   \documentstyle[12pt,epsf] {article}

 

\reversemarginpar

   \topmargin  -1in

  \oddsidemargin .25in

  \textheight  9.4in

 \textwidth 6.4in  



    

\input{tcilatex}



    

         \begin{document}

 

  \parindent 24pt

\parskip 10pt



 



\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

7 &  &    &   &  &    \\

\hline

8  &  &    &   &  &    \\

\hline

9 &  &    &   &  &    \\

\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 $c_i$  \\

 &  &    &   &  &  &  \\

\hline

  &  &    &   &  & &   \\

\hline

  &  &    &   &  &  &  \\

 \hline

 &  &    &   &  &  &  \\

\hline

  &  &    &   &  & &   \\

\hline

  &  &    &   &  &  &  \\

 \hline

 &  &    &   &  &  &  \\

\hline

  &  &    &   &  & &   \\

\hline

  &  &    &   &  &  &  \\

 \hline

 &  &    &   &  &  &  \\

\hline

   &  &    &   &  & &   \\

\hline

  &  &    &   &  &  &  \\

 \hline

 &  &    &   &  &  &  \\

\hline

  &  &    &   &  & &   \\

\hline

  &  &    &   &  &  &  \\

 \hline

 &  &    &   &  &  &  \\

\hline

   &  &    &   &  & &   \\

\hline

  &  &    &   &  &  &  \\

 \hline

   &  &    &   &  & &   \\

\hline

  &  &    &   &  &  &  \\

 \hline

 &  &    &   &  &  &  \\

\hline

  &  &    &   &  & &   \\

\hline

  &  &    &   &  &  &  \\

 \hline

 &  &    &   &  &  &  \\

\hline

   &  &    &   &  & &   \\

\hline

  &  &    &   &  &  &  \\

 \hline

   &  &    &   &  & &   \\

\hline

  &  &    &   &  &  &  \\

 \hline

 &  &    &   &  &  &  \\

\hline

  &  &    &   &  & &   \\

\hline

  &  &    &   &  &  &  \\

 \hline

 &  &    &   &  &  &  \\

\hline

   &  &    &   &  & &   \\

\hline

  &  &    &   &  &  &  \\

 \hline

\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

    &  &    &   &   &   \\

\hline

  &  &    &   &   &   \\

\hline

 &  &    &   &    &  \\

\hline

    &  &    &   &   &   \\

\hline

  &  &    &   &   &   \\

\hline

 &  &    &   &    &  \\

\hline

    &  &    &   &   &   \\

\hline

  &  &    &   &   &   \\

\hline

 &  &    &   &    &  \\

\hline

    &  &    &   &   &   \\

\hline

  &  &    &   &   &   \\

\hline

 &  &    &   &    &  \\

\hline

    &  &    &   &   &   \\

\hline

  &  &    &   &   &   \\

\hline

 &  &    &   &    &  \\

\hline

    &  &    &   &   &   \\

\hline

  &  &    &   &   &   \\

\hline

 &  &    &   &    &  \\

\hline

    &  &    &   &   &   \\

\hline

  &  &    &   &   &   \\

\hline

   &  &    &   &   &   \\

\hline

  &  &    &   &   &   \\

\hline

 &  &    &   &    &  \\

\hline

    &  &    &   &   &   \\

\hline

  &  &    &   &   &   \\

\hline

 &  &    &   &    &  \\

\hline

    &  &    &   &   &   \\

\hline

  &  &    &   &   &   \\

\hline

 &  &    &   &    &  \\

\hline

    &  &    &   &   &   \\

\hline

  &  &    &   &   &   \\

\hline

  &  &    &   &   &   \\

TOTALS:  & xxxxx & xxxxx   & xxxxx   &    &  \\

    &  &    &   &   &   \\

\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}