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\pagestyle{fancy} \lhead[\ref{chap07}--\thepage]{}    \chead{Natural Monopoly}   \rhead[]
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%\vspace*{\fill}

  \begin{center}
\begin{Huge}
{\bf \ref{chap07}: Natural Monopoly} \label{s07.0}   \\

\end{Huge}





  \end{center}


\vspace*{\fill}
\begin{bigquote}
%\begin{Large}
\noindent
(From {\it The Simpsons} TV cartoon):\\
 {\it {\sc  Mr.  Burns [menacing]:} ``I want that oil well.  I've got a monopoly to maintain!  I own
the electric company, and the water works ---plus the hotel on Baltic Avenue!''\\
 \hspace{1in}\\
{\sc  Principal  Skinner:} ``That hotel's a dump and your monopoly's pathetic.  This school's oil
well is not for sale, particularly to a blackhearted scoundrel like yourself.''
 }\\
%\end{Large}
 \end{bigquote}

\vspace*{\fill}

 \includegraphics[width=\linewidth]{fig07-octopus.jpg}



\vspace*{\fill}

{\small \hfill {\it    February 21, 2019}}\\


{\small \hfill  \url{http://rasmusen.org/g406/reg-rasmusen.htm}, erasmuse@Indiana.edu}


%------------------------------------------------------
 \newpage



  \noindent
 {\bf \ref{chap07}.1:  Introduction} \label{s07.1}



    Antitrust laws can't deal with all situations of monopoly.   Consider the following scenario:

\begin{bigquote}
 National Electric Company   has been serving Springfield for many years. It buys power from various
companies on the national power grid, and resells it to home and business customers in Springfield
using the company's network of underground cables. National pays a lot to maintain its cable system,
but it is a profitable company and it pays a 10\% dividend each year, even though most companies
only show  a 5\% return on capital. No other company even tries to sell electricity in Niceville.



  The new mayor of Springfield calls for the state Attorney-General to crack down on National.
``National is an obvious monopoly,'' he says. ``They are making monopoly profits, and they should be
broken up. If we had three different electrical companies competing, then service would be better
and rates would be lower.'' National's CEO replies, ``No--- to break us up would be disastrous. It
would result in destructive competition and heavy losses for all three companies, because we would
compete prices down to where we couldn't cover our investments in plant and equipment.   And it
would be silly to have each home served by three underground cables, when it only buys from one
electric company at  a time. Leave well enough alone.''
\end{bigquote}

    The mayor has a point. National is charging above marginal cost, so output is inefficiently low,
as we've already discussed in the previous chapter. But the CEO has a point too. If there were three
companies laying down and maintaining cable, costs would increase. So what should happen?


 This question is important. Electricity is a big business. Mostly it is sold by utilities,
companies which generate, transmit, and distribute electricity to consumers.  There are    3,273
traditional electrical utilities in the USA--- 210 investor-owned,  2,009 state and local, and 9
Federal  electric utilities, and  883   rural electric cooperatives.  There are also 1,738
nonutility power producers, the most important of which are  investor-owned companies that sell only
wholesale. These nonutilities do not have  regulated prices or  retail franchise territories.
Electricity companies vary tremendously in size. 38\% of the gigawatt capacity is from investor-
owned utilities, 9\% state-and-local, 7\% federal, 4\% cooperatives,  and 42\%
nonutilities.\footnote{U.S. Energy Information Administration (EIA), ``Electric Power Industry
Overview 2007,  ''\url{http://www.eia.doe.gov/electricity/page/prim2/toc2.html}. }
  It isn't just in  electricity that  it seems more efficient to have just one big supplier instead
of competition.  People have favored concentration of production in water, supply, railroads, mass
transit, schools, and steel mills.   There are lots of situations where it seems as if it's more
efficient to have one big company---or one big government agency---producing everything. In this
chapter, we'll try to figure out when ``big is  better''\index{big is  better} means we should allow
monopolies  but ``Monopolies restrict output''\index{Monopolies restrict output} means we should
regulate them.  It will turn out that we have to look carefully at each situation, and in this
chapter you'll learn what to look for to decide when monopoly is inevitable and when regulation is
helpful.



When should the  government decide  it is best for society to allow monopolies, but to regulate
them?



   Most of anti-trust law is devoted to preventing artificial monopolies---to prevent industries
that would otherwise be competitive from acting as monopolies.  If the government bans bad practices
such as price agreements, then the market will settle down to the natural equilibrium that maximized
social surplus, and companies will voluntarily choose to use efficient methods of production.

  Such reasoning assumes  that  the cost curves for the industry are U-shaped, so  average cost
first rises and then falls with output. If average cost falls with output, then the bigger the firm,
the lower its average cost.  Take a look at figure \ref{chap07}.\ref{fig07-0ushaped.pdf}, which
shows three different kinds of cost curves.


%\vspace*{24pt}
\begin{center}
\begin{minipage}[c]{\linewidth}
\begin{center}
 {\sc Figure \ref{chap09}.\ref{fig07-0ushaped.pdf}\\
   Three Kinds of Cost Curves } \\

\refstepcounter{figurecounter} \label{fig07-0ushaped.pdf}
 \includegraphics[width=\linewidth]{Figure07-01.jpg}
\end{center}
\end{minipage}
\end{center}
% \vspace*{-24pt}

  In Figure  \ref{chap07}.\ref{fig07-0ushaped.pdf}(a) the average-cost curve is U-shaped. If every
company has this cost curve, then the cheapest way to produce 200 units of electricity is to have
two different companies produce 100 units each, rather than one company producing 200. If they each
produce 100, they could charge  a price of \$20/unit  and break even. If one firm operated as  a
monopoly, it would produce less, charge more, and have higher costs than necessary. If two firms
operated as a cartel, they would keep costs lower, but they would still choose to produce less than
200 units so as to drive up the price and maximize their own profits. Antitrust law which encouraged
entry and discouraged price cooperation would help move the the outcome closer to the ideal of two
firms producing 100 units each. If the two firms could not cooperate, their competition would not
drive the price down all the way to \$20/unit and output all the way to 200 units. Since there are
only two of them, competition wouldn't force prices all the way down to zero profits, but
competition would at least limit  their ability to operate inefficiently and to raise prices.

In Figure  \ref{chap07}.\ref{fig07-0ushaped.pdf}(b) the average-cost curve is falling over its
entire length, and the marginal cost curve is flat.  This means   the company has a large fixed cost
but constant marginal cost; it has to pay for overhead, but its extra production cost to produce an
extra unit is always the same, no matter  how much it produces. Thus, the bigger a company's sales,
the lower its average cost.


In Figure   \ref{chap07}.\ref{fig07-0ushaped.pdf}(c) the average-cost curve is  falling over its
entire length,  as in Figure \ref{chap07}.\ref{fig07-0ushaped.pdf}(b), but  the marginal cost curve
is also falling. Moreover, the average and marginal costs start out the same. This means that the
firm has no fixed cost. The first unit's average cost is the marginal cost plus the entire fixed
cost, so if the first unit's average cost equals its marginal cost, the fixed cost must be zero.
As the firm produces more output, though, the cost of each extra unit falls, so the average cost is
dragged down as we average in the new cheaper units.

We say there are {\bf economies of scale}\index{economies of scale} whenever average cost falls with
output.
Average cost can fall for two reasons: because a fixed cost is averaged over more and more units, or
because the marginal cost is falling.  It's also possible to have a fixed cost and falling marginal
cost. A  good exercise is to try to  draw a new figure  to illustrate that.

  Now let's get back to the monopoly problem. We'll use the industry in Figure
\ref{chap07}.\ref{fig07-0ushaped.pdf}(c) for illustration. Suppose there are two firms in the
industry  and we think about having them compete price down to marginal cost and split the market,
our usual ideal. What would happen?

    The problem is that our usual equilibrium conditions of price equalling marginal cost and zero
profits are contradictory. Suppose the price equals marginal cost, and the firms split the market,
at outputs of 50 each. For one thing, the price will be below average cost, so each firm will make a
loss. For another thing, one of the firms would deviate by cutting its price, so it could increase
its market share, since with the increased output, its marginal cost would be lower and it would
profit from the extra sales. Whichever firm is bigger will have a cost advantage. So we would expect
a costly war of attrition as the two firms each struggled along making losses in the hopes that the
other firm would drop out, leaving it free to raise prices drastically as a monopoly.

   In addition, our earlier finding that   competition maximizes social surplus wouldn't apply. If
you were a  social planner, would you want to have two small firms split the market? No. Instead,
because there are economies of scale   you would want one big firm to operate and produce the same
output  but at lower cost.

\bigskip
\noindent
{\bf Network Externalities}

  Economies of scale are a supply-side reason for economies of scale. There is also a demand-side
reason: {\bf  network externalities.}\index{network externalities}  Network externalities are
present when buyers are willing to pay more for a product if they expect   other people to buy it
too. Telephone service is an example. It is useless to be the first person in the world to own a
telephone.  There is nobody else to call! The more people with telephones,  the more valuable it is
to own a telephone yourself. This was true in the early days of telephone  and it is true of
cellphones today.  If more of your friends have cellphones and are texting messages to each other,
that increases your willingness to pay for a cellphone yourself.


 Many information products are natural monopolies. Microsoft Windows dominates the operating system
market because if everybody else uses Windows, you want to use it yourself. Even if it costs more
or doesn't work as well, more software applications will be written for it because it's so popular.
Thus, there are network externalities. In addition, software in general has high fixed costs of
production-- the cost of developing it---and   low marginal cost---the cost of copying  and
marketing it.  We frequently see wars of attrition as companies introduce competing new products
knowing that whoever grabs  the biggest market share   first will get the entire market.

 \bigskip
\noindent
{\bf  \ref{chap07}.2: Solutions to Natural Monopoly} \label{s07.2}

 There are several policies to deal with natural monopoly.

\noindent
1.
  Just let it be an unregulated monopoly.

\noindent
2.
  The government sells  a license to be the unregulated monopoly in that industry.

\noindent
 3.
  Government ownership

\noindent
4.
  Marginal-cost pricing plus a subsidy

\noindent
5. Price caps

\noindent
 6.   Average-cost pricing

\bigskip
 We'll go through these one by one.

 \bigskip

\noindent
 {\bf   Unregulated Monopoly  }

     Just because there is market failure does not mean that the government should regulate the
industry. What will happen if the government does nothing? As just discussed, there may be a {\bf
war of attrition} \index{war of attrition} as several companies battle it out to be the surviving
monopoly.  Once it is clear which company will survive, it will operate as a monopoly. In  figure
\ref{chap07}.\ref{fig07-1methods.pdf}, the company has a fixed cost of \$300 and a constant marginal
cost of \$10.   If it is an unregulated monopoly, it will use the standard rule of maximizing profit
by choosing quantity to equate marginal revenue to marginal cost, which happens at a quantity of 80
and a price of \$20. That is less than the quantity which maximizes social surplus, 160, which
consumers would buy if the price equalled \$10, which is the marginal cost at Q=160.



\begin{center}
 \noindent
 \begin{minipage}[c]{.8\linewidth}
\begin{center}
 {\sc Figure \ref{chap07}.\ref{fig07-1methods.pdf}\\
Regulated and Unregulated Natural Monopoly  } \\
\refstepcounter{figurecounter} \label{fig07-1methods.pdf}
 \includegraphics[width=\linewidth]{Figure07-02.jpg}

  \end{center}
 \end{minipage}
\end{center}
%\vspace*{24pt}


 The bad things about not regulating are the usual bad things about monopoly:  too little trade
because the monopoly wants to force up the price, rentseeking to acquire the monopoly (that war of
attrition), and possible operating inefficiency because the company that has the monopoly might have
higher costs than a  potential rival.  In addition, a lot of the social surplus would go to the
seller instead of to buyers, which is bad if you value the welfare of consumers more than of
sellers, or if you don't like the idea of monopolists being rewarded for bad behavior.

 The good thing about not regulating is that it avoids the possibility of government failure.  As we
will see shortly in talking about the other policies towards natural monopoly, it is easy for the
government to make the wrong choices, and also tempting when so much money is at stake. We have to
balance the costs of market failure against the dangers of government failure.

This may explain why governments follow the ``do nothing'' policy with  information industries that
are natural monopolies.  The downside of monopoly is not so great when the product is a software
application instead of electricity, because software is an innovative industry where new products
are constantly appearing.   Microsoft may have a natural monopoly, with high profits, from MS-Word,
but consumers do have access to other word-processing applications and Microsoft always faces the
threat of some superior word-processing application being developed. Also, price regulation is a
slow and cumbersome process, and the mere administration of it would be difficult with such a
differentiated product  as software. Finally, monopoly profits are actually a good thing in
innovative industries, because we want to encourage companies to create new products by giving them
the prize of monopoly profits.

   Electricity distribution is different.  There is innovation, but it's in the production
technology, not the product. Electrons  are  electrons.   Demand is inelastic--insensitive to price,
with a steep demand curve.  Hence, a monopoly has a lot of market power, a lot of  profits, and a
lot of political power.  Leaving the monopoly unregulated is a bad idea.


 \bigskip

\noindent
 {\bf   Franchise Bidding }

 Monopolies have high profits, and restrict sales. If we're willing to accept the restriction of
sales, we can deal with the high profits by just taking them away.  The government could do this by
taxing the electricity monopoly enough to take away its profits. That, however, raises the question
of how the government knows how much to tax the monopoly. It could examine the monopoly's books, or
tax the dividends it pays.

A clever solution, known as {\bf franchise bidding} \index{franchise bidding} is to  sell the right
to be the monopoly by auction. The Niceville government could announce that whichever company paid
the biggest lump sum at an auction would have the exclusive right to   sell electricity in
Niceville. This turns the rentseeking to good use. If all potential companies had the same costs,
they would all bid amount $  80(\$20-\$10)- \$300= \$500$ in figure
\ref{chap07}.\ref{fig07-1methods.pdf}, and the government would choose one of them as a tiebreaker.
The company would charge the monopoly price, but its net profit, after subtracting the auction
payment, would be zero. And there would be no destructive war of attrition.

Even better, if one firm had lower costs than the others, it would be willing to bid higher. So this
method would select the lowest-cost company.

 A variant on this is to have each company's bid take the form of the price it would charge for
electricity.  The company that won would not have to pay anything to the government, but it would
have to charge buyers the electricity price it submitted in the auction.  Again, this would select
the lowest-price seller. In figure  \ref{chap07}.\ref{fig07-1methods.pdf}, the price would be \$12,
equal to average cost so that the profit was zero. No company would offer a lower price, since it
would make negative profits, and any company that tried to offer a higher price would be underbid.

    Of course, once one company is established, if the license comes up for renewal that company
will have a big advantage in the auction.  Thus, it makes more sense for new products such as cable
TV was in the 1980's than for old products such as electricity.


\bigskip

\noindent
 {\bf   Government Ownership }\index{Government Ownership}


 Socialism refers to a system of government in which the government produces goods and services.
There are varying degrees of socialism. In practically all modern countries, the government provides
roads. In most, it provides education, for free (grade schools) or for tuitition (at state
universities), often in competition with private-sector for-profit and non-profit companies. In
some, the government owns airlines, steel mills, and stores, though with the fall of Communism in
the 1990's  and privatization in many   countries that were partly socialist but not Communist this
has become less common.\footnote{One might also say an economy is socialistic if the government
makes the decisions of the firm that a board of directors or executive would otherwise make, even if
ownership in the sense of receiving some or all of the profits  is left to private  individuals.}


\begin{wrapfigure}{L}{2.4in}
\begin{center}
 {\sc  Figure  \ref{chap07}.\ref{fig07-2-davies77.pdf}\\
\href{
http://www.jstor.org/stable/725095}{ Government vs. Private Airlines}  }
 \end{center}
\refstepcounter{figurecounter}   \label{fig07-2-davies77.pdf}
 \includegraphics[width=\linewidth]{fig07-2-davies77.pdf}
\end{wrapfigure}




    Government failure means that governments generally will not provide goods and services at as
low costs as private companies, and they will be tempted to use laws and regulations to favor the
government companies at the expense of private competitors.   It has gone out of favor to have
governments owning steel mills and car companies. The U.S. government's acquisition of shares in General Motors, Chrysler, Citigroup, and AIG in 2009 was a desperate measure during the financial crisis, and the government sold its shares as soon as it felt the economy was stable again. 

In the case of industries that are not natural monopolies, private ownership is an easy policy
decision. It avoids government failure either via inefficient government operation or inefficient
government regulation. But in the case of a natural monopoly like electricity distribution,
government ownership might be the lesser of evils. Perhaps costs will be higher than for a private
company, but the government enterprise at least could set the price equal to marginal cost, and
cover the resulting losses (since $P <AC$ in that case) using revenue from income taxes. The price
would be \$10 and the subsidy would equal area  (\$11-\$10)(160) = \$160 in figure
\ref{chap07}.\ref{fig07-1methods.pdf}.

 Or, if government operation leads  to higher marginal costs, the marginal cost curve in figure
\ref{chap07}.\ref{fig07-1methods.pdf} would rise, and   there would be  a rectangle of   surplus
loss consisting of the amount of increase in the marginl cost times the quantity sold. Since the higher marginal cost would also lead to a
higher price, this would in the end lead to a lower quantity than under private ownership and $P=MC$,
so we would also lose some consumer surplus from underproduction.

 We also would have to worry about providing a service that should not be provided at all. It might be that consumers would pay a price equal to marginal cost for a product, but would drop the product entirely if the price rose to average cost.  Suppose government phone service  has an average cost of \$30/month and a marginal cost of \$5/month, while private cellphone service has marginal cost equal to average cost equal to \$10 month. If the government charged \$5/month, everybody would use its phone service, but for surplus maximization we want people to use cellphones instead. If the government charged average cost instead of marginal cost, it would discover this quickly and leave the phone business. Charging marginal cost, it might never realize how little consumers value the product.\footnote{Ronald Coase made this argument in the 1940's as a response to Harold Hotelling's 1930's proposal to use marginal cost pricing. An excellent  discussion is   at  Brett M. Frischmann and Christiaan Hogendorn (2015) ``The Marginal Cost Controversy,'' {\it 
 Journal of Economic Perspectives}, 29:193–206.}



   The very fact that the government can cover losses using tax revenue    should lead us to expect
problems with cost and quality, and perhaps inefficiently low prices, and regulations to protect
against low-cost private-sector competitors. Consider garbage collection, an industry that is
government-owned in many cities.   The government officials running the garbage operation  may well
find it easier to lobby   for extra subsidies than to find ways to save costs or to incur the anger
of unionized workers  by trying to reduce pay. Remember, too, that those workers are also voters.
The  officials also can expect little reward for saving so much on costs that they can return part
of the subsidy that is supposed to cover their loss. And if some competitor to city garbage
collection is provided by private companies, the government will be tempted to ban those competitors
so as to  help the government company. A true natural monopoly would not need protection against
entry unless its operating costs were far higher than that of potential competitors, but such might
be the case. Thus, city regulations often ban competition from mom-and-pop garbage haulers.

% \newpage

%\vspace*{24pt}
 \begin{center}
% \begin{minipage}[c]{.6\linewidth}
%\begin{figure}[h]

\refstepcounter{tablecounter} \label{tab7-1}

\begin{center}

 {\sc Table \ref{chap07}.\ref{tab7-1}\\
   Privatization in the United Kingdom---Year of First Sale of Shares } \\
\begin{scriptsize}
\medskip

 \begin{tabular}{l ll}
\hline
\hline
Organization & Industry &  Year   \\
\hline
British Petroleum & Oil & 1979\\
National Enterprise Board Investment & Various & 1980 \\
British Aerospace & Aerospace & 1981\\
Cable \& Wireless & Telecom & 1981\\
Amersham International & Scientific goods & 1982\\
 National Freight Corporation & Trucking  & 1982\\
Britoil  & Oil  & 1982\\
British Rail Hotels  & Hotels  & 1983\\
Associated British Ports  &Ports   & 1983\\
 British Leland (Rover) & Cars  &1984\\
British Telecom (BT) &  Telecom & 1984\\
Enterprise Oil  & Oil  & 1984\\
Sealink  &  Sea transport & 1984\\
British Shipbuilders and Naval Dockyards  & Ship building  & 1985\\
National Bus Company  & Bus service  & 1986\\
British Gas &  Gas & 1986\\
Rolls Royce  & Airplane engines & 1987\\
British Airports Authority  & Airports  & 1987\\
British Airways  &  Air travel & 1987\\
Royal Ordnance Factories  & Armaments  & 1987\\
 British Steel &  Steel & 1988\\
 Water industry & Water  & 1989\\
Electricity distribution industry  & Electricity  & 1990\\
Electricity generation industry  & Electricity  & 1991\\
Trust Ports  & Ports  & 1992\\
 Coal industry &  Coal & 1995\\
Railway industry  &  Rail transport & 1995--97\\
Nuclear energy industry  &  Nuclear energy & 1996\\
\hline
\hline
\end{tabular}
\end{scriptsize}
 \end{center}

 %\end{footnotesize}
 %\end{minipage}
%\end{figure}
\end{center}

%\vspace*{24pt}

In addition,  remember that  taxation itself creates deadweight loss. Thus, when P=MC and a subsidy
is used, we do not really avoid hurting economic value, because the subsidy requires increasing the
income tax or some other tax where the triangle loss might be even greater than from having higher
utility prices. Which loss is greater, from income tax or from higher electricity prices, would
depend on the elasticity of demands of labor supply and of electricity demand.

  Government ownership is actually in widespread use in the United States for public utilities.
Notable examples are the  federally owned Tennessee Valley Authority  and   garbage collection  and
water supply in many cities. Not all of these use marginal-cost pricing, however. It is common for
government enterprises to be required to break even, which amounts to using the average-cost pricing
system we will discuss later.  Government ownership  has been on the decline over the past fifty
years. The United Kingdom is notable for the number of industries that have been {\bf privatized}
\index{privatized}: sold off to become for-profit companies that may or may not be regulated,
depending on whether they are natural monopolies.  Table \ref{chap07}.\ref{tab7-1} shows what
happened from 1979 to 1996.


\bigskip
\noindent
 {\bf   Marginal-cost pricing plus a subsidy }\index{Marginal-cost pricing}

  
   \begin{wrapfigure}{l}{3in}
\begin{center}
 {\sc Figure \ref{chap07}.\ref{fig07-1methods.pdf} (again)\\
Regulated and Unregulated Natural Monopoly  }
  \end{center}
 \includegraphics[width=7in]{Figure07-02.jpg}
 \end{wrapfigure}


   In preference to government ownership, we could have private ownership, with a regulation
requiring the private company to set the price at marginal cost. The private company would operate
so as to maximize profits, which means it would try to minimize its costs for a given level of
output.  The price regulation would prevent it from restraining output to increase the price to the
monopoly level, and the subsidy would take care of the fact that then the price would be less than
average cost. In Figure  \ref{chap07}.\ref{fig07-1methods.pdf}, this would look just like government
ownership: the   price would be \$10/unit and the subsidy would equal  \$160. As with government ownership, there would be deadweight loss from the taxation needed for the subsidy, and that loss could easily overwhelm the benefit from pricing at marginal cost.  But we would  at least hope that
costs would not rise because of government failure.


 Government failure is still a problem, though. The private company would want to minimize costs,
but it would like to pretend that its costs are high so it can get a bigger subsidy to cover its
supposed losses.  Like the government-owned enterprise, its CEO might find that the most effective
use of his time is not to make a good product at a low cost, but to lobby the government for
additional help. Direct corruption would also be a concern, since the necessity of some subsidy
provides a cover to a government official to funnel extra money to someone who bribes him.

\bigskip
\noindent
 {\bf   Price caps}\index{price caps}

   Since the 1980's, an increasingly common way of regulating natural monopolies is by {\bf price
cap regulation}.  Under a price cap scheme, the government sets an initial price ceiling for the utility, and
then the utility can increase the price at the rate of inflation   minus an {\bf X-factor}. The X-
factor is an adjustment for technological improvement in the industry that is expected to  reduce
costs over time.   Thus, if the initial price was \$100,  the X-factor was 2\%, and the rate of
increase of the consumer price index  turned out to be  3.5\% in the first year, the second-year
price would be \$101.50,  an increase of 1.5\%. The scheme is like a contract between the utility and the government, one that lasts for a specified length of time with the same terms whether the utility makes a profit or  a loss. 

    The  United Kingdom was the first country to use price caps, introducing them when it privatized
government-owned monopolies on electricity and natural gas in the 1980's.  The reason to let prices
rise with inflation is that we would expect inflation to raise costs for the utility.   A good guess
for the rate of increase of wages, for example, is the rate of increase of prices generally.  A
utility's costs, however,  will not increase at the same rate as costs in the general economy. For
one thing, utilities are more capital-intensive than the economy generally,  and capital
productivity might rise more than labor productivity.   In addition, the product the utility
produces stays much the same, any innovation could be expected to reduce production costs rather
than improve the product (which might increase costs too---think of how automobiles have gotten
more expensive over time).  Also, with growth in the economy the scale of operation increases and
that should reduce costs too in a natural monopoly.   Thus, the X-factor is subtracted because we
expect the utility to be able to take advantage of cost growth lower than in the economy at large.
This can be combined with
 yardstick competition. This is done by adjusting the X-factor for the performance of other firms in
the same industry.


   The  main selling point of price cap regulation is that it encourages the utility to minimize
costs.  Whether its costs rise or fall, its rate of price increase remains fixed. Also, past the
initial year the government need not try to estimate the firm's costs.  A drawback is that it is
hard to commit to keeping the price cap scheme  the same.  In particular, if the firm   manages  to
reduce its costs faster than expected, the government will be very tempted to break the agreement
and either reduce prices or impose an excess-profits tax, as happened in the United Kingdom in the
1990's.\footnote{See \url{ http://www.ifs.org.uk/fs/articles/fslucy.pdf}.}

 
{\bf Earnings sharing regulation} is similar to price cap regulation in that it sets up a contract between the utility and the government for a relatively long period of time, but it does not allow such extremes of profitability and unprofitability. Also, it is set up in terms of rates of return on investment for the utility.  A typical plan sets a target rate of return on investment (say, 12\%) and  a ``no-sharing'' range of returns (say, 10\% to 14\%). If the rate of return is within the no-sharing range, that is exactly what the utility keeps. If the rate becomes lower (say, 9\%) then  the regulator allows a price increase so that the pain is shared between the utility and the customers. If the rate becomes higher (say, 15\%) then the regulator requires a price reduction to share the unexpected profits between the utility and the customers.  Thus, earning sharing regulation has the effect of raising the price cap if profits are too low and lowering the price cap if profits are too high.\footnote{
David E. M. Sappington  and  Dennis L. Weisman (2010) ``Price cap regulation: what have we learned from 25
years of experience in the telecommunications industry?'' {\it Journal of Regulatory Economics} 38: 227-257.}
 



  In practice, price cap regulation looks a lot like average-cost pricing regulation.  The greatest
similarity comes at the start of the process. How does the government set the initial price cap? It
wants to set it to yield an average of zero economic profit, but that is exactly the goal of
average-cost regulation. The difference is that under price cap regulation the prices are not
supposed to be reset, but resetting prices is inevitable after enough years have past, whether it is
because the utility is making embarassingly large profits or because its losses are so high it
cannot stay in business without price hikes.



\bigskip
\noindent
 {\bf \ref{chap07}.3:  Average-Cost Pricing }\index{Average-Cost Pricing} \label{s07.3}

 The traditional private monopolies
whose price is regulated to roughly equal their average cost. This is known as {\bf cost-of-service}
\index{cost-of-service} or {\bf rate-of-return}\index{rate-of-return}  regulation, since it tries to
set revenue  equal to cost by giving the company a fair return on its investment.

 The disadvantage of this scheme is that it results in a price higher than the ideal one: P=AC
instead of P=MC, amount P=\$12 in   figure  \ref{chap07}.\ref{fig07-1methods.pdf} rather than P=
\$10. Thus, there remains the  triangle welfare loss .5(160-150)(\$12 - \$10)=\$100, because the
company could produce more electricity and customers would be willing to pay the extra cost. But
average-cost pricing has the advantage that we don't need a government subsidy any more. The
government might still allow too generous a price, but at least no cash transfer is made from
government to private business.
The enterprise is  self-financed.

\begin{wrapfigure}{l}{3in}
\begin{center}
 {\sc Figure \ref{chap07}.\ref{fig07-1methods.pdf} (yet again)\\
Regulated and Unregulated Natural Monopoly  }
  \end{center}
 \includegraphics[width=7in]{Figure07-02.jpg}
\end{wrapfigure}

  The company also has an incentive to keep its costs low, because the actual way average-cost
pricing is implemented is to set a price every few years that aims at equalling average cost, but
which is fixed even if the companies costs go higher or lower.  Thus, in   figure
\ref{chap07}.\ref{fig07-1methods.pdf} the company is allowed to charge P=\$12, but if the company
finds some way to reduce costs  so that AC = \$10.5, it can keep the profits. Or, if it can find
some way to increase the demand for electricity so that sales at $P = \$12$ come to equal $Q=170$
instead of the $Q=150$ shown in the figure, it can also make positive profits.

  Next we'll see how the government figures out which  price equals average cost.





\bigskip

\noindent
{\bf  A Rate Case}

The general idea of average-cost pricing is to find a price which equals average cost.  Here's how
it's done.

First, the state legislature sets up a public utility commission. This is a committee of about five
members who vote on what price to grant the electrical and other regulated utilities in the state.
In some states, the members are elected. In others, they are appointed by the governor, but cannot
be fired by him.





Once the utility commission is set up, the utility company applies for permission to charge a
particular set of prices. This actually isn't just one single price for electricity; it is a whole
schedule of prices. There can be one price for businesses, and one for homes. There can be one price
for daytime, and one for night. There can one price for the small-quantity user and another for high
volume.



The utility company presents its case for why these prices can be expected to yield zero profits.
Importantly, by ``zero profits'' here we  mean zero economic profits. The company must be allowed to
cover its cost of capital, just as any private company must do.  The crucial equation in   rate-
of-return regulation\index{rate-of-return regulation} is
\begin{equation} \label{e1}
  \sum_{i=1}^m price_i * E   (Q^d_i (price_i)) =  E(\sum_{j=1}^n price_j *  input_j)  +
R*(\text{Rate  Base})
\end{equation}

Let's look at the terms in this equation carefully. The commission needs to choose   $m$ different
prices  for the company's $m$ different products,\\
 $price_1, price_2, ... price_m$. ``Product'' might mean a customer category---``home
electricity'', for example.  The company's sales of product $i$, $Q^d_i$, will be a function of the
price of $i$. The left-hand-side of the equation,  $\sum_{i=1}^m price_i \cdot E  Q^d_i (price_i)$,
equals the company's expected revenue, where the $E$ represents the fact that we have to estimate
what the output will be for a given price because demand curves shift over time.



The right-hand side of the equation is the company's expected costs. The first component of the
costs is $E (\sum_{j=1}^n price_j   \cdot   input_j)$, the
prices of the various inputs such as coal, labor, and capital  depreciation. The amount of inputs
used will depend on the output, of course, which itself has to be predicted. The prices of some
inputs are   volatile. Often, utility commissions will allow the utility to  use a formula under
which electricity prices  rise and fall  with  fuel prices. Also, the input may be electricity
itself, because a utility might choose to buy electricity from another company rather than generate
it using its own power plants.



 The {\bf rate base}\index{rate base} is the amount of capital  needed, and $R$ in the formula is
the fair  return on capital.


 The commission does not have to accept the electricity prices the company suggests. The commission
will decide for itself whether the company's estimates of revenue and costs are reasonable. The
commission will also decide whether every capital expenditure really is justified, and should be put
in the rate base. There have been some big denials. The two biggest were California's 1987  denial
of \$2 billion for the rate base of Pacific Gas \& Electric Company (``PG\&E'')  for the    Diablo Canyon
  One and Two  nuclear plants and  New York's 1987 denial   of \$2.1 billion for the  Nine Mile Two
nuclear plant, which was  41\% owned by
Niagara Mohawk Power, 14\% by     Rochester Gas \& Electric,  18\% by  New York State Electric and
Gas, 9\% by     Central Hudson Gas \& Electric, and 18\% by the    Long Island Power Authority.
\footnote{Lyon,\index{Lyon} Thomas P. \& Mayo,\index{Mayo} John W., \href{http://www.jstor.org/stable/4135233}{ ``Regulatory Opportunism and
Investment Behavior: Evidence from the U.S. Electric Utility Industry,''} {\it RAND Journal of
Economics}, 36: 628--644  (Autumn 2005). Eliot 
Spitzer, \index{Spitzer}Eliot, ``Comments of Eliot Spitzer Attorney General of the State of New York
Regarding Settlement Proposals,'' (September 25, 2001).
\url{www.ag.ny.gov/media_center/2001/sep/NIneMile.pdf}.}

%\vspace*{24pt}

% \begin{wrapfigure}{l}{\linewidth}

\begin{center} \begin{boxedminipage}[c]{.9\linewidth}
\refstepcounter{sidebarcounter} \label{sidebar7-3}
\begin{small}
{\sc  Box \ref{chap07}.\ref{sidebar7-3}\\
  NIPSCO's   Prices}\\


For households: \\
Customer Minimum Charge -\$5.95 including  the first 36 kilowatt hours per month\\
16.522 cents per kilowatt hour for the next 14   per month\\
12.041 cents per kilowatt hour for the next 150   per month\\
9.637 cents per kilowatt hour for all over 200   per month\\

 For any customer who regularly uses and depends on permanently installed electric spaceheating
facilities:\\
7.149 cents per kilowatt hour beyond 500    from October to April.\\


For non-industrial businesses:\\
\$206.15 for the first 10 kilowatts or less of Maximum Demand per month\\
\$7.59 per kilowatt per month for all over 10 kilowatts of Maximum Demand per month\\
6.206 cents per kilowatt hour for all kilowatt hours used per month\\


The above rates are subject to a Purchased Power Cost Adjustment Tracking Factor  and
 shall be adjusted for cost of fuel in accordance with the formula set forth in Rule 39 of the
accompanying Rules and Regulations.

\noindent
 NIPSCO, ``Rate 811:
Rate for Electric Service
Residential,'' (July 16, 1987). \\
NIPSCO,   ``Rate 823:
Rate for Electric Service
General Service,''  (June 8, 1994).
\end{small}
 \end{boxedminipage} \end{center}
%  \end{wrapfigure}
%\vspace*{24pt}


\bigskip
\noindent
 {\bf \ref{chap07}.4: The 2010  NIPSCO Rate Case} \label{s07.4}

The Northern Indiana Public Service Company (NIPSCO) is an investor-owned public utility that sells
electricity and natural gas in northern Indiana, in the city of Gary and the neighboring region. It
has 460,000 customers. Though only 1\% of its customers are industrial, they buy 53\% of the
electricity.  You cannot buy stock in just NIPSCO, because it is owned   by a holding company,
NiSource, which also owns utilities in other states.

\begin{center}\begin{boxedminipage}[c]{.9\linewidth}
\refstepcounter{sidebarcounter} \label{sidebar7-1}
\begin{footnotesize}
{\sc  Box \ref{chap07}.\ref{sidebar7-1} \\
  The  Indiana Utility Regulatory Commission }
\hspace{12pt}  Commissioners are appointed by the Governor to four-year  terms or to fill out
unfinished terms,   Indiana also has an Office of Utility Consumer Counsellor which generally
opposes rate increases.

 \begin{center}
   \includegraphics[height=0.8in]{fig07-commissioners.png} 
\end{center}

\hspace{12pt}James Huston has been Chairman since  2014,  and was      reappointed in  2018. He 
Previously he was  Executive Director of the Office of Faith Based and Community Initiatives  and deputy chief of staff for three different  U.S. congressmen. 

\hspace{12pt}  Sarah Freeman was appointed  in 2016. She was a lawyer with the Indiana Attorney General and the Indiana Legislative Services Agency.



\hspace{12pt}Stefanie Krevda was  appointed in 2018. She was formerly the Executive Director of External Affairs for the Commission and 
  Chief of Staff   at Indiana's State Personnel Department,

 


\hspace{12pt}  David Ober  was appointed in 2018, after having been an Indiana State Representative.  


\hspace{12pt}David E. Ziegner was appointed  in 1990.
He was senior    staff attorney for the Legislative Services Agency,  and then   General Counsel for
the Commission.


\end{footnotesize}
\end{boxedminipage} \end{center}
% \end{wrapfigure}
\bigskip

 NIPSCO is regulated by the
   Indiana Utility Regulatory Commission (IURC, ``the Commission''). Its electricity rates had last
been set in 1987 and had not changed for many years. In June 2008 it proposed an increase, which was
granted by the Commission  in  August 2010.  In between, NIPSCO filed memos and presented witnesses
arguing for a price increase, and the    Indiana Office of Utility Consumer Counsellor   (OUCC) and
customers argued for a smaller increase.
 Those opposing the rate increase included
the LaPorte County Board of Commissioners,
 the Board of Commissioners and Council of Newton County,
the city governments  of Crown Point East Chicago,   Hammond, and  Munster; the Citizens Action
Coalition of Indiana; industrial customers   Accurate Castings/INCMA, ArcelorMittal USA, Beta Steel,
Cargill, Marathon Petroleum, USG Corporation, and  U.S. Steel;  and the United Steel, Paper and
Forestry, Rubber, Manufacturing, Energy, Allied Industrial and Service Workers International
Union.\footnote{The   Indiana Office of Utility Consumer Counsellor   (OUCC), \href{http://www.indiana.gov/oucc/files/Majoros_Testimony_050809.pdf}{ ``Northern Indiana
Public Service Co. Electric Rate Case, IURC Cause No. 43526, Public Field Hearing ---Basic Facts,''}
4pp.  (July 15, 2009). } Here's a timeline.\\

\newpage
\begin{small}
\noindent
2008\\
June: NIPSCO filed its petition with the IURC.\\
August: The IURC issued a schedule. \\
 NIPSCO filed testimony and exhibits in support of its request. 

\noindent
2009\\
January: A two-week technical evidentiary hearing was held in Indianapolis.\\
March: An IURC public   hearing was held in Gary.\\
May: The OUCC and other parties filed testimony.\\
June: NIPSCO filed   rebuttal testimony.\\
July: An IURC public   hearing was held in  Michigan City.
July: An IURC technical evidentiary hearing is scheduled to begin in Indianapolis and last two
weeks.  \\
 October: NIPSCO filed its proposed order,what it would like the IURC to approve. \\
 December: The OUCC and others parties filed their proposed orders.  


\noindent
2010\\
 January: NIPSCO filed its reply to the OUCC and other parties. \\
 August: The IURC issued its final order, authorizing a rate increase and telling NIPSCO to come up
with specifics. \\
 September: The IURC authorized a specific schedule of prices.

\end{small}

\bigskip

  The first item of contention was the rate base.  An example of what was under consideration was
whether to include prepaid pension assets in the rate base. The OUCC argued that it should not be
included, and in the end it was not. Table \ref{chap07}.\ref{tab7-2} shows the Commission's final
decision as to how big the rate base should be. \\






\vspace*{24pt}
\noindent
\begin{minipage}[c]{\linewidth}
\noindent
\begin{center}
\refstepcounter{tablecounter} \label{tab7-2}
{\sc  Table \ref{chap07}.\ref{tab7-2}\\
 The NIPSCO Rate Base}\\
\vspace{12pt}

\begin{tabular}{lr}
\hline
\hline
Asset (Liability) & Amount\\
\hline
Utility Plant  &  5,205,578,748\\
Common Plant Allocated &  214,502,540\\
Less Schahfer 17 Disallowed Plant  & (31,733,655)\\
\hline
Total Utility Plant &  5,388,347,633\\
\hline
 & \\
Accumulated Depreciation and Amortization  & (2,800,380,478)\\
Sugar Creek Accumulated Depreciation and  & \\
Amortization   & (5,618,432)\\
Common Plant Accumulated   Depreciation Allocated  & (98,409,168)\\
Less Disallowed Plant Accumulated Depreciation   &  27,399,652\\
\hline
Total Accumulated Depreciation and Amortization    & (2,877,008,426)\\
\hline
 & \\
Net Utility Plant   &  2,511,339,207\\
\hline
 & \\
Schahfer 17 Deferred Depreciation        &  542,928\\
Schahfer 18 Deferred Depreciation         &  5,206,694\\
Schahfer 18 Deferred Carrying Charges      & 16,132,193
\\
Prepaid Pension Asset   &  0\\
Materials \& Supplies    & 46,907,735\\
Sugar Creek Materials \& Supplies &1,495,291\\
Production Fuel    & 57,566,559\\
 & \\
\hline
Total Rate Base   &  \$2,639,190,607\\
\hline
\hline
\end{tabular}\\
\end{center}
\end{minipage}
\vspace*{24pt}





 A second issue was the   cost of capital for NIPSCO. This had two parts: the capital structure to
be used, and the cost of equity capital.

  NIPSCO had 61\% common equity and 39\% long-term debt.  This is unusual for a public utility, and
the OUCC said it included too much equity capital, which is more expensive than debt
capital.\footnote{Capital structure is complicated, though. The Modigliani-Miller Theorem
\index{Modigliani-Miller Theorem}points out that adding debt to a company increases the riskiness of
its equity (and its existing debt),   which can cancel  out the cheapness of debt finance.  }  The
OUCC noted that  the average share of equity capital in a  comparison group of utilities they picked
was only  47\%. Moreover, NIPSCO is  a wholly owned subsidiary of  NiSource, which only has 52\%
equity.  The OUCC said that NIPSCO's revenue requirement should be reduced by \$30 million because
it was justified by too high a share of equity. The Commission sided with NIPSCO on this issue.\\





  The cost of debt capital  for NIPSCO was 6.6\%, which is straightforward to compute using the
actual interest rates on the debt. The cost of equity capital is much trickier to estimate.   NIPSCO
said its cost of equity capital was 12.0\%. The OUCC said it was 10.0\%.  The Industrial Group, an
alliance of  industrial customers, said it was 9.2\%.
Estimates were presented using a variety of finance methods  including the CAPM model.



To calculate the cost of capital using the CAPM model requires as ingredients {\bf the risk-free
interest rate},\index{the risk-free interest rate} the company's {\bf  beta}\index{beta} (how much
its stock rises on average when the entire stock market goes up---1 if when the  stock market rises
10\% as a whole,  the best guess for the increase in value of this stock is also 10\%), and the
extra  interest the market requires for riskier companies, the {\bf risk premium.}\index{risk
premium}\footnote{The CAPM is  one of the simplest models of stock pricing. Other models add more variables, such as the size of the company and its ratio of market value to book value. See Kent Womack, Ying Zhang, Adam Borchert, Lisa Ensz, Joep
Knijn, Greg Pope, and Aaron Smith (2003) ``Understanding Risk and Return, the CAPM,
and the Fama-French Three-Factor Model,'' Tuck School at Dartmouth No. 03-111. \url{http://www.portfoliosolutions.com/pdfs/FF_3_Factor_Tucks.pdf}.  }   Thus,   the required return on a company's stock  is
$$
r= riskfree\; rate + \beta (risk\; premium)
$$

NIPSCO  used a 4.5\% risk-free rate based on recent historical yields on long-term treasury bonds,
Blue Chip forecasts and  recent trends,  a beta of 0.85,  which is the average of the  betas for the
companies in the Electric Group as estimated by Value Line (a financial information company)  and a
risk  premium of 8.44\%, which averages    the difference between historical market returns and
treasury bond returns (6.5\%) and   the difference between forecasted market returns and treasury
bond returns (10.37\%).

The OUCC   used a risk-free rate of 4.00\%, the upper end of the range of yields in 10-  and 20-year
treasury bonds,  a beta of 0.68,  the  average in his comparison group of utilities, and a risk
premium of 4.61\%, less than historical returns because   the   risk premium has declined with the
big increase in stock prices 2001-2008.  This estimate was the average   of  7 historical studies
for periods beginning as early as 1872;  25   equity-premium-puzzle   studies   published between
1999 and 2009 (which tried to explain why equity seemed to have so much higher a return than debt
before 2001); four surveys of forecasters,chief financial officers,  and academics; and   two
ground-up estimates based on current conditions, including one that the OUCC's expert witness did
himself. The purpose was no doubt to impress the regulatory commission with the number of studies
used, but often what is best is  simply to decide which of many studies is best and use just that
one.

The Industrial Group  used a 4.30\% risk-free rate based on  a Blue Chip projected treasury bond
yield;  a beta of 0.73   based on the average   Value Line estimate for a  group of similar
companies, and  a risk premium of 6.5--7.0\% based on its estimate of historical returns and  the
expected return on the S\&P 500.

The Commission chose 9.9\% as the cost of equity. Table \ref{chap07}.\ref{tab7-3} shows how it
calculated the weighted average cost of capital.







 \vspace*{24pt}
\noindent
\begin{minipage}[c]{.9\linewidth}
\begin{footnotesize}
\begin{center}
\noindent
\refstepcounter{tablecounter} \label{tab7-3}
{\sc Table \ref{chap07}.\ref{tab7-3}\\
 NIPSCO's Cost of Capital}\\
\vspace{12pt}
\begin{tabular}{l rrr|r}
\hline
\hline
Capital Source& Amount& Percent   & Cost & Weighted  \\
 &  &   of Capital  &   &   Average Cost\\
\hline
Common Equity  &  \$ 1,395,245,772  &  49.95\%  &  9.90\%  &  4.94\%\\
Long-Term Debt  &  \$ 906,631,137   & 32.46\%   & 6.52\%   & 2.12\%\\
Customer Deposits  &  \$ 63,684,199  &  2.28\%   & 6.00\%   & 0.14\%\\
Deferred Income Taxes  &  \$ 294,780,249   & 10.55\%   & 0.00\%   & 0.00\%\\
Post-Retirement Liability    &   \$ 102,637,766  &  3.67\%   & 0.00\%  &  0.00\%\\
Post-1970 Investment  &    &     &    &  \\
Tax Credit   & \$ 30,350,460   & 1.09\%   & 8.57\%  &  0.09\%\\
\hline
Totals   & \$ 2,793,329,583  &  100.00\%  & ---  & 7.29\% \\
\hline
\hline
\end{tabular}
\end{center}
\end{footnotesize}
\end{minipage}
\vspace*{24pt}

As  you can see, rate cases become quite involved. My summary so far  only takes us to page 33 of
the Commission's 131-page Final Order, and the Final Order itself is only a summary of the much
lengthier testimony the various parties presented, but it gives the flavor of a typical rate case.
We will refrain from looking at the discussion of operating costs, however, and go straight to the
result.
NIPSCO asked for prices that would give it gross revenue of    \$974,062,979. What the Final Order
said was:
\begin{bigquote}
  Petitioner Northern Indiana Public Service Company shall be and hereby is authorized to revise its
basic rates and charges for electric utility service to provide annual gross margin revenue of
\$899,401,890 plus non-trackable fuel expense of \$11,015,038 which on the basis of annual electric
operating expenses of \$706,976,357 (net of revenues and expenses relating to trackable and non-
trackable fuel and purchased power and related Utility Receipts Tax) are estimated to provide net
operating income of \$192,425,533.\footnote{{\it Petition of Northern Indiana Public Service Company
(``NIPSCO") For (1) Authority to Modify Its Rates  \ldots Indiana Utility Regulatory Commission
Cause No. 43526, Final Order,} pp. 129--130 (August 25,
2010).\url{http://www.in.gov/iurc/files/Order_in_Cause_No._43526.pdf.} }
\end{bigquote}

 Thus, the Final Order gave NIPSCO rates expected to generate \$910 million in revenue, as opposed
to the \$974 million that NIPSCO asked for.
This is a typical result; the utility asks for their rates on various kinds of electricity to
increase by a certain amount, customers object, and the regulatory commission grants some but not
all of the requested rate increases.



\bigskip

\noindent
{\bf \ref{chap07}.5:  Ramsey Pricing} \label{s07.5}


  Suppose the company in the story at the start of the chapter   comes back to the mayor and says,

\begin{bigquote}
 ``Mayor, we've settled into the new regulatory regime, and we're not going to try to get rid of it.
We do, however, wish that the regulation weren't so rigid. Right now, the regulatory commission sets
a price for each product that gives us a fair return on that product. So, of course we have a fair
return overall. But wouldn't it be okay if we made a profit on some products, so long as it was
balanced by  a loss on others?''
\end{bigquote}

 The mayor is   suspicious, because he knows that companies try to come up with fancy schemes to
fool the government. But the CEO actually has a point. Social surplus can be increased by raising
some prices, if other prices are lowered at the same time. The idea is to raise prices on goods
whose quantity demanded is   insensitive to price, while reducing prices on goods whose quantity
demanded is sensitive.  That would give us an increase in the quantity demanded of goods, while not
allowing profits overall to stay at zero. The idea is called   Ramsey pricing.


 To see this we will use  a numerical example.\footnote{This is based on an example in Chapter 11 of W. Kip 
Viscusi,\index{Viscusi}  Joseph E. Harrington,\index{Harrington}, and John M.
Vernon,\index{Vernon}  {\it Economics of Regulation and Antitrust}, 4th edition, MIT Press
(2005).} Let the company sell   business electricity ($Q_b$) and home electricity ($Q_h$), with a
total cost of
\begin{equation}
TC= 1800 + 20Q_b + 20Q_h.
\end{equation}
Let the demand curves be
\begin{equation}
Q_b  = 100- P_b
\end{equation}
and
\begin{equation}
Q_h = 120- 2P_h.
\end{equation}

 As shown  in figure \ref{chap07}.\ref{fig07-3-ramsey.pdf}, home electricity has  a flatter, more
elastic,  demand curve.




\vspace*{24pt}
\noindent
\begin{minipage}[c]{\linewidth}
\begin{center}
 {\sc Figure \ref{chap07}.\ref{fig07-3-ramsey.pdf}\\
 Ramsey Pricing   } \\

\refstepcounter{figurecounter} \label{fig07-3-ramsey.pdf}
 \includegraphics[width=\linewidth]{fig07-4-ramsey.jpg}
\end{center}
\end{minipage}
\vspace*{24pt}

 The marginal cost is \$20 for sales to either kind of customer.
If the firm charges   $P=\$20$  it will sell 80 units of each good (a coincidence to make the
computations easier here)  and  suffer a loss of  \$1,800 since it won't cover its fixed costs.
There would be zero triangle loss,  because at that price and quantity the marginal cost to the firm
equals the marginal benefit to consumers. We are aiming to use average-cost pricing so the firm will
break even, and that means the prices must rise and we must accept a certain amount of deadweight
loss.

The simplest pricing scheme would be for the firm to raise both prices to $P_b=P_h=\$37$,   selling
63 units  to B and 46 units to H. It would be  receiving net revenue of   \$1,071  ($ = 63(37-20)$)
from B and \$736 ($ = 46  (37-20)$)  from H, which when summed   covers the fixed cost of   \$1,800
with a little bit left over. The deadweight loss   would be  \$144.50 ($ = .5  (80-63) (37-20)$)
from B and \$289  ($ = .5(80-46)(37-20)$)  from H, a total loss of \$433.50.

As you can see, the same price increase from \$20 to \$37 gives us less extra revenue and more
triangle loss from good H than from good B. The problem is that the quantity demanded falls so much
more from H, because its demand is more elastic, more price sensitive.   The elasticity of demand is
\begin{equation}
 \text{Elasticity  of  demand} = \frac{\text{\% Change in quantity demanded}}{\text{\% Change in
price}} = \frac{dQ}{dP} \frac{P}{Q}.
\end{equation}

   It is useful to write the elasticity of demand as $\frac{dQ}{dP} \frac{P}{Q}$ here because we can
use the demand equations to estimate the elasticities when the price is \$37.
\begin{equation}
 \text{Elasticity  of  demand}_b =   (-1) \frac{37}{63} \approx -.59.
\end{equation}

   \begin{equation}
 \text{Elasticity  of  demand}_h =  (-2)   \frac{37}{46}\approx -1.61.
\end{equation}


 The solution is to    increase the price of H   to less above marginal cost  and  to  increase the
price of B to further above marginal cost to recoup the lost profit.

Instead of both groups being charged 37, let the firm use  prices of $P_b=  \$40$ and $P_h=\$30$.
These will still be able to cover the fixed cost without so much    welfare loss. The company would
get  net revenue of \$1,200  ($ =60(\$40-\$20)$) from B and \$600 ($ =  60 (\$30-\$20)$) from H,
which when summed would cover the fixed cost of   \$1,800. The triangle losses of  social surplus
would be \$200 ($ = .5 (80-60)(\$40-\$20)$) from B and \$100 ($ = .5(80-60) (\$30-\$20)$) from H, a
total loss of just \$300. The elasticities are now closer together:

\begin{equation}
 \text{Elasticity  of  demand}_b =   (-1) \frac{40}{60} = -\frac{2}{3}
\end{equation}
 and
   \begin{equation}
 \text{Elasticity  of  demand}_h =  (-2)   \frac{30}{60}= -1.
\end{equation}


 The idea of marking goods up less if they have more elastic demand to attain a given  net revenue
target is known as {\bf Ramsey pricing}. \index{Ramsey Pricing}
  The equation that determines the optimum is known as the {\bf Ramsey rule}\index{Ramsey rule}. The
Ramsey rule, which I will not prove here, requires prices of both goods $i=b,h$ to be set
so:\footnote{Frank P. Ramsey,  \index{Ramsey} \href{http://www.jstor.org/stable/2222721}{ ``A Contribution to the Theory of Taxation,"} {\it The
Economic Journal}  (1927). }
\begin{equation}\label{e1}
 \frac{Price_i - MC_i}{Price_i} = \frac{ \lambda}{-Elasticity_i},
\end{equation}
 where $\lambda$ is a parameter between 0 and 1 that is made just big enough to generate the
required revenue.   If the company doesn't need to make any profit to survive,  then  $\lambda=0$
and
   price equals marginal cost for each good.  Here, the Ramsey rule    yields
\begin{equation}\label{e1}
(Business) \;\; \frac{40-20}{40} = \frac{ \lambda}{ \frac{2}{3}},
\end{equation}
and
 \begin{equation}\label{e1}
(Home) \;\; \frac{30-20}{30} = \frac{ \lambda}{ 1},
\end{equation}

 Thus, $\lambda =\frac{1}{3}$, which makes both equations true ($\lambda$ is the Greek letter
lambda). At the optimum, the elasticity is still higher for  home electricity, but it is marked up
less over cost than business electricity is.

   A curious feature of Ramsey pricing which I will not prove here is that another way to find the
optimum is to reduce quantity by the same percentage for each product below the quantity where $P=
MC$. Here, the quantity where P=MC was 80 units for both products, and both were reduced by 25\% to
60 units.


  In this electricity example there are just two goods, but the Ramsey rule applies even if there
are three or more goods---just make sure each has its price increased above marginal cost in
inverse proportion to its elasticity of demand. If the company wants to make as much profit as
possible, set set $\lambda$  equal to 1, which makes the firm's profit as large as possible and we
get---surprise!---the
  {\bf Lerner Rule}\index{Lerner Rule}:
 $$
 \frac{ P - MC}{P} = \frac{ 1}{-Elasticity}
 $$

  Thus, one implication of the Ramsey Rule is that a multi-product monopolist should mark up  the
price of the less elastic good  more, at least  if the demand for the two goods is independent. (If
demand for one of the goods depends on the prices of both goods, things become more complicated).

 
%-----------------------------
%\cleardoublepage

\vspace*{48pt}


 

%\newpage
\begin{center}
{\sc   Review Questions }
\end{center}
 \begin{enumerate}
\item
   What is natural monopoly and what problems does it create?

\item
   What are the solutions to natural monopoly?

\item
   How does rate-of-return regulation work?

\item
 How would you figure out a regulated utility's cost of equity capital? 

\item
   How can firms use Ramsey pricing to reach a profit target with less allocative
   inefficiency?



 \end{enumerate}




 %-----------------------------




 

 
\newpage

    \vspace{48pt}
%\cleardoublepage
\begin{center}
{\sc Readings}
\end{center}
 \begin{enumerate}

 

\item
\href{http://www.ncppp.org/wp-content/uploads/2013/02/CRS-Insights-Indiana-Toll-Road-Bankruptcy-Chills-Climate-for-P3s.pdf}{``Indiana Toll Road Bankruptcy Chills
Climate for Public-Private Partnerships," } William J. Mallett, {\it  CRS Insights}.

\item
\href{http://www.dallasnews.com/business/business/2015/08/31/texas-looks-into-price-spike-at-hunt-owned-sharyland-utilities}{``Texas Looks into Price Spike at Hunt-Owned Sharyland Utilities," }{\it Dallas Morning News}.

\item
 \href{http://www.wsj.com/articles/SB10001424052970204224604577030862463404848}{``Trashy Politics: Why Dallas Is Dealing in Garbage;
Local Governments Have a Creative New Revenue-Raising Method:
Take Over from a Profitable Private Enterprise,'' }{\it The Wall Street Journal}.


\item
\href{http://blogs.reuters.com/jackshafer/2014/02/19/whos-afraid-of-comcast/}{
 ``Who's  Afraid of Comcast?,''} Jack Shafer,  {\it Reuters}.
 

\item
\href{ http://regulationbodyofknowledge.org/wp-content/uploads/2013/03/Alexander_Price_Caps_Rate.pdf }{``Price Caps, Rate-of-Return Regulation,
and the Cost of Capital,''} Ian Alexander
and Timothy
Irwin, The World Bank.

 


\end{enumerate}


 \end{document}




