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authorKarl Berry <karl@freefriends.org>2007-01-09 23:28:00 +0000
committerKarl Berry <karl@freefriends.org>2007-01-09 23:28:00 +0000
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-%% BEGIN semsamp1.tex
-%
-% This is a sample document for seminar.sty, v0.93 (and maybe later).
-%
-% Try this with and without the article option:
-
-\documentstyle[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