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\noindent
7 March 2005. Eric Rasmusen, Erasmuse@indiana.edu.
Http://www.rasmusen.org. Comments welcomed.
\begin{LARGE}
\begin{center}
{\bf Regulatory Ratcheting: A Classroom Game for Chapter 10}
\end{center}
\end{LARGE}
\bigskip
\noindent
{\bf The Rules of the Game}
Electricity demand is perfectly inelastic, at 1 gigawatt per firm.
The price is chosen by the regulator. The regulator cares about two
things: (1) getting electrical service, and (2) getting it at the
lowest price possible.
The utilities like profit and dislike effort. Throughout the game,
utility $i$ has ``cost reduction'' parameter $x_i$, which it knows but
the regulator does not. This parameter is big if the utility can
reduce its costs with just a little effort.
\noindent
Each year, the following events happen.
\noindent
1. The regulator offers price $P_i$ to firm $i$.
\noindent
2. Firm $i$ accepts or rejects.
\noindent
3. If Firm $i$ accepts, it secretly chooses its effort level $e_i$,
\noindent
4. Nature secretly and randomly chooses the economywide shock $u$
(uniform from 1 to 6) and Firm $i$'s shock $u_i$ (uniform from 1 to
6) and announces Firm $i$'s cost, $c_i$. That cost equals
\begin{equation}
c_i = 20 + u + u_i - x_i e_i.
\end{equation}
\noindent
5. Firm $i$ earns a period payoff of 0 if it rejects the contract.
If it accepts, its payoff is
\begin{equation}
\pi_i = p_i (1) - c_i - e_i^2
\end{equation}
The regulator earns a period payoff of 0 from firm $i$ if its
contract is rejected. Otherwise, its payoff from that firm is
\begin{equation}
\pi_{regulator} (i) = 50 - p_i
\end{equation}
All variables take integer values.
The game repeats for as many years as the class has time for, with
each firm keeping the same value of $x$ throughout.
\newpage
\bigskip
\noindent
{\bf The Mechanics}
Each electric utility is a group of three students.
Either the instructor or a group of 1 to 3 students is Nature. At
the
start of the game, Nature gives each utility a card showing its cost-
reduction parameter, where equal number of cards have $x$ equal to 3
or to 5.
At the same time, Nature writes down the parameters
for each firm for later use.
Utilities announce publicly whether they accept the regulator's
price, but they secretly write down their effort level and give it to
Nature. Nature then secretly picks $u$ to be equal to the roll of a
die, and secretly picks $u_i$ for each firm by rolling the die more
times. Nature then reveals the $c_i$ for each firm. This can be done
all at once, or one by one as each firm submits its effort level.
Nature also writes down $u$, $u_i$, and $c_i$ on an overhead slide,
which can be shown to everyone at the end of the game, if an overhead
projector is used (this is not crucial).
Either the instructor or a group of 5 students is the Regulator. If
a student group is the regulator, that will slow down regulation
considerably, but it does permit the instructor to be Nature. If the
instructor is the Regulator, he should not be Nature, since it is
essential to the game that the Regulator not know what effort each
firm has chosen.
The Regulator displays Table 3 on an overhead slide (or on the
blackboard). Each round, the Regulator writes down $P_i$ for each
firm, and then $c_i$ or $REJECT$, so everyone can see what has
happened.
\newpage
%\begin{LARGE}
\vspace*{-24pt}
\noindent
\hspace*{-72pt}Your Names: \hspace*{48pt} Your Firm:
\hspace*{48pt} Your Cost-Reduction Parameter $x$:
\vspace{32pt}
\hspace*{-72pt}
\begin{tabular} {| l | l| l| l | l| l| }
\hline
& & & & & \\
Year & Price Offered & (Effort $e$) or REJECT & Cost $c$ & Profit&
Cumulative Profit\\
& & & & & \\
\hline
1 & & & & & \\
\hline
2 & & & & & \\
\hline
3 & & & & & \\
\hline
4 & & & & & \\
\hline
5 & & & & & \\
\hline
6 & & & & & \\
\hline
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\hline
10 & & & & & \\
\hline
\end{tabular}
\begin{center}
{\bf TABLE 1: ELECTRIC UTILITY SCORESHEET }
\end{center}
Profit equals zero if the firm chose REJECT. If it did not, profit is
(Price minus Cost minus Effort Squared).
Cumulative Profit is the sum of the firm's profits in that industry
up to and including that period.
% \end{LARGE}
\newpage
\newpage
%\begin{LARGE}
\vspace*{-24pt}
\noindent
\hspace*{-72pt}Your Names:
\vspace{32pt}
\hspace*{-72pt}
\begin{tabular} {| l | l| l| l | l| l|l| }
\hline
& & & & & & \\
Year & Shock $u$ & Firm & Parameter $x_i$ & (Effort $e_i$) or
REJECT
& Shock $v_i$ & Cost $c_i$ \\
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\end{tabular}
\begin{center}
{\bf TABLE 2: NATURE'S SCORESHEET }
\end{center}
% \end{LARGE}
\newpage
%\begin{LARGE}
\vspace*{-24pt}
\noindent
\hspace*{-72pt}Your Names:
\vspace{32pt}
\hspace*{-72pt}
\begin{tabular} {| l | l| l| l | l|l| }
\hline
& & & & & \\
Year & Firm & $P_i$ & Cost $c_i$ & 50 if ACCEPT; 0 Otherwise
& $-P_i$
if
ACCEPT; 0 Otherwise \\
& & & & & \\
\hline
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TOTALS: & xxxxx & xxxxx & xxxxx & & \\
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\hline
\end{tabular}
\noindent
{\bf Overall Payoff}:
\begin{center}
{\bf TABLE 3: REGULATOR'S SCORESHEET }
\end{center}
% \end{LARGE}
\newpage
\bigskip
\noindent
{\bf Instructor's Notes }
Equipment: Two six-sided dice. Index cards with cost parameters, half
of them with ``x=3'' and half with ``x=5''.
This is a complicated game, not one of the easiest to make work,
because students take some time to become accustomed to how their
effort affects their profit. It would work best as an online game,
played by email, since that would give the players (especially the
regulator) plenty of time to think.
Before starting play, the instructor needs to work out some examples
of what a firm's profit will be if it has $x=3$ and accepts a given
price.
If the instructor is the regulator, he should think out loud as he
decides his
prices for each firm.
The maximum cost is 32. The expected cost with zero effort is 26.
The minimum cost with zero effort is 22.
\noindent
{\it Strategy Note:} If your firm has a high value of $x$, it is
lucky, because it doesn't have to exert as much effort to get the same
cost reduction. If the regulator figures that out, however, he will
offer you a low price, eliminating your profits. That is the ``ratchet
effect''. Thus, you must think carefully about whether your actions
will reveal your cost advantage.
\newpage
\begin{LARGE}
\noindent
{\bf Lessons: }
\noindent
(1) A regulator must be careful not to set prices too low, or firms
will not replace their capital.
\noindent
(2) If a regulator finds that a firm can reduce its cost, it will
lower the price the firm is offered (the ``ratchet effect'').
\noindent
(3) It is hard to figure out a firm's cost reduction possiblities
from
observing its actual costs, because there are a lot of random shocks
to costs.
\noindent
(4) Firms will try not to reveal their abilities to keep costs low,
pretending to be less efficient than they really are.
\noindent
(5) If firms do not worry about future price reductions (as in a last
period) they will reduce costs more.
\noindent
(6) This same game fits government procurement. When the government
buys airplanes from a company, it tries to set the price as low as it
can such that the firm will still accept the contract. Once the order
is placed, the government and seller are in bilateral monopoly, since
it would be inefficient to switch to a second seller that would need
to incur the big fixed cost of R \& D again. When the contract is
renewed for further purchases, the government will try to reduce the
price if it thinks it overestimated the seller's costs the first time
round.
\end{LARGE}
\end{document}