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\documentclass{beamer}
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\usepackage{graphicx} % Allows including images
\usepackage{booktabs} % Allows the use of \toprule, \midrule and \bottomrule in tables
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% TITLE PAGE
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\title[Managerial Economics]{VW Invasion of North America} % The short title appears at the bottom of every slide, the full title is only on the title page
\author{Group 7} % Your name
\institute[FDSM] % Your institution as it will appear on the bottom of every slide, may be shorthand to save space
{
\textit{Fudan Business} \\\textit{School of Management} \\ % Your institution for the title page
\medskip
%\textit{bofu20131@163.com} % Your email address
}
\date{\today} % Date, can be changed to a custom date
\begin{document}
\begin{frame}
\titlepage % Print the title page as the first slide
\end{frame}
\begin{frame}
\frametitle{Overview} % Table of contents slide, comment this block out to remove it
\tableofcontents % Throughout your presentation, if you choose to use \section{} and \subsection{} commands, these will automatically be printed on this slide as an overview of your presentation
\end{frame}
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% PRESENTATION SLIDES
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%------------------------------------------------
\section{Before 1964, why VW can increase sales revenue every time when it increase its price?} % Sections can be created in order to organize your presentation into discrete blocks, all sections and subsections are automatically printed in the table of contents as an overview of the talk
%------------------------------------------------
\section{VW built sales network after 1964, what is its influence on the demand of Beetles in the US market? Why VW can increase its revenue through increasig price again ?}
\section{Assume we have the same slope of demand curve before 1964 and after 1964. Draw the two demand curve, write down the two demand function, and calculate the elasticities when price increases from \$800 to \$1000, from \$1200 to \$1350, and then from \$1500 to \$1800.}
\section{Raise one or two examples which you think the seller should set better price. And explain.}
\begin{frame}
\frametitle{Question 1}
1. Before 1964, why VW can increase sales revenue every time when it increase its price ?\\~\\
\begin{itemize}
\item VW has an inelastic price demand curve, which means that every 1\% increase in price leads less than $1\%$ drop in quantity demanded.
\end{itemize}
\end{frame}
%------------------------------------------------
\begin{frame}
\frametitle{Question 2}
2. VW built sales network after 1964, what is its influence on the demand of Beetles in the US market? Why VW can increase its revenue through increasig price again ?\\~\\
\begin{itemize}
\item The demand curve of Beetles in the US market moves upward. In other words, we have an increase in demand of Bettles in the US market after 1964. Since the increase in demand will cause the original unit elastic price point to be at the inelastic price, the revenue at that price will increase again.
\end{itemize}
\end{frame}
%------------------------------------------------
\begin{frame}
\frametitle{Question 3}
3. Assume we have the same slope of demand curve before 1964 and after 1964. Draw the two demand curve, write down the two demand function, and calculate the elasticities when price increases from \$800 to \$1000, from \$1200 to \$1350, and then from \$1500 to \$1800.\\~\\
\end{frame}
%------------------------------------------------
\begin{frame}
\frametitle{Question 3: Steps of Finding Price Elasticity}
\begin{block}{Step 1: Obtain the Demand Curve After 1964}
$$ \left\{
\begin{aligned}
1500 = 562000a + b\\
1800 = 538000a + b\\
\end{aligned}
\right.\Rightarrow
P_{\textit{after}} = -\dfrac{1}{80} Q_{\textit{after}} + 8525
$$
\end{block}
\begin{block}{Step 2: Obtain the Demand Curve Before 1964}
$$ \left\{
\begin{aligned}
Q_{\pi_{max}} &= 40d\\
1350 &= -\dfrac{1}{80} 40d + d\\
\end{aligned}
\right.\Rightarrow
P_{\textit{before}} = -\dfrac{1}{80} Q_{\textit{before}} + 2700
$$
\end{block}
\begin{block}{Step 3: Obtain the Elasticity}
$$ \left\{
\begin{aligned}
P_{\textit{after}} &= -\dfrac{1}{80} Q_{\textit{after}} + 8525\\
P_{\textit{before}} &= -\dfrac{1}{80} Q_{\textit{before}} + 2700\\
\end{aligned}
\right.\Rightarrow
E_{(Q,P)}
$$
\end{block}
\end{frame}
%------------------------------------------------
\begin{frame}
\frametitle{Profit Maximization}
\begin{theorem}[Profit Maximization]
\centering
If the linear demand curve is unit elastic or $E_{(P,Q)}= -1$:\\
Then $MR = 0$
\end{theorem}
\end{frame}
%------------------------------------------------
\begin{frame}
\frametitle{Question 3: Calculate Price Elasticity}
\begin{table}
\begin{tabular}{l l l l l l}
\toprule
\textbf{Price Range} & \textbf{$Q_{before}$} & \textbf{$Q_{after}$} & \textbf{$\dfrac{\Delta P}{P}$} & \textbf{$\dfrac{\Delta Q}{Q}$} & \textbf{Elasticity}\\
\midrule
800-1000 & 152000 & 136000 & 0.2222 & -0.1111 & -0.50\\
1200-1350 & 120000 & 108000 & 0.1176 & -0.1053 & -0.89\\
1500-1800 & 562000 & 538000 & 0.1818 & -0.0436 & -0.24\\
\bottomrule
\end{tabular}
\caption{\textit{Price Elasticity of Demand}}
\end{table}
\end{frame}
%------------------------------------------------
\begin{frame}
\frametitle{The Demand Curves}
We draw VW's demand curves both before and after 1964 with the same slope.
\begin{figure}
\includegraphics[width=0.8\linewidth]{vw.png}
\caption{The Demand Curves}\label{fig:digit}
\end{figure}
\end{frame}
%------------------------------------------------
\begin{frame}
\frametitle{Question 4}
4. Raise one or two examples which you think the seller should set better price. And explain.\\~\\
\begin{itemize}
\item One exampe is \textit{Moutai}, whose demand curve is inelastic and whose demand is too high so that there is always a shortage of supply. In order to solve the shortage of supply problem and to maximize the revenue, it is better for the company to raise the price.
\end{itemize}
\end{frame}
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\begin{frame}
\Huge{\centerline{The End}}
\end{frame}
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\end{document}
