections and naming

Question

I'd appreciate some help creating the above diagram. I have had some success but still struggling with the naming of the graphs (not in an agenda), the intersections as well as the marking of the intersection values on the x and y axis.

    \documentclass{article}
    \usepackage{pgfplots}
    \pgfplotsset{ticks=none}
    \usetikzlibrary{intersections, calc}

    \begin{document}

    \begin{tikzpicture}
    \begin{axis}[
      %grid = major,   
      axis x line=center,
      axis y line=center,
      xlabel={$k_t$},
      ylabel={$f(k_t)$},
      xlabel style={below right},
      ylabel style={above left},
      xmin=-1,
      xmax=12,
      ymin=-1,
      ymax=5]

    \addplot+[color=green,mark=none,samples=200,domain=0:10,smooth,thick] {sqrt(1*x)} node[below,pos=1,color=black] {$f(k_t)$};

    \addplot+[color=black,mark=none,samples=200,domain=0:10,smooth,thick] {2/3*sqrt(1*x)} node[below,pos=1,color=black] {$s f(k_t)$};

    \addplot+[color=red,mark=none,samples=200,domain=0:10,smooth,thick] {2/5*x} node[above,pos=1,color=black] {$\delta k_t$};

    \end{axis}
    \end{tikzpicture}

\end{document}

Okay, I have reworked it and already coming much closer:

Still hoping for input on the intersections and markings on the axis.

Answer 1

A PSTricks solution:

\documentclass{article}

\usepackage{pst-plot}

% constants
\def\xA{2/3}
\def\xB{1}
\def\xC{2/5}
\def\xEnd{9.8}

% intersection point, $k^{\ast}$
\def\point{(\xA)^2/(\xC)^2}

% functions
\def\fA(#1){(\xA)*sqrt(#1)}
\def\fB(#1){(\xB)*sqrt(#1)}
\def\fC(#1){(\xC)*(#1)}

\psset{
  algebraic,
  plotstyle = curve,
  plotpoints = 500
}

\begin{document}

\begin{pspicture}%
  (-0.5,-0.5)%
  (\fpeval{\xEnd+1.15},\fpeval{max(\fA(\xEnd),\fB(\xEnd),\fC(\xEnd))+0.55})
  \pnodes(\fpeval{\point},0){A}%
         (\fpeval{\point},\fpeval{\fB(\point)}){B}%
         (0,\fpeval{\fB(\point)}){C}
  \psaxes[labels = none]{->}%
    (0,0)(-0.5,-0.5)(\fpeval{\xEnd+0.7},\fpeval{\fC(\xEnd)+0.55})
    [$k_{t}$,135][$f(k_{t})$,315]
  \psplot[linecolor = black]{0}{\xEnd}{\fA(x)}
  \uput[0](\xEnd,\fpeval{\fA(\xEnd)}){$sf(k_{t})$}
  \psplot[linecolor = green!70!black]{0}{\xEnd}{\fB(x)}
  \uput[0](\xEnd,\fpeval{\fB(\xEnd)}){$f(k_{t})$}
  \psplot[linecolor = red!70!black]{0}{\xEnd}{\fC(x)}
  \uput[0](\xEnd,\fpeval{\fC(\xEnd)}){$\delta k_{t}$}
  \psline[linestyle = dashed](A)(B)(C)
  \psdots[dotsize = 3pt 2, dotstyle = o, fillcolor = blue!60](A)(B)(C)
  \psdot(\fpeval{\point},\fpeval{\fC(\point)})
  \uput[270](A){$k^{\ast}$}
  \uput[180](C){$y^{\ast}$}
\end{pspicture}

\end{document}

All you have to do is change the values of the constants and the drawing will be adjusted automatically.

Answer 2

You already loaded the intersections library, but then just didn't make use of it. Here one possible way to achieve the desired result. For details please have a look at the comments in the code.

% used PGFPlots v1.14
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
    \usetikzlibrary{intersections}
    % use this `compat' level or higher so that TikZ coordinates don't have to be prefixed
    % with `axis cs:'
    \pgfplotsset{compat=1.11}
\begin{document}
\begin{tikzpicture}[
    % define a style for the dots
    dot/.style={
        draw=black,
        fill=blue!90,
        circle,
        minimum size=3pt,
        inner sep=0pt,
        solid,
    },
]
    \begin{axis}[
        xmin=-1,
        xmax=12,
        ymin=-0.5,
        ymax=5,
        axis lines=center,
        ticks=none,
        xlabel={$k_t$},
        ylabel={$f(k_t)$},
        xlabel style={below right},
        ylabel style={above left},
        % (moved common `addplot' options here)
        smooth,
        domain=0:10,
        samples=101,
        no markers,
    ]
        % to use the `intersections' library you have to give a `name path' to path that
        % should be used for intersection calculations
        \addplot+ [green,thick,name path=sqrt] {sqrt(x)}
            node [below,pos=1,color=black] {$f(k_t)$}
        ;
        \addplot+ [black,thick,name path=mod sqrt] {2/3*sqrt(x)}
            node [below,pos=1,color=black] {$s f(k_t)$}
        ;
        \addplot+ [red,thick,name path=line,samples=2]   {2/5*x}
            node [above,pos=1,black] {$\delta k_t$}
        ;

        % find the intersection of the modified sqrt function and the straight line,
        % draw a circle on it and store the coordinate
        % (here we have to use the second found intersection point, the first one is at (0,0))
        \fill [name intersections={of=mod sqrt and line}] (intersection-2) circle (1.5pt)
            coordinate (a)
        ;
        % draw an invisible vertical path at the x coordinate of the found intersection point
        \path [name path=vertical line]
            (a |- 0,\pgfkeysvalueof{/pgfplots/ymin}) -- (a |- 0,\pgfkeysvalueof{/pgfplots/ymax});
        % now find the other intersection point with the sqrt function and again store the
        % the found coordinate
        \path [name intersections={of=sqrt and vertical line}] (intersection-1) circle
            coordinate (b)
        ;
        % draw the dots (using the above defined style) and labels
        \draw [dashed]
            (b -| 0,0)      node [dot,label=left:$y^*$]  {}
            -- (b)          node [dot]                   {}
            -- (b |- 0,0)   node [dot,label=below:$k^*$] {}
        ; 
    \end{axis}
\end{tikzpicture}
\end{document}

Answer 3

Pure TikZ solution:

\documentclass[tikz, border=5pt]{standalone}
\usetikzlibrary{arrows.meta, intersections}

\begin{document}
    \begin{tikzpicture}[yscale=2,
         > = Stealth,
dot/.style = {circle, draw=black, solid, 
              fill=#1, % default blue!50
              minimum size=3pt, inner sep=0pt,
              node contents={}},
dot/.default = blue!50,
domain=0:5, samples=100,
                        ]
% axis
\draw[->] (-0.6,0) -- (6,0.0) node [below left] {$k_t$};
\draw[->] (0,-0.2) -- (0,2.5) node [below left] {$f(k_t)$};
\coordinate (O) at (0,0);
% curves
\draw[green,thick,name path=sqrt green] plot (\x, {sqrt(\x)})
            node [right,text=black] {$f(k_t)$};
\draw[black,thick,name path=sqrt black] plot (\x, {2*sqrt(\x)/3})
            node [right,text=black] {$s f(k_t)$};
\draw[red,thick,name path=line red] plot (\x, 2*\x/5)
            node [right,text=black] {$\delta k_t$};
% intersection sqrt black and line red
\path[name intersections={of=line red and sqrt black, by={not used,a}}]
    (a) node[dot=black];
% draw an invisible vertical path through coordinate a
\path[name path=vertical line]
            (a |- O) -- + (0,2);
% intersection sqrt green and vertical line
\path [name intersections={of=sqrt green and vertical line, by={bb}}]
    (bb) node (b) [dot=blue!50];
% draw the dashed lines snd dots on axis
\draw[dashed] (b) -- (b -| O) node [dot,label=left:$y^*$]
              (b) -- (b |- O) node [dot,label=below:$k^*$];
    \end{tikzpicture}
\end{document}