\documentclass[12pt]{article}
  
%------------------------------------------------------------
% This is   a comment too. The last one was a separator comment. 

\begin{document}
 
 \parskip 12pt 
 
\parindent 16pt

  
\vspace*{-1.5in}

\begin{Huge}
  \begin{center}
{\bf How To Use Latex} 


  \end{center}
\end{Huge}

\noindent
February 23, 2011. 
Http://rasmusen.org/a/latex-sample.tex,http://rasmusen.org/a/latex-sample.pdf.
 
%------------------------------------------------------
 

  \noindent
 {\bf 8.1:   Discounting }\\
$\frac{1}{1+r}=$  \$9,100 at 10\% interest. Bond A pays out \$10,000 plus inflation of $\pi$.\footnote{Note that   $\forall$  quasi-concave $f :
X   \rightarrow   L^1$,  we let    $m \in X$ denotes the   point at which $f$ is maximized. }  To process this file, first go to  http://miktex.org/ and set up the free Miktex program on your computer. That's easy. Then, figure out how to issue a command to miktex saying ``pdflatex latex-sample.tex''. That could be hard, because of figuring out what directories files have to be in, how to get a DOS shell in which to issue the command, so forth, but the Miktex directions will help. That command will turn the *.tex file into a pretty-looking *.pdf file. Look at the latex-sample.pdf file and see if it looks good. If it doesn't, change the commands in the latex-sample.tex file and re-run it. If you mess up and forget brackets or write latex commands with typos, then Miktex will stop midway with an error message telling you what line has a mistake.    
See also: http://rasmusen.org/a/latex-rasmusen.pdf and  http://rasmusen.org/g492/latex-example.tex,http://rasmusen.org/g492/latex-example.pdf (which is like this page, but with some fancier commands such as for tables).  

 
 Here is an equation: 
\begin{equation}  
MSE_{exact} =  \int_0^{2c}
\left( q_1-c\right)^2 (1) dq
+   \int_{2c}^1         \left( \alpha-q\right)^2 (1)dq=     \frac{2 \Sigma}{3}      c^3. 
\end{equation}
But the next one has no number even though it is indented: 
$$
\exists  \overline{D}f(x)=\limsup_{h  \rightarrow     0}
\frac{f(x_2+h^3)-f(x)}{\sqrt{h_{23}}}.
$$

\begin{small}
\hspace{.5in} Kannai, Yakar  (1977)    ``Concavifiability and  \underline{ Constructions}  of  Concave Utility Functions,''   {\it Journal  of Mathematical  Economics},   4:  l-56.
\end{small}


\begin{verbatim}
 If you don't want Latex to format for      you, 
      use verbatim as I do here. 
                      Column 1   Column 2
Row 1              345            2444
Row 2                45             44444
\end{verbatim}
 
\end{document}
