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%% This file may be distributed and/or modified under the conditions of
%% the LaTeX Project Public License, either version 1.2 of this license
%% or (at your option) any later version. The latest version of this
%% license is in:
%%
%% http://www.latex-project.org/lppl.txt
%%
%% and version 1.2 or later is part of all distributions of LaTeX version
%% 1999/12/01 or later.
%%
%% BEGIN semsamp1.tex
%
% This is a sample document for seminar.sty, v0.93 (and maybe later).
%
% Try this with and without the article option:
\documentclass[fancybox,article]{seminar}
\def\printlandscape{\special{landscape}} % Works with dvips.
\articlemag{1}
%\twoup % Try me.
\newpagestyle{327}%
{Economics 327 \hspace{\fill}\rightmark \hspace{\fill}\thepage}{}%
\pagestyle{327}
\markright{Choice under uncertainty}
\slideframe{Oval}
\newcommand{\heading}[1]{%
\begin{center}
\large\bf
\shadowbox{#1}%
\end{center}
\vspace{1ex minus 1ex}}
\newcommand{\BF}[1]{{\bf #1:}\hspace{1em}\ignorespaces}
\begin{document}
\begin{slide}
\heading{A heading}
One thing this example illustrates is how the {\tt article} style option is
good for printing slides two-up, for distribution to a seminar audience or
class, or just for proofreading.
\BF{Definition}
$p$ (weakly) first-order stochastically dominates $q$ if for every $\bar z\in
Z$,
\[
p(z\leq \bar z) \leq q(z\leq \bar z)
\]
\end{slide}
\begin{slide}
\heading{Problems with stochastic dominance as a DT}
\begin{center}
\begin{tabular}{|r|l|}\hline
$z$ & $p(z)$\\ \hline
\$999 & .01\\ \hline
\$1,000,000 & .99 \\ \hline
\end{tabular}%
\hspace{1cm}%
\begin{tabular}{|r|l|}\hline
$z$ & $q(z)$\\ \hline
\$1,000 & 1\\ \hline
\end{tabular}
\end{center}
\end{slide}
\begin{slide}
\heading{Candidate Theory \#3: Expected utility}
Let $Z$ be an arbitrary set of outcomes. Let $u:Z\rightarrow R$ be a utility
representation of the DM's preferences over the elements of $Z$ as certain
outcomes. (I.e., $u(y)\geq u(z)$ iff $y \geq z$.)
\end{slide}
\begin{slide}
\heading{Expected utility \& the St.\ Petersburg Paradox}
This can get around even St.\ Petersburg Paradox, because we don't require
that utility be linear in money:
\begin{center}
\begin{tabular}{r|c|c|c|c|c}\cline{2-6}
Prize & \$2 & \$4 & \$8 & \$16 & $\ldots$\\ \cline{2-6}
$u(z)=\log_2(z)$ & 1 & 2 & 3 & 4 & $\ldots$ \\ \cline{2-6}
Prob. & 1/2 & 1/4 & 1/8 & 1/16 & $\ldots$\\ \cline{2-6}
\end{tabular}
\end{center}
Expected utility is $\sum_{k=1}^\infty k/2^k = 2$, and so lottery gives same
expected utility as getting \$4 for sure.
\end{slide}
\end{document}
%% END semsamp1.tex
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