TikzExamples.tex

\documentclass[
hyperref={colorlinks,citecolor=blue,linkcolor=blue,urlcolor=blue}
]{beamer}
\usetheme{metropolis}           % Use metropolis theme
\useoutertheme{metropolis}
\useinnertheme{metropolis}

\usepackage{tikz}
\usetikzlibrary{patterns, backgrounds}
\usepackage{pgfplots}
\usepgfplotslibrary{groupplots, fillbetween}

\usepackage{xcolor}
% Using the Set1 palette from colorbrewer (http://colorbrewer2.org/#type=qualitative&scheme=Set1&n=3)
\definecolor{myred}{HTML}{e41a1c}
\definecolor{myblue}{HTML}{377eb8}
\definecolor{mygreen}{HTML}{4daf4a}
\definecolor{mygray}{gray}{0.6}

\title{Some TikZ and PGFplot examples}
\subtitle{(Tailored toward environmental economics topics)}
\author{Grant R. McDermott}
\date{\href{mailto:grantmcd@uoregon.edu}{grantmcd@uoregon.edu}}
\institute{University of Oregon}
\begin{document}
	\maketitle

%----------- new slide ---------------------------------------%

\begin{frame}{Quick links}
\tableofcontents
\end{frame}

%----------- new section -------------------------------------%

\section{Equimarginal principle}

%----------- new slide ---------------------------------------%

\begin{frame}{Equimarginal principle}

	\begin{figure}[!h]
		\centering
		\begin{tikzpicture}
		\begin{groupplot}[
		axis lines=middle,
		xlabel=Abatement,
		ylabel near ticks, 
%		every axis x label/.style={
%			at={(ticklabel* cs:1.01)},
%			anchor=west,
%		},
		xlabel style={at={(ticklabel* cs:1.05)}, anchor=north},
		every axis y label/.style={
			at={(ticklabel* cs:1)},
			anchor=south,
		},
		group style={
			group name = equimarginal,
			group size = 1 by 2,
			xlabels at = edge bottom,
			xticklabels at = edge bottom,
			vertical sep = 0.75cm
		},
		%			footnotesize,
		width = 0.9\textwidth, %% As big as this example can be without spilling over onto the next slide
		height = 0.5\textheight, %% ditto
		%			ticks = none,
		ytick=\empty,
		xtick={2}, xticklabels={{\color{myred}$A^*$}},
		xmin = 0, 
		xmax = 5, 
		]
		\nextgroupplot[ymax=22, ylabel=\$, xlabel=Abatement]
		\addplot[name path=TB, domain={0:4.5}, thick] {8*x-x^2} node[right]{$TB$};
		\addplot[name path=TC, domain={0:4.5}, thick] {x^2} node[right]{$TC$};
		%% Show maximum difference
		\draw[decoration={brace,mirror,raise=3pt},decorate,myred]
		(200, 47) -- node[right=4pt] {\footnotesize\color{myred}max} (200,116);
		%% Top part of vertical line
		\coordinate (top) at (axis cs:2,\pgfkeysvalueof{/pgfplots/ymax});
		\nextgroupplot[ymax=12, ylabel=\$/unit]
		\addplot[name path=MB, domain={0:4}, thick] {8-2*x} node[above right]{$MB$};
		\addplot[name path=MC, domain={0:4}, thick] {2*x} node[right]{$MC$};
		%% Bottom part of vertical line
		\coordinate (bottom) at (axis cs:2,\pgfkeysvalueof{/pgfplots/ymin});
		\end{groupplot}
		\draw [densely dashed, myred] (top) -- (bottom);
		\end{tikzpicture}
	\end{figure}

\end{frame}

%----------- new section -------------------------------------%

\section{Public goods}

%----------- new slide ---------------------------------------%

\begin{frame}{Public goods taxonomy}
	\begin{figure}
		\centering
		\begin{tikzpicture}%[scale=.8]
		\draw [<->,thick] (0,-0) rectangle (10,6);
		\draw [->, very thick] (0.25,-0.5) -- (9.75,-0.5) node [pos=0.5, below] {Nonrivalry}; 
		\draw [->, very thick] (-0.5,0.25) -- (-0.5,5.75) node [rotate=90, pos=0.5, above] {Nonexcludability};
		\node[right] at (0.5,1.75) {\scriptsize \textbf{PURE PRIVATE GOODS}};
		\node[right] at (0.5,4.25) {\scriptsize \textbf{OPEN-ACCESS RESOURCES}};
		\node[left] at (9.5,1.75) {\scriptsize \textbf{CLUB GOODS}};
		\node[left] at (9.5,4.25) {\scriptsize \textbf{PURE PUBLIC GOODS}};
		\end{tikzpicture}
	\end{figure}
\end{frame}

%----------- new slide ---------------------------------------% 

\begin{frame}{Public goods example}

	For this example, $X$ and $Y$ are neighbours that both benefit if either of them spend some hours gardening ($H$).
	\begin{itemize}
		\item {\color{myblue}$MB_X = 5 + \frac{1}{2}H$}
		\item {\color{mygreen}$MB_Y = 5 + H$}
	\end{itemize}

	Note that the implied social marginal benefit curve (i.e. $SMB = MB_X + MB_Y$) has a kink.
	% 
	{\color{myred}\begin{align*}
		SMB =	&= 10 + \frac{3}{2}  &\text{if } H < 5 \\
				& = 5 + \frac{1}{2}  &\text{if } H \geq 5 
	\end{align*}}
	% 
	We'll also assume that $MC = 4$.
	
\end{frame}
%----------- new slide ---------------------------------------%

\begin{frame}{Public goods example (cont.)}

	\begin{figure}
		\centering
		\begin{tikzpicture}%[yscale=1.25, xscale=1.25]
			\begin{axis}[
				axis lines=middle,
				xlabel=\textbf{Hours},
				ylabel=\textbf{Utility},
				ylabel near ticks, 
				every axis x label/.style={
					at={(ticklabel* cs:1.05)},
					anchor=west,
				},
				every axis y label/.style={
					at={(ticklabel* cs:1.05)},
					anchor=south,
				},
				xtick={2, 4, 5, 10}, 
				ytick={10, 5, 4, 2.5},
				% xmin = 0, 
				xmax = 12, 
				% ymin = 0, 
				ymax = 12,
				% width = 8cm,
				% height = 8cm,
				]
		
				%%% Define MC curve
				\addplot[name path=MC, domain={0:10}, thick, dashed] {4} node[right]{$MC$};
				%% SMB curve (1)
				\addplot[name path=SMB1, domain={0:5}, very thick, myred] {5-0.5*x + 5-x};
				%% SMB curve (2)
				\addplot[name path=SMB2, domain={5:10}, very thick, myred] {5-0.5*x} node[above right]{$SMB$};
				%% MB_X curve
				\addplot[name path=MB_X, domain={0:10}, thick, densely dashed, myblue] {5-0.5*x} node[pos=0.1, above]{$MB_X$};
				%% MB_Y curve
				\addplot[name path=MB_Y, domain={0:5}, thick, densely dashed, mygreen] {5-x} node[pos=0.35, left]{$MB_Y$};
				
				%% Equilibria
				\coordinate (yend) at (0,100);
				\coordinate (xend) at (100,0);
				\path [name intersections={of=MB_X and MC, by={eqm_X}}];
				\draw[thin, densely dashed, myblue]  (eqm_X) -- (eqm_X |- xend); 
				\path [name intersections={of=MB_Y and MC, by={eqm_Y}}];
			%	\draw[thin, densely dashed, mygreen]  (eqm_Y) -- (eqm_Y |- xend); 
				\path [name intersections={of=SMB1 and MC, by={eqm_s}}]; 
				\draw[thin, densely dashed, myred]  (eqm_s) -- (eqm_s |- xend);
				\path [name intersections={of=SMB1 and MB_X, by={eqm_kink}}]; 
				\draw[thin, densely dashed, lightgray]  (yend |- eqm_kink) -- (eqm_kink) -- (eqm_kink |- xend);
			
			\end{axis}
		\end{tikzpicture}
	\end{figure}

\end{frame}


%----------- new section -------------------------------------%

\section{Externality with deadweight loss}

%----------- new slide ---------------------------------------% 

\begin{frame}{Externality with deadweight loss}

	For this example:
	\begin{itemize}
		\item Marginal benefits: $MB(e) = 40-e^2$
		\item Private marginal cost: $PMC(e) = 15$
		\item Marginal damages: $MD(e) = e^2+7$
	\end{itemize}

	We'll compare the unregulated and social outcomes, and highlight the resulting deadweight loss.
	
\end{frame}

%----------- new slide ---------------------------------------%

\begin{frame}{Externality with deadweight loss (cont.)}

\begin{figure}
	\centering
	\begin{tikzpicture}[%yscale=1.05, 
	xscale=1]
	\begin{axis}[
	width = .9\textwidth,
	height = .9\textheight,
	axis lines=middle,
	xlabel=Emissions ($e$),
	ylabel=Price,
	ylabel near ticks,  
	xlabel style={at={(ticklabel* cs:1)}, anchor=north},
	ylabel style={at={(ticklabel* cs:1)}, anchor=south},
%	every axis y label/.style={
%		at={(ticklabel* cs:1.05)},
%		anchor=south,
%	}, 
	xtick={3, 5}, xticklabels={$e^*$,$e_u$},
	ytick={15, 31}, yticklabels={$p_u$,$p^*$},
	xmin = 0, 
	xmax = 8, 
	ymin = 0, 
	ymax = 75
	]
	
	%% MB curve
	\addplot[name path=MB, domain={0:7}, thick] {40-x^2} node[pos=0, above right]{$MB$};
	%%% PMC curve
	\addplot[name path=PMC, domain={0:7}, thick] {15} node[right]{$PMC$};
	%%% Define MD curve
	\addplot[name path=MD, domain={0:6.5}, thick, dashed] {\x^2+7} node[right]{$MD$};
	%% SMC curve
	\addplot[name path=SMC, domain={0:6.5}, thick] {x^2+22} node[above right]{$SMC$};
	
	%% Equilibria
	\coordinate (yend) at (0,75);
	\coordinate (xend) at (8,0);
	\path [name intersections={of=MB and PMC, by={eqm_u}}]; 
	\path [name intersections={of=MB and SMC, by={eqm_s}}]; 
	\draw[densely dashed]  (yend |- eqm_u) -- (eqm_u) -- (eqm_u |- xend);
	\draw[densely dashed]  (yend |- eqm_s) -- (eqm_s) -- (eqm_s |- xend);
	
	%% DWL
	\addplot[fill=myred!50]fill between[of=SMC and MB, soft clip={domain=3:5}];
	\node[coordinate, pin={[pin edge={myred, thick}]25:{\textbf{{\color{myred}DWL}}}}, thick] at (axis cs:4.75,25){};
	
	\end{axis}
	\end{tikzpicture}
\end{figure}
\end{frame}

%----------- new section -------------------------------------%

\section{Tradeable permits}

%----------- new slide ---------------------------------------% 

\begin{frame}{Tradeable permits}

	For this example:
	\begin{itemize}
		\item {\color{myred}$MAC_1 = 2 + \frac{1}{2}A_1$}
		\item {\color{myblue}$MAC_2 = \frac{3}{2}A_2$}
		\item Total cap = 20 tons
	\end{itemize}

	We'll compare outcomes and gains from trade versus a uniform allocation (i.e. where each firm abates 10 tons).
	
\end{frame}

%----------- new slide ---------------------------------------% 

\begin{frame}{Tradeable permits (cont.)}

	\begin{figure}
		\centering
		\begin{tikzpicture}%[scale=1.25]
		
		%% First y-axis (and shared x-axis)
		\begin{axis}[
		width = .85\textwidth,
		height = .9\textheight,
		axis x line*=bottom,
		axis y line=left,
		xmin=0, xmax=20,
		ymin=0, ymax=35,
		xtick=\empty,
		ytick=\empty,
		xtick={10,14}, xticklabels={{\color{myred}10} {\color{myblue}(10)},{\color{myred}14} {\color{myblue}(6)}},
		ytick={7,9}, yticklabels={{\color{gray} 7}, 9},
		xlabel=$\longleftarrow$ Abatement (20 tons total) $\longrightarrow$,
		ylabel={\color{myred} \$/ton},
		ylabel style={at={(ticklabel* cs:1.05)}, anchor=south east},
		]
		% MAC_1 curve
		\addplot[name path=MAC1, domain={0:20}, thick, myred] {(2+1/2*x)} node[above left]{$MAC_1$};
		
		% MAC_2 curve
		\addplot[name path=MAC2, domain={0:20}, thick, myblue] {30-3/2*x} node[pos=0,anchor=south west]{$MAC_2$};
		
		% Equilibria
		%% Have to multiply all these numbers by 10. (Why? Not sure...)
		\coordinate (xorig) at (0,0);
		\coordinate (xend) at (200,0);
		\coordinate (yend1) at (0,350); 
		\coordinate (yend2) at (200,350);
		
		\path [name intersections={of=MAC1 and MAC2, by={eqm_trade}}];
		\draw[densely dashed]  (eqm_trade) -- (eqm_trade |- xorig);
		\draw[densely dashed]  (xorig |- eqm_trade) -- (eqm_trade -| xend);
		
		% Uniform allotment
		\addplot[name path=u, draw=none] (10,0) -- (100,350);
		\path [name intersections={of=MAC1 and u, by={eqm_u1}}];
		\path [name intersections={of=MAC2 and u, by={eqm_u2}}];
		
		\draw[densely dashed, gray]  (xorig |- eqm_u1) -- (eqm_u1);
		\draw[densely dashed, gray]  (eqm_u2) -- (xend |- eqm_u2);
		\draw[densely dashed, gray]  (eqm_u2) -- (eqm_u2 |- xorig);
		
		%% Gains from trade
		\addplot[name path=g, draw=none, domain={0:20}] {(9)};
		\addplot[fill=myred!50]fill between[of=g and MAC1, soft clip={domain=10:14}];
		\addplot[fill=myblue!50]fill between[of=MAC2 and g, soft clip={domain=10:14}];
		
		\end{axis}
		
		%% Second y-axis
		\begin{axis}[
		width = .85\textwidth,
		height = .9\textheight,
		axis y line=right,
		axis x line=none,
		xmin=0, xmax=20,
		ymin=0, ymax=35,
		ylabel={\color{myblue} \$/ton},
		ylabel style={at={(ticklabel* cs:1.05)}, anchor=north east},
		ytick=\empty,
		ytick={15,9}, yticklabels={{\color{gray} 15}, 9},
		]
		\end{axis}
		
		\end{tikzpicture}
	\end{figure}
\end{frame}

%----------- new section -------------------------------------%

\section{Prices vs Quantities (Weitzman rule)}

%----------- new slide ---------------------------------------% 

\begin{frame}{Prices vs Quantities (1): Permits preferred}

	\begin{figure}
		\centering
		\begin{tikzpicture}%[%yscale=1.05, xscale=1]
		\begin{axis}[
		width = .9\textwidth,
		height = .9\textheight,
		axis lines=middle,
		%xlabel=A,
		%ylabel=P,
		ylabel near ticks,  
		xlabel style={at={(ticklabel* cs:1)}, anchor=north},
		ylabel style={at={(ticklabel* cs:1)}, anchor=south},
	%	every axis y label/.style={
	%		at={(ticklabel* cs:1.05)},
	%		anchor=south,
	%	}, 
		xtick={6, 8}, xticklabels={$A_H^*$, $A_E$},
		ytick={9, 7}, yticklabels={$\tau_H^*$,$\tau_E$},
		xmin = 0, 
		xmax = 18, 
		ymin = 0, 
		ymax = 18
		]
		
		%% MAB curve
		\addplot[name path=MAB, domain={0:15}, thick] {15-x} node[above right]{$MAB$};
		%% MAC_L curve
		\addplot[name path=MAC_L, domain={0:15}, thick] {0.5*x} node[right]{$MAC_L$};
		%%% Define E[MAC] curve
		\addplot[name path=EMAC, domain={0:15}, thick, dashed] {3 + 0.5*x} node[right]{$E\left[MAC\right]$};
		%% MAC_H curve
		\addplot[name path=MAC_H, domain={0:15}, thick] {6 + 0.5*x} node[right]{$MAC_H$};
		
		%% Equilibria
		\coordinate (yend) at (0,50);
		\coordinate (xend) at (50,0);
		\path [name intersections={of=MAB and EMAC, by={eqm_e}}]; 
		\fill (eqm_e) circle (2pt);
		\path [name intersections={of=MAB and MAC_H, by={eqm_t}}]; 
		\fill (eqm_t) circle (2pt);
		\draw[dashed]  (yend |- eqm_e) -- (eqm_e) -- (eqm_e |- xend);
		\draw[densely dotted]  (yend |- eqm_t) -- (eqm_t) -- (eqm_t |- xend);
		
		%% DWL
		\addplot[fill=myred!50]fill between[of=MAC_H and MAB, soft clip={domain=2:6}];
		\node[coordinate, pin={[pin edge={myred}]86:{{\scriptsize \color{myred}Tax DWL}}}] at (axis cs:3, 10.5){};
		\addplot[fill=myblue!50]fill between[of=MAC_H and MAB, soft clip={domain=6:8}];
		\node[coordinate, pin={[pin edge={myblue}]88:{{\scriptsize \color{myblue}Permits DWL}}}] at (axis cs:7, 9){};

		\end{axis}
		\end{tikzpicture}
	\end{figure}

	$MAC$ \underline{flat} relative to $MAB$, but uncertain. (Truth is $MAC_H$.)

\end{frame}

%----------- new slide ---------------------------------------% 

\begin{frame}{Prices vs Quantities (2): Tax preferred}

	\begin{figure}
		\centering
		\begin{tikzpicture}%[%yscale=1.05, xscale=1]
		\begin{axis}[
		width = .9\textwidth,
		height = .9\textheight,
		axis lines=middle,
		%xlabel=A,
		%ylabel=P,
		ylabel near ticks,  
		xlabel style={at={(ticklabel* cs:1)}, anchor=north},
		ylabel style={at={(ticklabel* cs:1)}, anchor=south},
	%	every axis y label/.style={
	%		at={(ticklabel* cs:1.05)},
	%		anchor=south,
	%	}, 
		xtick={4, 6}, xticklabels={$A_H^*$, $A_E$},
		ytick={10, 9}, yticklabels={$\tau_H^*$,$\tau_E$},
		xmin = 0, 
		xmax = 12, 
		ymin = 0, 
		ymax = 16
		]
		
		%% MAB curve
		\addplot[name path=MAB, domain={0:11}, thick] {12-0.5*x} node[below]{$MAB$};
		%% MAC_L curve
		\addplot[name path=MAC_L, domain={0:9}, thick] {x} node[right]{$MAC_L$};
		%%% Define E[MAC] curve
		\addplot[name path=EMAC, domain={0:9}, thick, dashed] {3 + x} node[right]{$E\left[MAC\right]$};
		%% MAC_H curve
		\addplot[name path=MAC_H, domain={0:9}, thick] {6 + x} node[right]{$MAC_H$};
		
		%% Equilibria
		\coordinate (yend) at (0,50);
		\coordinate (xend) at (50,0);
		\path [name intersections={of=MAB and EMAC, by={eqm_e}}]; 
		\fill (eqm_e) circle (2pt);
		\path [name intersections={of=MAB and MAC_H, by={eqm_t}}]; 
		\fill (eqm_t) circle (2pt);
		\draw[dashed]  (yend |- eqm_e) -- (eqm_e) -- (eqm_e |- xend);
		\draw[densely dotted]  (yend |- eqm_t) -- (eqm_t) -- (eqm_t |- xend);
		
		%% DWL
		\addplot[fill=myred!50]fill between[of=MAC_H and MAB, soft clip={domain=3:4}];
		\node[coordinate, pin={[pin edge={myred}]95:{{\scriptsize \color{myred}Tax DWL}}}] at (axis cs:3.5, 10){};
		\addplot[fill=myblue!50]fill between[of=MAC_H and MAB, soft clip={domain=4:6}];
		\node[coordinate, pin={[pin edge={myblue}]90:{{\scriptsize \color{myblue}Permits DWL}}}] at (axis cs:5.25, 10.75){};

		\end{axis}
		\end{tikzpicture}
	\end{figure}

	$MAC$ \underline{steep} relative to $MAB$, but uncertain. (Truth is $MAC_H$.)

\end{frame}

% %----------- new slide ---------------------------------------% 

% \begin{frame}{Prices vs Quantities (3)}

% 	\begin{figure}
% 		\centering
% 		\begin{tikzpicture}%[%yscale=1.05, xscale=1]
% 		\begin{axis}[
% 		width = .9\textwidth,
% 		height = .9\textheight,
% 		axis lines=middle,
% 		%xlabel=A,
% 		%ylabel=P,
% 		ylabel near ticks,  
% 		xlabel style={at={(ticklabel* cs:1)}, anchor=north},
% 		ylabel style={at={(ticklabel* cs:1)}, anchor=south},
% 	%	every axis y label/.style={
% 	%		at={(ticklabel* cs:1.05)},
% 	%		anchor=south,
% 	%	}, 
% 		xtick={10, 8}, xticklabels={$A_L^*$, $A_E$},
% 		ytick={7, 5}, yticklabels={$\tau_E$, $\tau_L^*$},
% 		xmin = 0, 
% 		xmax = 18, 
% 		ymin = 0, 
% 		ymax = 18
% 		]
		
% 		%% MAB curve
% 		\addplot[name path=MAB, domain={0:15}, thick] {15-x} node[above right]{$MAB$};
% 		%% MAC_L curve
% 		\addplot[name path=MAC_L, domain={0:15}, thick] {0.5*x} node[right]{$MAC_L$};
% 		%%% Define E[MAC] curve
% 		\addplot[name path=EMAC, domain={0:15}, thick, dashed] {3 + 0.5*x} node[right]{$E\left[MAC\right]$};
% 		%% MAC_H curve
% 		\addplot[name path=MAC_H, domain={0:15}, thick] {6 + 0.5*x} node[right]{$MAC_H$};
		
% 		%% Equilibria
% 		\coordinate (yend) at (0,50);
% 		\coordinate (xend) at (50,0);
% 		\path [name intersections={of=MAB and EMAC, by={eqm_e}}]; 
% 		\fill (eqm_e) circle (2pt);
% 		\path [name intersections={of=MAB and MAC_L, by={eqm_t}}]; 
% 		\fill (eqm_t) circle (2pt);
% 		\draw[dashed]  (yend |- eqm_e) -- (eqm_e) -- (eqm_e |- xend);
% 		\draw[dashed] (eqm_e) -- (140, 70);
% 		\draw[densely dotted]  (yend |- eqm_t) -- (eqm_t) -- (eqm_t |- xend);
		
% 		%% DWL
% 		\addplot[fill=myred!50]fill between[of=MAC_L and MAB, soft clip={domain=10:14}];
% 		\addplot[fill=myblue!50]fill between[of=MAC_L and MAB, soft clip={domain=8:10}];
% 		\node[coordinate, pin={[pin edge={myred}]345:{{\scriptsize \color{myred}Tax DWL}}}] at (axis cs:13.5, 4.5){};
% 		\node[coordinate, pin={[pin edge={myblue}]205:{{\scriptsize \color{myblue}Permits DWL}}}] at (axis cs:8.5, 5.5){};
		

% 		\end{axis}
% 		\end{tikzpicture}
% 	\end{figure}

% 	$MAC$ \underline{flat} relative to $MAB$, but uncertain. (Truth is $MAC_L$.)

% \end{frame}

%----------- new section -------------------------------------%

\section{Environmental Kuznets curve}

%----------- new slide ---------------------------------------% 
\begin{frame}{EKC}
	\begin{figure}
		\centering
		\begin{tikzpicture}
		\begin{axis}[
		axis lines=middle,
		xlabel=GDP per capita,
		ylabel=Environmental degradation,
		xlabel near ticks, 
		ylabel near ticks, 
		xmax=12,xmin=0,
		ymin=0,ymax=40,
		ytick=\empty, 
		xtick=\empty
		]
		\addplot[name path=EKC, domain={0:12}, thick] {11*x-x^2};
		\end{axis}
		\end{tikzpicture}
	\end{figure}
\end{frame}

\end{document}