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equilibria.tex
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equilibria.tex
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\documentclass{scrartcl}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc,intersections,through,backgrounds,patterns}
\usetikzlibrary{decorations.text, decorations.markings, fit, arrows, arrows.meta}
\def\centerarc[#1](#2)(#3:#4:#5)% Syntax: [draw options] (center) (initial angle:final angle:radius)
{ \draw[#1] ($(#2)+({#5*cos(#3)},{#5*sin(#3)})$) arc (#3:#4:#5); }
%Chiang & Wainwright - Fundamental Methods of Mathematical Economics (4th Ed.), p. 619, fig 19.3
\begin{document}
%\begin{figure}
% \centering
\begin{tikzpicture}
%axis
\draw[thick] (-2.5,-2.514)--(-2.5,2.5); %vertical line
\draw[thick] (-2.5,-2.5)--(2.5,-2.5); %horizontal line
\node at (-2.65,-2.65) {{\scriptsize $O$}};
\node at (2.45,-2.7) {{\scriptsize $x$}};
\node at (-2.7,2.45) {{\scriptsize $y$}};
%inner lines
\fill (0,0) circle (2pt);
\draw[very thick] (0,-2)--(0,2.15); %vertical line
\draw[very thick] (-2,0)--(2.15,0); %horizontal line
%inner captions
\node at (0,2.4) {{\scriptsize $x'\!= 0$}}; %NB: reversed in rest
\node at (2.7,0) {{\scriptsize $y'\!= 0$}};
%\node at (-0.2,0.2) {{\scriptsize $E$}}; %overlaps small arrow - fix somehow
\node at (-0.25,2) {{\scriptsize $-$}}; %upper-left
\node at (0.25,2) {{\scriptsize $+$}}; %upper-right
%
\node at (2,0.25) {{\scriptsize $+$}}; %right-upper
\node at (2,-0.25) {{\scriptsize $-$}}; %right-lower
%corner arrows
\draw[->,>=latex,thick] (-1.5,1.836)--(-1.5,2.35); %NW: up
\draw[->,>=latex,thick] (-1.5,1.85)--(-2,1.85); %NW: left
%
\draw[->,>=latex,thick] (1.5,1.836)--(1.5,2.35); %NE: up
\draw[->,>=latex,thick] (1.5,1.85)--(2,1.85); %NE: left
%
\draw[->,>=latex,thick] (-1.5,-1.7357)--(-1.5,-2.25);%SW: up
\draw[->,>=latex,thick] (-1.5,-1.75)--(-2,-1.75); %SW: left
%
\draw[->,>=latex,thick] (1.5,-1.7357)--(1.5,-2.25); %SE: up
\draw[->,>=latex,thick] (1.5,-1.75)--(2,-1.75); %SE: right
%inner arrows
\draw[->,>=latex,thick] (-0.15,0.15) to[bend left=10] (-1.2,1.2); %NW - small
\draw[->,>=latex,thick] (-0.25,0.1) to[bend left=15] (-1.7,1.45); %NW - big
%
\draw[->,>=latex,thick] (0.15,0.15) to[bend right=10] (1.2,1.2); %NE - small
\draw[->,>=latex,thick] (0.25,0.1) to[bend right=15] (1.7,1.45); %NE - big
%
\draw[->,>=latex,thick] (-0.15,-0.15) to[bend right=10] (-1.2,-1.2); %SE - small
\draw[->,>=latex,thick] (-0.25,-0.1) to[bend right=15] (-1.7,-1.45); %SE - big
%
\draw[->,>=latex,thick] (0.15,-0.15) to[bend left=10] (1.2,-1.2); %NE - small
\draw[->,>=latex,thick] (0.25,-0.1) to[bend left=15] (1.7,-1.45); %NE - big
%for smaller arrows, can also use:
%\draw[->,>=latex,thick] (-0.15,0.15) to[bend left=10] (-0.75,1); %NW - small
%\draw[->,>=latex,thick] (-0.25,0.1) to[bend left=10] (-1.35,1.35); %NW - big
%arrows on axis
\draw[->,>=latex,very thick] (0,1.65)--(0,1.7); %N
\draw[->,>=latex,very thick] (0,-1.65)--(0,-1.7); %S
\draw[->,>=latex,very thick] (-1.65,0)--(-1.7,0); %E
\draw[->,>=latex,very thick] (1.65,0)--(1.7,0); %W
\end{tikzpicture}
% \caption{(a)}
%\end{figure}
%
%
\hspace{0.75cm}
%
%
%\begin{figure}
% \centering
\begin{tikzpicture}
%axis
\draw[thick] (-2.5,-2.514)--(-2.5,2.5); %vertical axis
\draw[thick] (-2.5,-2.5)--(2.5,-2.5); %horizontal axis
\node at (-2.65,-2.65) {{\scriptsize $O$}};
\node at (2.45,-2.7) {{\scriptsize $x$}};
\node at (-2.7,2.45) {{\scriptsize $y$}};
%inner lines
\draw[very thick] (-2,-1) to[bend left=10] (2,0.5); %x-axis
\draw[very thick] (-1.1,-1.75) to[bend right=10] (0.5,2); %y-axis
\fill (-0.17,-0.09) circle (2pt);
%inner captions
\node at (0.5,2.15) {{\scriptsize $y'\!= 0$}};
\node at (2.45,0.55) {{\scriptsize $x'\!= 0$}};
\node at (-0.2,0.2) {{\scriptsize $E$}};
\node at (0.25,1.8) {{\scriptsize $-$}}; %upper-left
\node at (0.65,1.8) {{\scriptsize $+$}}; %upper-right
%
\node at (1.85,0.65) {{\scriptsize $+$}}; %right-upper
\node at (1.85,0.30) {{\scriptsize $-$}}; %right-lower
%inner arrows
\draw[->,>=latex,thick] (-0.27,-0.19)--(-1.5,-1.4); %SW
\draw[->,>=latex,thick] (-0.07,0.01)--(1.45,1.5); %NE
%\draw[thick,red] (-1.5,-1.4)--(1.45,1.5); %test
\draw[->,>=latex,thick] (-1.25,1.25) to[bend right=5] (-0.27,0.01); %NW
\draw[->,>=latex,thick] (1.25,-1.25) to[bend left=5] (-0.07,-0.19); %SE
%
\draw[->,>=latex,thick] (-0.5,1.25) .. controls (-0.25,0.85) and (0.25,0.7) .. (0.75,1.2); %N
\draw[->,>=latex,thick] (1.1,-0.5) .. controls (0.7,-0.25) and (0.55,0.25) .. (1.05,0.75); %E
\draw[->,>=latex,thick] (-1.63,0.5) .. controls (-0.98,-0.25) and (-1.18,-0.75) .. (-1.38,-1.05); %W
\draw[->,>=latex,thick] (0.52,-1.58) .. controls (-0.33,-0.93) and (-0.83,-1.13) .. (-1.13,-1.33); %S
%dashed lines
\draw[thick,dashed] (-0.35,0.85)--(0.685,0.85); %N
\draw[thick,dashed] (-1.15,-0.85)--(-1.15,0.1); %W
\draw[thick,dashed] (-1.05,-1.1)--(0,-1.1); %S
\draw[thick,dashed] (0.7,-0.35)--(0.7,0.685); %E
%corner arrows
\draw[->,>=latex,thick] (-1.75,2.014)--(-1.75,1.5); %NW: down
\draw[->,>=latex,thick] (-1.75,2)--(-1.25,2); %NW: right
%
\draw[->,>=latex,thick] (1.75,1.836)--(1.75,2.35); %NE: up
\draw[->,>=latex,thick] (1.75,1.85)--(2.25,1.85); %NE: left
%
\draw[->,>=latex,thick] (-1.75,-1.7357)--(-1.75,-2.25); %SW: up
\draw[->,>=latex,thick] (-1.75,-1.75)--(-2.25,-1.75); %SW: left
%
\draw[->,>=latex,thick] (1.75,-2.014)--(1.75,-1.5); %SE: up
\draw[->,>=latex,thick] (1.75,-2)--(1.25,-2); %SE: left
%\draw[help lines] (-2.5,-2.5) grid (2.5,2.5);
\end{tikzpicture}
% \caption{(b)}
%\end{figure}
\vspace{1.25cm}
%\begin{figure}
% \centering
\begin{tikzpicture}
%axis
\draw[thick] (-2.5,-2.514)--(-2.5,2.25); %vertical line
\draw[thick] (-2.5,-2.5)--(2.5,-2.5); %horizontal line
\node at (-2.65,-2.65) {{\scriptsize $O$}};
\node at (2.45,-2.7) {{\scriptsize $x$}};
\node at (-2.7,2.45) {{\scriptsize $y$}};
%inner lines
\draw[very thick] (-2,1) to[bend left=15] (1,-1.5); %x-axis
\draw[very thick] (-1.75,-1.75) to[bend right=10] (0.5,2); %y-axis
\fill (-0.415,0.05) circle (2pt);
%inner captions
\node at (0.5,2.15) {{\scriptsize $y'\!= 0$}};
\node at (1,-1.65) {{\scriptsize $x'\!= 0$}};
\node at (-0.38,-0.22) {{\scriptsize $E$}};
\node at (0.25,1.85) {{\scriptsize $-$}}; %upper-left
\node at (0.65,1.85) {{\scriptsize $+$}}; %upper-right
%
\node at (0.65,-1.3) {{\scriptsize $+$}}; %right-upper
\node at (1.10,-1.3) {{\scriptsize $-$}}; %right-lower
%inner arrows - from outermost to innermost
%\draw[->,>=latex,thick] (-0.5,1.25) .. controls (-0.25,0.85) and (0.25,0.7) .. (0.75,1.2);
\draw[->,>=latex,thick] (-1.9,-0.2) to[bend right=10] (-1.52,-0.75);
\draw[->,>=latex,thick] (-1.55,-0.72) .. controls (-1.25,-1) and (-1.15,-1.08) .. (-0.35,-0.8);
\draw[->,>=latex,thick] (-0.4,-0.82) .. controls (0.3,-0.52) and (0.12,-0.12) .. (-0.15,0.15);
\draw[thick] (-0.12,0.12) .. controls (-0.25,0.28) and (-0.55,0.28) .. (-0.6,0);
%dashed lines
\draw[thick,dashed] (-0.6,0.25)--(0.15,0.25); %N
\draw[thick,dashed] (-1.6,-1)--(-0.6,-1); %S
\draw[thick,dashed] (0.125,0.05)--(0.125,-0.7); %E
%corner arrows
\draw[->,>=latex,thick] (-0.415,1.964)--(-0.415,1.45); %N: down
\draw[->,>=latex,thick] (-0.415,1.95)--(-0.915,1.95); %N: left
%
\draw[->,>=latex,thick] (-0.915,-1.9643)--(-0.915,-1.45); %S: up
\draw[->,>=latex,thick] (-0.915,-1.95)--(-0.415,-1.95); %S: right
%
\draw[->,>=latex,thick] (-2.25,0.264)--(-2.25,-0.25); %W: down
\draw[->,>=latex,thick] (-2.25,0.25)--(-1.75,0.25); %W: right
%
\draw[->,>=latex,thick] (2.25,-0.264)--(2.25,0.25); %E: up
\draw[->,>=latex,thick] (2.25,-0.25)--(1.75,-0.25); %E: left
%\draw[help lines] (-2.5,-2.5) grid (2.5,2.5);
\end{tikzpicture}
% \caption{(c)}
%\end{figure}
%
%
\hspace{1.3cm}
%
%
%\begin{figure}
% \centering
\begin{tikzpicture}
%axis
\draw[thick] (-2.5,-2.514)--(-2.5,2.5); %vertical line
\draw[thick] (-2.5,-2.5)--(2.5,-2.5); %horizontal line
\node at (-2.65,-2.65) {{\scriptsize $O$}};
\node at (2.45,-2.7) {{\scriptsize $x$}};
\node at (-2.7,2.45) {{\scriptsize $y$}};
%inner lines
\fill (0,0) circle (2pt);
\draw[very thick] (0,-2)--(0,2.15); %vertical line
\draw[very thick] (-2,0)--(2.15,0); %horizontal line
%inner captions
\node at (0,2.4) {{\scriptsize $y'\!= 0$}};
\node at (2.7,0) {{\scriptsize $x'\!= 0$}};
\node at (-0.2,0.2) {{\scriptsize $E$}}; %overlaps small arrow - fix somehow
\node at (-0.25,2) {{\scriptsize $-$}}; %upper-left
\node at (0.25,2) {{\scriptsize $+$}}; %upper-right
%
\node at (2,0.25) {{\scriptsize $+$}}; %right-upper
\node at (2,-0.25) {{\scriptsize $-$}}; %right-lower
%circle
\draw[thick] (0,0) circle (1.25cm);
\draw[thick,dashed] (-0.685,1.27)--(0.685,1.27); %N
\draw[thick,dashed] (-1.27,-0.685)--(-1.27,0.685); %W
\draw[thick,dashed] (-0.685,-1.27)--(0.685,-1.27); %S
\draw[thick,dashed] (1.27,-0.685)--(1.27,0.685); %E
%arrows on circle
\centerarc[->,>=latex,thick](0,0)(40:37:1.25) %NE
\centerarc[->,>=latex,thick](0,0)(135:132:1.25) %NW
\centerarc[->,>=latex,thick](0,0)(220:217:1.25) %SW
\centerarc[->,>=latex,thick](0,0)(315:312:1.25) %SE
%corner arrows
\draw[->,>=latex,thick] (-2,1.436)--(-2,1.95); %NW: up
\draw[->,>=latex,thick] (-2,1.45)--(-1.5,1.45); %NW: right
%
\draw[->,>=latex,thick] (1.5,1.964)--(1.5,1.45); %NE: down
\draw[->,>=latex,thick] (1.5,1.95)--(2,1.95); %NE: right
%
\draw[->,>=latex,thick] (-1.5,-1.964)--(-1.5,-1.45);%SE: up
\draw[->,>=latex,thick] (-1.5,-1.95)--(-2,-1.95); %SE: left
%
\draw[->,>=latex,thick] (2,-1.436)--(2,-1.95); %SW: down
\draw[->,>=latex,thick] (2,-1.45)--(1.5,-1.45); %SW: left
\end{tikzpicture}
% \caption{(d)}
%\end{figure}
\end{document}