\makeatletter
\let\ifGm@compatii\relax
\makeatother
\documentclass[12pt]{beamer} %use for presentation
% \documentclass[12pt,handout]{beamer} %use for handouts

\setbeameroption{show notes} %uncomment to see notes
\usefonttheme{serif}

\usefonttheme{structuresmallcapsserif}

\newcommand{\its}{\vskip 10pt \item}
\newcommand{\pits}{\vskip 10pt \pause \item}
\newcommand{\st}{\operatorname{st}}
\newcommand{\var}{\operatorname{var}}
\newtheorem{prop}{Proposition}
\newcommand{\R}{\mathbb{R}}
\newcommand{\E}{\mathbb{E}}
\newcommand{\BR}{\operatorname{BR}}
%\newtheorem{theorem}{Theorem}
\newcommand{\un}{\underline}
\newcommand{\ov}{\overline}
\newcommand{\gp}{\succ}
\newcommand{\lp}{\prec}
\newcommand{\gep}{\succsim}
\newcommand{\lep}{\precsim}


\newcommand{\T}{\ensuremath{\mbox{\footnotesize\textsc{occupation}}}}
\renewcommand{\S}{\ensuremath{\mbox{\footnotesize\textsc{suicide}}}}
%\newcommand{\R}{\ensuremath{\mbox{\footnotesize\textsc{religious}}}}



\usepackage{graphicx}
\usepackage{ragged2e}



% -----------------------------------------
% Center the Frame Title
% -----------------------------------------

\setbeamertemplate{frametitle} {
\begin{centering}
\vspace{0.1in} \insertframetitle
\par
\end{centering}}

% -----------------------------------------
% Number the slides
% -----------------------------------------

\setbeamertemplate{footline}[frame number]

% -----------------------------------------
% Get rid of the irritating navigation bar
% -----------------------------------------

\setbeamertemplate{navigation symbols}{}

% -----------------------------------------
% Begin Document
% -----------------------------------------

\title[Information] % (optional, use only with long paper titles)
{The Need for Information}

\author{}
% \author{Ethan Bueno de Mesquita\\ \small{Harris School of Public Policy Studies}\\ \small{University of Chicago}}




\date[]% (optional, should be abbreviation of conference name)

% Delete this, if you do not want the table of contents to pop up at
% the beginning of each subsection:
\AtBeginSection[]
{
 \begin{frame}<beamer>{Outline}
   \tableofcontents[currentsection,currentsubsection]
 \end{frame}
}


% Delete this, if you do not want the table of contents to pop up at
% the beginning of each subsection:
\AtBeginSubsection[]
{
 \begin{frame}<beamer>{Outline}
   \tableofcontents[currentsection,currentsubsection]
 \end{frame}
}



\begin{document}

\begin{frame}
  \titlepage
\end{frame}


\begin{frame}{The Fundamentals}
	
	Benevolent government trying to implement Pareto efficient policies

\

	Population members have private information
		\begin{itemize}
			\item Personal preferences
			\item Effort choices
			\item Costs
		\end{itemize}
		
		\
		
	This private information is relevant for determining socially optimal policy

\

	Government needs to elicit citizens' private information

\

	Citizens may have a strategic incentive to lie

\end{frame}	

\begin{frame}{Mechanism Design}
	Design incentive scheme (i.e., a game) that extracts as much information as possible in equilibrium
	
	\
	
	Also concerned about the costs of extracting that information
	
	\
	
	Focus on mechanisms that induce good behavior in \textbf{weakly dominant strategies}
	
	\
	
		\begin{quotation}\noindent A strategy is  \textbf{weakly dominant} if it is a best response to any
profile of strategies by other players. \end{quotation}
\end{frame}
	
\section{Auctions}

\subsection{Private Value Auctions}
\begin{frame}{Private Values}
	
	Single asset to be allocated to one individual
		\begin{itemize}
			\item Spectrum
			\item Pollution rights
			\item Passage of a bill
		\end{itemize}

\

	Utilitarian Outcome: Prize goes to highest valuation player

\

	Bidders have private information about valuations
		\begin{itemize}
			\item Person $i$'s valuation is $v_i$
		\end{itemize}
\end{frame}

\begin{frame}{Just Ask}	
	
	Ask people their valuations
	
	\
	
	Give to highest claimed valuation
	
	\
	
	Induces lying
	\end{frame}
	
	\begin{frame}{First Price Auction}
		Bidders submit sealed bids
		
		\
		
		All bids are final

\

		Highest bidder wins prize and pays bid

\

		Losers pay nothing
\end{frame}
\begin{frame}{Is telling the truth weakly dominant?}
	
	Suppose player $i$ values prize $v_i > 0$

\

	If bid $v_i$ or higher, never have positive payoff

\

	If bid less than $v_i$, payoffs sometimes positive (and never negative) 

\

	Bidding $v_i$ not a best response to everyone else bidding their true valuation
			
	\
	
	Unless  players' valuations  drawn from exact same distribution,  positive probability of inefficient allocation
\end{frame}

	
	
	\begin{frame}{The Second Price Auction}
		Bidders submit sealed bids ($b_i$)

\

		Highest bidder wins prize and pays second-highest bidder's bid

\

		Losers pay nothing
	\end{frame}
	
	
\begin{frame}{Bidding $b_i = v_i$ dominates any bid $b_i' < v_i$}
	
	Suppose highest other bid, $B$, with $b_i' < v_i < B$ 
		\begin{itemize}
			\item Lose if bid $b_i'$ or $v_i$, so indifferent
		\end{itemize}
		
		\
		
	Suppose $b_i' < B < v_i$
		\begin{itemize}
		\item If bid $v_i$ payoff is $v_i - B > 0$
		\item If bid $b_i'$ payoff is 0
	\end{itemize}
	
	\
	
	
	Suppose $B < b_i' < v_i $
		\begin{itemize}
				\item Win and make payoff  $v_i - B > 0$ under either bid, so indifferent
			\end{itemize}
		\end{frame}
	
\subsection{Common Value Auctions}

\begin{frame}{Common Values}
	
	Single asset to be auction, that we all value equally, $v$
	
	\
	
	We are uncertain about value of the asset
		\begin{itemize}
			\item Foreclosed home
			\item Toxic financial asset
		\end{itemize}
		
	\
	
	Each person has some unbiased, private information about the likely value
	
	\
	
	Let's try such an auction
\end{frame}

\begin{frame}{Is bidding your value weakly dominant?}
	
	
If everyone is bidding their true belief, the winner's information must have been \emph{the most} positive

\

Since everyone's information is unbiased, this means that the winner's bid was probably too high 

\

The Winner's Curse
\end{frame}
\section{Regulating a Monopolist}

	\begin{frame}{The Fundamental Problem}
		
		The government needs to regulate a firm
			\begin{itemize}
				\item Monopoly
				\item Externalities
			\end{itemize}
			
		\
		
		The optimal regulation depends on information only the firm has
			\begin{itemize}
				\item Marginal cost of production
				\item Marginal cost of mitigating the externality
			\end{itemize}
			
		\
		
		In order to regulate well, the government must first extract information from the firm, which may have incentives to lie

\end{frame}

\begin{frame}{Implications}

Lack of information limits the government's ability to regulate well

\

The best the government can do (i.e., the second best)  involves the government behaving in ways that appear to favor a firm it legally shouldn't have to negotiate with 

\

Sometimes the government can improve matters by hiring an expert agent

\

Concern about the agent being ``captured'' by industry leads to new shifts in optimal regulatory policy
\end{frame}

\begin{frame}{Regulating a Monopolist}
	
	A graphical version of classic model 
	
	\
	
	Monopolistic firm decides quantity of production
	
	\
	
	Can hold down production to raise prices and profits 
	
	\
	
	This creates deadweight loss and so is not socially optimal
	
	\
	
	Regulator wants to require more production, but right level depends on firm's marginal costs, which are firm's private information
\end{frame}


\subsection{The Basic Model}

\begin{frame}{The Economy}
	
	Firm produces $q$ widgets at constant marginal cost $c$
	
	\
	
	If price is $p$, then firm profits are
	\[ \pi(p,q,c) = q(p-c).\]

	\

	Demand is linear in price:
	\[ D(p)  =100 -p.\] 

	\
	
	Equilibrium price, given production $q$ is:
	\[ p^*(q) = 100 - q.\]
\end{frame}


\begin{frame}{Consumer Surplus for Arbitrary $q$}
	\begin{figure}
		\begin{center}
			\includegraphics[width=\textwidth]{figures/price.pdf}
		\end{center}
		\end{figure}
	\end{frame}
	
\begin{frame}{Firm Profits for Arbitrary $q$}
	\begin{figure}
		\begin{center}
			\includegraphics[width=\textwidth]{figures/profits.pdf}
		\end{center}
		\end{figure}
	\end{frame}
	
\begin{frame}{Social Welfare}
	
	Utilitarian social welfare is consumer surplus plus firm profits
	

	\end{frame}	
	
	\begin{frame}{First Best: Price Equals Marginal Cost}
		\begin{figure}
			\begin{center}
				\includegraphics[width=\textwidth]{figures/so.pdf}
	\end{center}
			\end{figure}
		\end{frame}
		
\subsection{Monopolistic Equilibrium}

\begin{frame}{The Monopolist's Problem}
	
Monopolist maximizes profits:
	\[ \max_q q(p^*(q)  - c).\]

\

	Since $p^*(q) = 100 - q$, this is equivalent to solving
	\[ \max_q q (100 - q - c).\]

\

	\[ q^M(c) = \frac{100 - c}{2}.\]

\

	Price under a monopolist is
	\[ p^M = p^*(q^M(c)) = 100 - \frac{100-c}{2} =  \frac{100+c}{2}.\]
\end{frame}

\begin{frame}{Social Welfare with Monopolist}

\vskip 20pt
	Profits plus Consumer Surplus:

	\begin{figure}
		\begin{center}
			\includegraphics[width=\textwidth]{figures/monopolist-surplus.pdf}
			\end{center}
		\end{figure}
\end{frame}
	
	
	\subsection{Optimal Regulation with Full Information}
	
	\begin{frame}{Utilitarian Optimum}
		
		The monopolist maximizes profits, not social welfare
		
		\
		
		Holds down production
		 	\begin{itemize}
				\item Increases profits and reduces consumer surplus
			\end{itemize}
		
		\
		
		The increase in profits is more than off-set by the reduction in consumer surplus
		 	\begin{itemize}
			\item Deadweight loss
		\end{itemize}
		
		\
		
		So the utilitarian optimum involves higher production, less profits, and more consumer surplus
	\end{frame}
		
	\begin{frame}{First Best: Price Equals Marginal Cost}
		\begin{figure}
			\begin{center}
				\includegraphics[width=\textwidth]{figures/so.pdf}
	\end{center}
			\end{figure}
		\end{frame}


\subsection{Introducing Private Information}

\begin{frame}{Unknown Marginal Costs}

Government uncertain whether firm has high ($c_H$) or low $(c_L)$ marginal costs

\

The probability   marginal costs are low is $\lambda\in (0,1)$

\

The government can regulate the firm, but cannot force the firm to operate at a loss
\end{frame}

\begin{frame}{What the Government Would Like To Do}

\begin{figure}
	\begin{center}
		\includegraphics[width=\textwidth]{figures/fb-2.pdf}
\end{center}
	\end{figure}
\end{frame}

\begin{frame}{Attempting the First-Best Results in Manipulation} 
	
	Ask firm its marginal costs, then implement first-best policy assuming the answer  is truthful
		
	\
	
	High marginal cost firm has no incentive to lie
		\begin{itemize}
			\item If claim costs are low, forced to do more production for a lower price
		\end{itemize}
		
		\
		
		Low marginal cost firm will lie
			\begin{itemize}
				\item Claim to have high costs, do less production for higher price
				\its Positive profits
			\end{itemize}
		\end{frame}


\begin{frame}{Low Marginal Cost Firm's Incentive to Lie}
\begin{figure}
	\begin{center}
		\includegraphics[width=\textwidth]{figures/No-IC.pdf}
\end{center}
	\end{figure}
\end{frame}

\subsection{The Second Best}

\begin{frame}{Using Transfers to Induce Truth Telling}
\begin{figure}
	\begin{center}
		\includegraphics[width=\textwidth]{figures/with-transfers.pdf}
\end{center}
	\end{figure}
\end{frame}	


\begin{frame}{Distortionary Transfers}
	
	

A one dollar transfer from the consumers to the firm costs the consumers $\tau >1$ 

\

Government can transfer profits from firms to consumers without loss (i.e., 1 for 1)
	\begin{itemize}
		\item This is a simplification but it has an intuition
		\its Government can use revenue collected from firms as a
substitute for revenue from more distortionary tools (e.g., income or
sales taxes)
	\its Moving money from firms to consumers is less distortionary
\end{itemize}
\end{frame}

\begin{frame}{Reducing Transfers}
	
Achieving full truth telling by low marginal cost firm involved large,  distortionary transfers 

\

How can the government reduce distortionary transfers while still getting information?

\

Make lying less attractive by reducing profits from claiming to be high marginal cost
\end{frame}

\begin{frame}{Making Lying Less Attractive}

 Reduce the amount produced by a firm claiming to have high marginal costs
	\begin{itemize}
		\item This leaves some profits even to a high marginal cost firm
	\end{itemize}
	
	\
	
	Transfer the profits a high marginal cost firm would make to consumers
	 	\begin{itemize}
			\item This is non-distortionary
			\end{itemize}
			
	\
	
	Leaves high marginal cost firm with exactly zero profits and reduces  attractiveness of  lying for a low marginal cost firm
\end{frame}

\begin{frame}
\begin{figure}
	\begin{center}
		\includegraphics[width=.9\textwidth]{figures/with-transfers-2.pdf}
\end{center}
	\end{figure}
	
	If $c_H$: reduce to $q_H' < q_H$ and transfer $B$ to consumers
	
	\
	
	If $c_L$: $q_L^{FB}$ and transfer $D$

\
	

 GOOD: Truth-telling by $c_L$ transfering $D$ instead of  $D+E$ 

\

 BAD: Deadweight loss of $C$ when $c_H$
	


\end{frame}


\begin{frame}{Some Notation}
	The first-best social welfare with full information, if $c_L$
\[ \Delta_L = A+B+C+D+E+F.\]

The first-best social welfare with full information, if $c_H$
\[\Delta_H = A+B+C.\]
\end{frame}

\begin{frame}{Social Welfare Under Policy $q_H'$ and Transfers}

For any given $q_H'$, the total social surplus if the firm has low marginal costs is
\[ \Delta_L + D(1-\tau).\]

\

If firm has  high marginal costs
	\begin{itemize}
		\item Consumer surplus: $A +B$ 
		\its Firm profits: 0
	\end{itemize}

\

If firm has high marginal costs, total social surplus is first-best social surplus minus deadweight loss:
		
\[ \Delta_H-C\]

\end{frame}

\begin{frame}{Social Welfare, continued}
	
	Probability firm  has low marginal costs is $\lambda$
	
	\
	
	Expected social welfare under our  policy  is
\[ U(q_H') = \lambda(\Delta_L + D(1-\tau)) + (1-\lambda)(\Delta_H -C)\]

\

Note that we can calculate $D$ and $C$ as functions of $q_H'$ and substitute (see the book)

\[D = q_H'(q_L^{FB} - q_H^{FB})\]

\[C = \frac{(q_H^{FB} - q_H')^2}{2}\]

\end{frame}

\begin{frame}{The Second Best}

\[ \max_{q_H'} U(q_H')\]

\

\[ q_H^{SB} = q_H^{FB} +\frac{\lambda}{1-\lambda}(1-\tau)(q_L^{FB} - q_H^{FB}).\]


\

Second-best  production by  high marginal cost firm is  lower than  first-best production
 \begin{itemize}
	\item Larger is $\tau$, the lower is the second-best level of production by $c_H$
	\its Smaller is $\lambda$, the larger is the second-best level of production by $c_H$
\end{itemize}

\end{frame}

\begin{frame}{The Costs of Informational Deficits}

 Deadweight loss due to underproduction by high marginal cost firms

\

 Distortionary transfers by the government from consumers to low marginal cost firms
\end{frame}

\begin{frame}{The Power of Information}
		
		The transfers to  low marginal cost firm result in positive firm profits
		
		\
		
	Government has legal authority to regulate monopolies,  but we nonetheless will observe  negotiations with monopolistic firms over the terms of regulation 
			
		\
		
		One might interpret this 
 as failure to exercise  authority or  evidence of  malfeasance

\

But it could actually be optimal policy given that the firm has information the government needs  to exercise its regulatory authority effectively
\end{frame}
\section{Take Aways}

\begin{frame}{Take Aways}
	
	Making Pareto-improving policy often requires information that the policy maker doesn't have. 
	
\

 When relevant information resides with interested parties, the policy maker must design incentives for those parties to reveal the information. 

\

The challenge is that, revealing its information may sometimes lead to disadvantageous policy responses for a given party, giving that party an incentive to lie or fail to reveal information. 
	
\

 Informational asymmetries place an additional second-best constraint on how much good can be done through policy.

\end{frame}


		 \end{document}