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%TCIDATA{Created=Thu Sep 02 10:38:58 1999}
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\begin{document}
\author{Philip A. Viton \\
%EndAName
Department of City and Regional Planning\\
The Ohio State University\\
275 W. Woodruff Avenue\\
Columbus OH 43210}
\title{Competing with the Private Sector:\\
The Welfare-Maximizing Response\\
{\Large The Case of Urban Public Transit}}
\date{\today{} }
\begin{abstract}
It is becoming increasingly common for the public sector to face competition
from private for-profit providers of the same goods and services. How should
the public sector respond? This paper examines its \emph{optimal }response,
defined as the one that maximizes community welfare, and applies it to the
case bus transit provision in an urban corridor. We show that an optimal
response to entry can significantly increase community welfare, and that
this is likely to be possible in a wide variety of urban settings. However,
since the optimal response can increase deficits, it may be politically
infeasible. We therefore study the opportunity costs of non-optimal
responses and show that they can generate more than 80\% of the benefits
achievable by an optimal response. Finally, if the public sector can
directly control transport externalities, competition can increase welfare
even further.
\end{abstract}
\maketitle
\subsection{Social Welfare Maximization}
The public transit provider responds to entry by choosing its iteration-$j$
operations plan $y_{3}^{j}$ to maximize corridor social welfare, which
consists of user benefits from the transportation system, profits generated
by the private entrant, and net public sector revenues. We assume that
public sector deficits are financed by non-distortionary taxation raised
wholly within the corridor, that all net revenues are distributed within the
corridor, and that there are no income-distributional considerations.%
\footnote{%
That is, \$1 in profits contributes \$1 to corridor welfare no matter which
group receives it.}
Given the logit model of mode choice, a money measure of the user benefits
for a representative member of group $g$ in state $j,$ generated by the
operations plans of all providers, is:\footnote{%
See \cite{small-rosen:81} for a derivation of this benefits measure.}
\begin{equation}
B_{g}^{j}=\frac{1}{\lambda _{g}}\ln \sum_{m}e^{x_{gm}^{j}\beta _{g}}
\label{indivb}
\end{equation}%
where $\lambda _{g}$ is the marginal utility of income for a representative
member of group $g$. The welfare of all users of transport services in the
corridor at the end of iteration $j$ is then $\sum_{g}N_{g}B_{g}^{j}.$ Since
we assume that highway costs are constant, we take the public sector's cost
function to be its \emph{transit} cost function $C_{3}^{j}(y_{3}^{j})$. We
allow for the possibility that the public sector can levy fees (for example,
congestion tolls) on other modes: thus public sector revenues $R_{3}^{j}$
are the direct fare revenues from its transit operation, plus any other fee
revenues. Corridor social welfare in state $j$ is therefore%
\begin{equation}
W^{j}=\sum_{g}N_{g}B_{g}^{j}+(R_{3}^{j}-C_{3}^{j})+\Pi ^{j-1}
\end{equation}%
recalling that the public sector's iteration $j$ takes the current level of
private profits ($\Pi ^{j-1})$ as given.
\end{document}