A very minimal introduction to Tik Z∗
Jacques Crémer
Toulouse School of Economics
jacques.cremer@tse-fr.eu

March 11, 2011

Contents
1 Introduction

3

2 Setting up a picture

3

3 Drawing lines and curves
3.1 Simple straight lines . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Scaling pictures . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Arrows and the like . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Changing the thickness of lines . . . . . . . . . . . . . . . . . . .
3.5 Dashes and dots . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Colors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7 Pictures in the middle of the text . . . . . . . . . . . . . . . . . .
3.8 Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9 Plotting functions . . . . . . . . . . . . . . . . . . . . . . . . . .

4
4
5
6
7
8
8
8
8
11

4 Filling up areas
12
4.1 Filling up simple areas . . . . . . . . . . . . . . . . . . . . . . . . 12
4.2 Filling up arbitrary areas . . . . . . . . . . . . . . . . . . . . . . 13
5 Putting labels in pictures

13

6 Integration with Beamer

16

7 Hints and tricks

17∗ Thanks to Christophe Bontemps, Michel-Benoı̂t Bouissou and Florian Schuett for comments which have improved this document.

1

8 Examples
17
8.1 Hotelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
8.1.1 The whole picture . . . . . . . . . . . . . . . . . . . . . . 17
8.1.2 Step by step . . . . . . . . . . . . . . . . . . . . . . . . . 18
8.2 Vertical differentiation . . . . . . . . . . . . . . . . . . . . . . . . 18
8.2.1 The whole picture . . . . . . . . . . . . . . . . . . . . . . 18
8.2.2 Step by step . . . . . . . . . . . . . . . . . . . . . . . . . 18
8.3 A curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
8.3.1 The whole picture . . . . . . . . . . . . . . . . . . . . . . 19
8.3.2 Step by step . . . . . . . . . . . . . . . . . . . . . . . . . 20
8.4 Tangency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
8.4.1 The whole picture . . . . . . . . . . . . . . . . . . . . . . 20
8.4.2 Step by step . . . . . . . . . . . . . . . . . . . . . . . . . 21
8.5 Consumer surplus . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
8.5.1 The whole picture . . . . . . . . . . . . . . . . . . . . . . 22
8.5.2 Step by step . . . . . . . . . . . . . . . . . . . . . . . . . 22
8.6 Plotting lots of curves . . . . . . . . . . . . . . . . . . . . . . . . 23
9 Conclusion

24

2

1

Introduction

The aim of this document is to provide the minimum useful introduction to the
Tik Z package (written by Till Tantau), which enables you to do nice figures in
LATEX. I hope it will encourage for further exploration, but I also believe thatat least 70% of the figures found in the economic literature can be drawn withthe commands I present here.1
There are certainly mistakes left in this document. Be careful and if you
find a mistake, drop me an e-mail!
The latest version of this document can be found at http://bit.ly/gNfVn9.

2

Setting up a picture

Just write2 \usepackage{tikz} in the preamble of your document. Modern
TEX engines3 such as MikTeX will automatically install the package. Then
when you want to do a picture just write\begin{tikzpicture}code\end{tikzpicture}

If you want to do a figure (you know the kind of thing that “floats” to the topof the page) you need to set it up as\begin{figure}\begin{tikzpicture}code\end{tikzpicture}\caption{Do not forget!
Make it explicit enough that readers
can figure out what you are doing.}\end{figure}You then compile your document using pdfTEX or XeTEX.
1 There is another popular package for doing figures in L
AT X, PSTricks, whose originalEversion is due to the economist Tim van Zandt. The two packages are pretty much equivalent
in terms of ease of use and features. Tik Z has the advantage of better compatibility with
pdfTEX; PSTricks has the advantage of some nice commands for drawing curves. You canfind an introduction to PSTricks in the book “The LATEX Graphics Companion”.
2 This assumes that you are using L
AT X. Tik Z can also be used in raw T X, but if youEE
are hardcore enough to do that, you probably are better off going straight to the manual.
3 I do not know how to set up Tik Z for use with Scientific Word (which you should not be
using in any case). If you know how to do it, please tell me so that I can put the instructions in
the next version of this document. (I assume that if you can do it is still pretty uncomfortable,
as the code for the pictures will be in the infamous gray boxes.)

3

There is a very extensive (over 700 pages!) manual. You can find it at
http://bit.ly/e3eQQd.4,5,6

3

Drawing lines and curves

3.1

Simple straight lines

To draw a line you do something like\begin{tikzpicture}\draw (0,0) --(1,2);\end{tikzpicture}and you get

Tik Z automatically draws a line between the points (0,0) and (1,2) and sets
up the right space for the figure (by default, coordinates are in centimeters).
You can do a sequence of segments which goes from point to point:\begin{tikzpicture}\draw (0,0) --(1,2) -- (2,3) -- (1,0);\end{tikzpicture}

to get(I have added the grid lines on the graphic to make it clearer. This is done
through the command \draw[help lines] (0,0) grid (2,3);, which draws agrid from (0,0) to (2,3). The “help lines” option makes the presentation neater
4 You can also find it on your computer once Tik Z is installed. Go to the command line
window and type texdoc pgf and choose pgfmanual.pdf in the list which is offered. Or, if
you are using the WinEdt editor, you you can go to LATEX help and ask it for the help of thepgf package. (See the manual about the reasons for the two names Tik Z and pgf.)
5 In French, there also exists an introduction to Tik Z which is shorter (but still 189 pageslong) and may be more accessible than the manual. It is called “Tik Z pour l’impatient”, waswritten by Gérard Tisseau and Jacques Duma, and can be found at http://math.et.info.
free.fr/TikZ/bdd/TikZ-Impatient.pdf.
6 There are a number of wysiwyg or semi-wysiwyg tools which can help you do graphics.
For instance, while still in beta state Tik ZEdt seems useful (http://code.google.com/p/tikzedt/).

4

— I discuss this below. I will add grid lines as useful in what follows without
putting the corresponding line in the code.)
Of course, you can put several lines on the same graph:\begin{tikzpicture}\draw (0,0) --(1,2) -- (2,3) -- (1,0);\draw (3,0) -- (1.5,0.5);\end{tikzpicture}yields

Notice the semi-colons “;” at the end of lines — it is these semi-colons whichmark the end of instructions. You will see below examples where one instructionis spread over several lines. We could also put several instructions on one line:in the last picture I could have written\draw (0,0) --(1,2) -- (2,3) -- (1,0); \draw (3,0) -- (1.5,0.5);

without changing the output. You can also add and suppress spaces, for instancein order to make the code easier to read, without changing anything in the
output.

3.2

Scaling pictures

One very useful feature of Tik Z is that you can blow up the picture, by adding
an option “scale” to the environment.
\begin{tikzpicture}[scale=3]\draw (0,0) -- (1,1);\end{tikzpicture}

to getwhich you can compare to the following:\begin{tikzpicture}\draw (0,0) -- (1,1);\end{tikzpicture}5

which yields

You can scale only one dimension:\begin{tikzpicture}[xscale=3]\draw (0,0) -- (1,1);\end{tikzpicture}

to getor both dimensions in different proportions:\begin{tikzpicture}[xscale=2.5,yscale=0.5]\draw (0,0) -- (1,1);\end{tikzpicture}

to get

3.3

Arrows and the like

You can “decorate” the lines. For instance we can put arrows or bars on one ofboth extremities:\begin{tikzpicture}\draw [->] (0,0) -- (2,0);\draw [<-] (0, -0.5) -- (2,-0.5);\draw [|->] (0,-1) -- (2,-1);\end{tikzpicture}

which yields

When you draw several segments, the arrows are placed at the extremities ofthe first and the last segments. This is convenient, among other things to draw
axes (we will see later how to label them):\begin{tikzpicture}\draw [<->] (0,2) -- (0,0) -- (3,0);\end{tikzpicture}

which gives you

6

3.4

Changing the thickness of lines

Other decorations include changing the thickness:\begin{tikzpicture}\draw [ultra thick] (0,1) -- (2,1);\draw [thick] (0,0.5) -- (2,0.5);\draw [thin] (0,0) -- (2,0);\end{tikzpicture}

to obtain

You can use: ultra thin, very thin
, thin, semithick, thick,very thickand ultra thick
There is also the “help lines” option, discussed above, which is made speciallyto be fine gray lines for showing special points:\begin{tikzpicture}\draw [<->] (0,2) -- (0,0) -- (4,0);\draw [thick] (0,1.5) -- (3,0);\draw [ultra thick] (0,0) -- (2,2);\draw [help lines] (1,0) -- (1,1) -- (0,1);\end{tikzpicture}

which yields

You can also use custom widths:\begin{tikzpicture}\draw [line width=12] (0,0) -- (2,0);\draw [line width=0.2cm] (4,.75) -- (5,.25);\end{tikzpicture}

which gives a line 12pt wide ( the default dimension for width is point) andanother one .2cm wide:

7

3.5

Dashes and dots

You can also make dotted and dashed lines\begin{tikzpicture}\draw [dashed, ultra thick] (0,1) -- (2,1);\draw [dashed] (0, 0.5) -- (2,0.5);\draw [dotted] (0,0) -- (2,0);\end{tikzpicture}

This gives:

The top line shows you that you can mix types of decorations. You have lots ofcontrol over the style of your dotted and dashed lines (see the manual).

3.6

ColorsAnd finally, you can color your lines.
\begin{tikzpicture}\draw [gray] (0,1) -- (2,1);\draw [red] (0, 0.5) -- (2,0.5);\draw [blue] (0,0) -- (2,0);\end{tikzpicture}

This gives

You have direct access to the following colors: red, green, blue, cyan, magenta, yellow, black, gray, darkgray, lightgray,brown, lime, olive, orange, pink, purple, teal, violetand white. And you can define all the colors you might want — see themanual.

3.7

Pictures in the middle of the text

By the way, you may wonder how I included these rectangles in the text. Tik Z
makes a picture wherever
you want; I just typed
wherever \begin{tikzpicture} \draw [yellow, line width=6](0,0) -- (.5,0); \end{tikzpicture} you want

(To make these constructions easier to type you can use the command \tikz— see the manual.)

3.8

Curves

You are not limited to straight lines:8

\begin{tikzpicture}\draw [blue] (0,0) rectangle (1.5,1);\draw [red, ultra thick] (3,0.5) circle [radius=0.5];;\draw [gray] (6,0) arc [radius=1, start angle=45, end angle= 120];\end{tikzpicture}

This gives:(The arc is of radius 1, starts at the point (6,0) leaving it at an angle of 45
degrees and stops when its slope is 120 degrees — this is not the most convenient
notation!)
You can make paths take smoother turns:\begin{tikzpicture}\draw [<->, rounded corners, thick, purple] (0,2) -- (0,0) -- (3,0);\end{tikzpicture}

which gives you

If you want a precise curve you can do it by computing lots of points in a
program such as Mathematica c and then putting them into Tik Z:\begin{tikzpicture}[xscale=25,yscale=5]\draw [<->, help lines] (0.6,1.34) -- (0.6,1) -- (1.05,1);\draw[orange] (0.6, 1.0385) -(0.61, 1.06372) -- (0.62, 1.08756) -- (0.63, 1.11012) -- (0.64,
1.13147) -- (0.65, 1.15166) -- (0.66, 1.17074) -- (0.67, 1.18874) -- (0.68,
1.20568) -- (0.69, 1.22157) -- (0.7, 1.23643) -- (0.71, 1.25026) -- (0.72,
1.26307) -- (0.73, 1.27486) -- (0.74, 1.28561) -- (0.75, 1.29534) -- (0.76,
1.30402) -- (0.77, 1.31165) -- (0.78, 1.31821) -- (0.79, 1.32369) -- (0.8,1.32806) -- (0.81, 1.33131) -- (0.82, 1.3334) -- (0.83, 1.33431) -- (0.84,
1.334) -- (0.85, 1.33244) -- (0.86, 1.32956) -- (0.87, 1.32533) -- (0.88,
1.31966) -- (0.89, 1.3125) -- (0.9, 1.30373) -- (0.91, 1.29325) -- (0.92,
1.2809) -- (0.93, 1.26649) -- (0.94, 1.24976) -- (0.95, 1.23032) -- (0.96,
1.2076) -- (0.97, 1.18065) -- (0.98, 1.14763) -- (0.99, 1.1038) -- (0.991,
1.09836) -- (0.992, 1.09261) -- (0.993, 1.0865) -- (0.994, 1.07994) -- (0.995,
1.07282) -- (0.996, 1.06497) -- (0.997, 1.0561) -- (0.998, 1.04563) -- (0.999,
1.03209) -- (0.9991, 1.03042) -- (0.9992, 1.02866) -- (0.9993,
1.02679) -- (0.9994, 1.02478) -- (0.9995, 1.0226) -- (0.9996, 1.02019) -- (0.9997,
1.01747) -- (0.9998, 1.01424) -- (0.9999, 1.01005) -- (0.9999,
1.01005) -- (0.99991, 1.00953) -- (0.99992, 1.00898) -- (0.99993,
1.0084) -- (0.99994, 1.00778) -- (0.99995, 1.0071) -- (0.99996,
1.00634) -- (0.99997, 1.00549) -- (0.99998, 1.00448) -- (0.99999, 1.00317) -- (1,1) ;\end{tikzpicture}9

which gives you

Two remarks:• This was overkill: I do not need so many points;• This can also serve as a reminder that one Tik Z instruction can be spreadover several lines and cut arbitrarily over several lines. The marker is thesemi-colon, not the end of line!
There are a number of ways by which you can do curves without plotting all
the points. Here is an easy one:\begin{tikzpicture}\draw[very thick] (0,0) to [out=90,in=195] (2,1.5);\end{tikzpicture}

This gives us a curve from (0,0) to (2,1.5) which leaves at an angle of 90◦ andarrive at an angle of 195◦ :Note that I had to replace the – by “to”. Notice how the angles work:• When the curves goes “out” of (0,0), you put a needle with one extremity
on the starting point and the other one facing right and you turn it counterclockwise until it is tangent to the curve. The angle by which you haveto turn the needle gives you the “out” angle.
• When the curves goes “in” at (2,1.5), you put a needle with one extremity
on the arrival point and the other one facing right and you turn it counterclockwise until it is tangent to the curve. The angle by which you haveto turn the needle gives you the “in” angle.
As with straight lines you can put several to instructions in the same Tik Z
instruction:\begin{tikzpicture}\draw [<->,thick, cyan] (0,0) to [out=90,in=180] (1,1)
to [out=0,in=180] (2.5,0) to [out=0,in=-135] (4,1) ;\end{tikzpicture}

which gives you

10Note that we can put arrows on curves also. They are put at the extremities ofthe first and last segments. If you want an arrow on each segment, you have tobuild the curve from individual components.

3.9

Plotting functions

Tik Z also has a math engine which enables you to plot functions:\begin{tikzpicture}[xscale=13,yscale=3.8]\draw [<->] (0,0.8) -- (0,0) -- (0.5,0);\draw[green, ultra thick, domain=0:0.5] plot (\x, {0.025+\x+\x*\x});\end{tikzpicture}

gives you

The domain instruction shows the range of x which is plotted. In this case weare plotting the function 0.025 + x + x2 . Note the braces around the functionthat we plot in plot (\x, {function}).
Many mathematical functions are possible; you will probably have enoughwith factorial(\x), sqrt(\x), pow(\x,y) (which gives xy ), exp(\x), ln(\x),
log10(\x), log2(\x), abs(\x) (the absolute value of x), mod(\x,y) (x moduloy), round(\x) (rounds x to the nearest integer), floor(\x) (the largest integer
smaller than x), ceil(\x) (the smallest integer larger than x), sin(\x) (sin(x),it assumes that x is in degrees; if x is expressed in radians use sin(\x r)),cos(\x) (cos(x), it assumes that x is in degrees; if x is expressed in radians use
cos(\x r)), tan(\x) (tan(x), it assumes that x is in degrees; if x is expressedin radians use tan(\x r)), min(\x,y,), max(\x,y). You can even use rnd(without argument) which yields a random number between 0 and 1.
In mathematical expressions the two following variables can be useful: e,which is equal to 2.718281828, and pi, which is equal to 3:141592654.
You can mix functions to compute more complicated expressions (see above
for the reason for the r parameter in the argument of sin and cos and note theuse of pi to define the domains):\begin{tikzpicture}[yscale=1.5]\draw [help lines, <->] (0,0) -- (6.5,0);\draw [help lines, ->] (0,-1.1) -- (0,1.1);\draw [green,domain=0:2*pi] plot (\x, {(sin(\x r)* ln(\x+1))/2});\draw [red,domain=0:pi] plot (\x, {sin(\x r)});\draw [blue, domain=pi:2*pi] plot (\x, {cos(\x r)*exp(\x/exp(2*pi))});\end{tikzpicture}

which gives you

11

4

Filling up areas

4.1

Filling up simple areas

You can also fill paths when they are closed:\begin{tikzpicture}\draw [fill=red,ultra thick] (0,0) rectangle (1,1);\draw [fill=red,ultra thick,red] (2,0) rectangle (3,1);\draw [blue, fill=blue] (4,0) -- (5,1) -- (4.75,0.15) -- (4,0);\draw [fill] (7,0.5) circle [radius=0.1];\draw [fill=orange] (9,0) rectangle (11,1);\draw [fill=white] (9.25,0.25) rectangle (10,1.5);\end{tikzpicture}

to get

Notice the difference between the first two squares. The second red in [fill=red,ultra thick,red]tells Tik Z to draw the line around the shape in red. We have indicated no color
in the first, so the line is black.
If you do not want to see the outline at all, replace the \draw command by\path:\begin{tikzpicture}\path [fill=gray] (0,0) rectangle (1.5,1);\draw [fill=yellow] (2,0) rectangle (3.5,1);\end{tikzpicture}

gives you

Of course, we could have replaced the first line by \draw [fill=yellow,yellow] (0,0) rectangle (1.5,1);:
we would have obtained a square like the second one, except for the fact that it
is surrounded by a yellow line.

12

4.2

Filling up arbitrary areas

The content in this subsection are not necessary to understand the rest of the
document. You can skip it at first reading. (But example 8.5 uses these techniques.)
You can draw paths which mix the -- and the to constructions above. Thisis useful for filling up strange looking areas.
\begin{tikzpicture}\draw [ultra thick] (0,0) to [out=87,in=150] (1,1) -- (.85,.15) -- (0,0);\draw [ultra thick, fill=purple] (2,0) to [out=87,in=150] (3,1) -- (2.85,.15) -- (2,0);\path [fill=purple] (4,0) to [out=87,in=150] (5,1) -- (4.85,.15) -- (4,0);\end{tikzpicture}

to getActually if you put the to constructions without any “options” you get astraight line:\begin{tikzpicture}\draw [ultra thick] (0,0) to (1,1) to (.85,.15) to (0,0);\end{tikzpicture}

gives you5

Putting labels in pictures

When you do a picture, in 99% of cases you also need to put labels. This iseasy. Let us start by seeing how we would place some text in a picture.
\begin{tikzpicture}\draw [thick, <->] (0,2) -- (0,0) -- (2,0);\node at (1,1) {yes};\end{tikzpicture}yieldsyes

Notice how the “yes” is positioned: the center of its “baseline” is at (1,1).
Sometimes you want a label to be situated relative to a point. Tik Z has neatcommands for this. For instance you can write
13\begin{tikzpicture}\draw [thick, <->] (0,2) -- (0,0) -- (2,0);\draw[fill] (1,1) circle [radius=0.025];\node [below] at (1,1) {below};\end{tikzpicture}

to getbelow
You are not limited to put things below a point:\begin{tikzpicture}\draw [thick, <->] (0,2) -- (0,0) -- (2,0);\draw[fill] (1,1) circle [radius=0.025];\node [below] at (1,1) {below};\node [above] at (1,1) {above};\node [left] at (1,1) {left};\node [right] at (1,1) {right};\end{tikzpicture}yieldsabove
left rightbelow
And, you can also mix and match\begin{tikzpicture}[scale=2]\draw [thick, <->] (0,1) -- (0,0) -- (1,0);\draw[fill] (1,1) circle [radius=0.025];\node [below right, red] at (.5,.75) {below right};\node [above left, green] at (.5,.75) {above left};\node [below left, purple] at (.5,.75) {below left};\node [above right, magenta] at (.5,.75) {above right};\end{tikzpicture}yieldsabove left above right
below left below rightThis makes it possible to label axes and points:\begin{tikzpicture}[xscale=3, yscale=1.5]\draw [thick, <->] (0,1) -- (0,0) -- (1,0);\node [below right] at (1,0) {$x$};

14

\node [left] at (0,1) {$y$};\draw[fill] (.4,.6) circle [radius=.5pt];\node[above right] (.4,.6) {$A$};\end{tikzpicture}

gives youyAx
You can avoid some typing by mixing nodes in the middle of paths. For
instance the last figure could have been written as follows:\begin{tikzpicture}[xscale=3, yscale]\draw [thick, <->] (0,1) node [left] {$y$}-- (0,0) -- (1,0) node [below right] {$x$};\draw[fill] (.4,.6) circle [radius=.5pt]
node[above right] (.4,.6) {$A$};\end{tikzpicture}

which would have given exactly the same result. Note that the node is put after
the point to which it is attached and that we suppress the \ in \node.
Sometimes, you may want to put several lines in your “node” (this is convenient when drawing time lines for instance). This can be done by using thestandard LATEX \\ for indicating a new line but you must tell Tik Z how to alignthings. Type\begin{tikzpicture}[xscale=1.3]\draw [thick] (0,0) -- (9,0);\draw (0,-.2) -- (0, .2);
\draw (3,-.2) -- (3, .2);
\draw (6,-.2) -- (6, .2);
\draw (9,-.2) -- (9, .2);
\node[align=left, below] at (1.5,-.5)%{This happens\\in period 1\\and is aligned\\ left};\node[align=center, below] at (4.5,-.5)%{This happens\\in period 2\\and is centered};\node[align=right, below] at (7.5,-.5)%{This happens\\in period 2\\and is right\\aligned};\end{tikzpicture}

to obtain

This happens
in period 1
and is aligned
leftThis happens
in period 2
and is centered

This happens
in period 2
and is rightalignedWithout the option align= Tik Z will make one big line. If I made the mistaketo write15\begin{tikzpicture}\draw [->] (0,0) -- (2,0);\node [right] at (2,0) {above\\below};\end{tikzpicture}

I would have obtained
abovebelow
The Tik Z manual will give you information about the way in which you cancontrol more precisely the position and shapes of the labels, and also on theway in which you can put labels on lines and curves as in

6

label

.

Integration with Beamer

Tik Z works very well with Beamer (they were written by the same person!). In
particular it is very easy to uncover figures progressively. For instance\begin{frame}a few lines\begin{center}\begin{tikzpicture}\draw [blue, ultra thick] (-1,2) -- (6,3);\uncover<1>{\draw [green,thick] (-4,3) -- (2,2.5);}\uncover<2>{\draw [red,thick] (0,0) -- (0,5);}\end{tikzpicture}\end{center}and something under.
\end{frame}

gives you two slides:a few lines

a few lines

and something under.

and something under.

It is important to use \uncover and \cover (or, nearly equivalently, \visible
and \invisible) rather than \only. If I replace \uncover by \only in thecode above I get

16

a few lines

a few lines

and something under.

and something under.

Notice how the text changes position. With \uncover the lines are “drawn” on
all the slides but made invisible when not called for. With \only the lines are
only drawn when called for.

7

Hints and tricks• It takes some time to draw figures. And it is normal to make mistakes.
Proceed by trial and error, compiling your code often.
• If you have problems placing things, it is useful to draw a grid; you cancomment it out when compiling the final version. Put the grid as the first
instruction in the picture, so that it does not overwrite the interesting
part! (There are lots of possible options for the grid: see the manual.)

8

ExamplesA few examples.

8.1

Hotelling

8.1.1

The whole picture0

a = b = 1/2\begin{tikzpicture}[xscale=8]\draw[-][draw=red, very thick] (0,0) -- (.5,0);\draw[-][draw=green, very thick] (.5,0) -- (1,0);\draw [thick] (0,-.1) node[below]{0} -- (0,0.1);\draw [thick] (0.5,-.1) node[below]{$a=b=1/2$} -- (0.5,0.1);\draw [thick] (1,-.1) node[below]{1} -- (1,0.1);\end{tikzpicture}

171

8.1.2

Step by step

\draw[-][draw=red, very thick] (0,0) -- (.5,0);\draw[-][draw=green, very thick] (.5,0) -- (1,0);\draw [thick] (0,-.1) node[below]{0} -- (0,0.1);
0\draw [thick] (0.5,-.1) node[below]{$a=b=1/2$} -- (0.5,0.1);
0a = b = 1/2

0a = b = 1/2\draw [thick] (1,-.1) node[below]{1} -- (1,0.1);

8.2

Vertical differentiation

8.2.1

The whole picture
q2 vendue
au prix p2

dépend de p1 et p2
q1 vendue
au prix p1\begin{tikzpicture}[yscale=4]\draw[-][draw=red, very thick] (0,0) -- (0,.45);\draw[-][draw=green, very thick] (0,.45) -- (0,1);\draw [thick] (-0.1,0.2) -- (0.1,.2) node[align=left, right]{$q_1$ vendue\\au prix $p_1$};\node[right] at (0.1,.45) {d\’epend de $p_1$ et $p_2$};\draw [thick] ((-0.1,0.85) -- (0.1,.85) node[align=left, right]{$q_2$ vendue\\ au prix $p_2$};\draw (-0.1,0) -- (0.1,0);\draw (-0.1,1) -- (0.1,1);\end{tikzpicture}

The figure looks better with the labels “qi vendue au prix pi ” on one line,
but I wanted to remind you of the possibility of writing the text in a node over
several lines! Note that in [align=left, right] the align=left tells Tik Z toalign the text to the left whereas the right option tells it to put the node to
the right of the coordinate.
8.2.2

Step by step

\begin{tikzpicture}[yscale=4]
1. \draw[-][draw=red, very thick] (0,0) -- (0,.45);
2. \draw[-][draw=green, very thick] (0,.45) -- (0,1);
3.a. \draw [thick] (-0.1,0.2) -- (0.1,.2);

18

1

3. \draw [thick] (-0.1,0.2) -- (0.1,.2) node[align=left, right]{$q_1$ vendue\\au prix $p_1$};
4. \node[right] at (0.1,.45) {d\’epend de $p_1$ et $p_2$};
4. \draw [thick] ((-0.1,0.85) -- (0.1,.85) node[align=left, right]{$q_2$ vendue\\ au prix $p_2$};
5. \draw (-0.1,0) -- (0.1,0);
5. \draw (-0.1,1) -- (0.1,1);\end{tikzpicture}

q1 vendue
au prix p1

1

2

3.a

8.3

A curve

8.3.1

The whole picture3

q2 vendue
au prix p2

q2 vendue
au prix p2

dépend de p1 et p2dépend de p1 et p2

q1 vendue
au prix p1

q1 vendue
au prix p1

4

5

V (q)

q
\begin{center}\begin{tikzpicture}\draw[<->] (6,0) node[below]{$q$} -- (0,0) -(0,6) node[left]{$V(q)$};\draw[very thick] (0,0) to [out=90,in=145] (5,4.5);\end{tikzpicture}\end{center}198.3.2

Step by step

\begin{tikzpicture}
1.a. \draw[<->] (6,0) -- (0,0) -(0,6);
1. \draw[<->] (6,0) node[below]{$q$} -- (0,0) -(0,6) node[left]{$V(q)$};2. \draw[very thick] (0,0) to [out=90,in=145] (5,4.5);\end{tikzpicture}
V (q)

V (q)

q

1.a

8.4

Tangency

8.4.1

The whole picture1\begin{tikzpicture}\draw [help lines] (0,0) grid (5,5);\draw [<->] (5,0) -- (0,0) -- (0,5);\draw (4,0) -- (0,4);\draw[dashed,ultra thick](1.5,3.5) to [out=-80,in=135] (2.5,1.5);\draw [dashed,ultra thick](2.5,1.5) to [out=-45,in=160] (4.2,0.5);\end{tikzpicture}

20

q

3

You have recognized a consumer! Note the use of “in” and “to” to get thetangents. We could have made this a bit more compact by writing the dashedline in one instruction:\draw[dashed,ultra thick](1.5,3.5) to[out=-80,in=135] (2.5,1.5)
to [out=-45,in=160] (4.2,0.5);

Notice also that the curves goes “in” (2.5,1.5) at an angle of 135◦ and goes “out”
at an angle of 45◦ . This is consistent with the behavior explained on page 10.
8.4.2

Step by step

\begin{tikzpicture}
1. \draw [help lines] (0,0) grid (5,5);
1. \draw [<->] (5,0) -- (0,0) -- (0,5);
1. \draw (4,0) -- (0,4);
2. \draw[dashed,ultra thick](1.5,3.5) to [out=-80,in=135] (2.5,1.5);
3. \draw [dashed,ultra thick](2.5,1.5) to [out=-45,in=160] (4.2,0.5);\end{tikzpicture}

1

2

21

3

8.5

Consumer surplus

8.5.1

The whole pictureP

P ∗ = .8(0,0)

Q∗ = 3Q\begin{tikzpicture}\path [fill=yellow] (0,0) -- (0,5) to [out=-80, in=160](3,.8) -- (3,0) -- (0,0);\draw [<->] (0,6) node [left] {$P$} -- (0,0)
node [below left] {(0,0)} -- (7,0) node [below] {$Q$};\draw [ultra thick, dashed] (0,.8) node [left] {$P^*=.8$} -- (3,.8)-- (3,0) node [below] {$Q^*=3$};\draw [fill] (3,.8) circle [radius=.1];\draw [thick] (0,5) to [out=-80, in=160] (3,.8) to[out=-20, in=175] (6,0);\end{tikzpicture}

Note that I color the filled area before drawing the lines, to make sure thatthose come on top and are visible. (There is, of course, no serious reason for
the P ∗ and the Q∗ to be equal to the “real” coordinates of the circled point in
the picture, except to help you understand what is happening.)
8.5.2

Step by step

\begin{tikzpicture}
1. \path [fill=yellow] (0,0) -- (0,5) to [out=-80, in=160](3,.8) -- (3,0) -- (0,0);
2. \draw [<->] (0,6) node [left] {$P$} -- (0,0)
node [below left] {(0,0)} -- (7,0) node [below] {$Q$};
2. \draw [ultra thick, dashed] (0,.8) node [left] {$P^*=.8$} -- (3,.8)-- (3,0) node [below] {$Q^*=3$};
2. \draw [fill] (3,.8) circle [radius=.1];
3. \draw [thick] (0,5) to [out=-80, in=160] (3,.8) to22

[out=-20, in=175] (6,0);\end{tikzpicture}PP

P ∗ = .8
(0,0)

1

8.6

P ∗ = .8
∗

Q

Q =3

Q∗ = 3

(0,0)

2

Q

3

Plotting lots of curves
EUR

2 min[v1 , v2 ]v2 (x)
v1 (x)

q\begin{center}\begin{tikzpicture}[domain=0:0.5,xscale=13,yscale=3.8]\draw[<->] (0,2) node[left]{EUR}-- (0,0) -- (.7,0) node[below] {$q$};\draw[red] plot (\x, {0.25+\x/2+\x*\x/2}) node[right] {$v_1(x)$};\draw[green] plot (\x, {0.025+\x+\x*\x}) node[right] {$v_2(x)$};\draw[thin, dashed] plot (\x, {0.275+1.5*\x+1.5*\x*\x}) ;\draw[thick,domain=0:0.33666] plot (\x, {0.05+2*\x+2*\x*\x}) ;\draw[thick,domain=0.33666:0.5]
plot (\x, {0.5+\x+\x*\x}) node[right] {$2\min[v_1,v_2]$};\end{tikzpicture}\end{center}

You should be able to figure it out. Note that I can also attach nodes to theplots of mathematical functions.
23

9Conclusion

Tik Z is a very large program which can do lots of things. You will find commands
to draw hierarchial trees, to draw lots of different types of shapes, to do someelementary programming, to align elements of a picture in a matrix frame, todecorate nodes, to compute the intersections of paths, etc. The main message
is “if it is not in these notes, it is most probably somewhere in the manual”.

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