Suppose that two owners of refreshment stands, George and
Henry, are trying to decide where to locate along a stretch
of beach. Suppose further that there are 100 customers
located at even intervals along this beach, and that a
customer will buy only from the closest vendor. Finally,
assume that the beach is short enough so that total sales
are independent of where the vendors locate.
Suppose that initially the vendors locate at points
A and C in the illustration below. These
locations would minimize the average traveling costs of the
buyers and would result in each vendor getting one half of
the business. However, this solution would not be an
equilibrium. If George moved from point A to point
B, he would keep all customers to his left and get some of Henry's customers. For similar reasons, Henry would move toward the center, and in equilibrium, both vendors would locate together in the middle.
This story of the beach was first told in 1929 by Harold Hotelling and is called Hotelling's model. Although it can give some insights into businesses decisions
concerning location and product characteristics, the model
has been more useful in explaining certain political
phenomena. Instead of two refreshment stands along a beach
trying to attract dollars from customers, consider two
political candidates along the political spectrum trying to
attract votes from voters. Only the candidate who attracts
the most votes will win, and a candidate must locate nearer
to more voters than his opponent to attract votes. With
these rules, there is a strong tendency for each candidate
to move to the middle.
In American politics this tendency has a predictable
consequence for presidential candidates, who must "sell" on
two beaches. To gain the nomination, the candidate must
position himself in the middle of the party. Because the
average Democrat has significantly different views than the
average Republican, Republican and Democratic candidates
sound quite different before nominations are decided. After
the party nominations are determined, the two candidates
must "sell" to the same beach. Republican candidates move to
the left and Democratic candidates move to the right. By election time, their positions on issues often seem close enough to many voters so that factors such as personality emerge as keys to the election.
There have been some notable exceptions to this pattern.
In 1964, Barry Goldwater won the Republican nomination
standing well to the right of the average voter, and was
unable or unwilling to reposition himself in the center. In
1972, George McGovern won the Democratic nomination standing
well to the left of the average voter, and was unable or
unwilling to reposition himself. Both lost in landslides.
A problem with the Hotelling model when applied to
commerce is that the results are very sensitive to the cost
assumption. There must be some cost to traveling because
customers prefer the closest vendor. But these costs must be
small, because the people at the end of the beach continue
to buy the same amount no matter how far they are from the
nearest vendor. If traveling costs are less, then people
might not care whether they go to the nearest vendor. If
they are greaterso that when the vendor gets far
away, people do not bother to gothe vendors will no longer cluster at the middle.
Suppose that the beach is a long beach, and people more
than 1000 feet away from any seller buy nothing. Also assume
that the beach is 4000 feet long, and the two vendors start
at the middle. Originally George sells to customers located
from the 1000-foot mark to the middle at 2000 feet, and
Henry sells from 2000 feet to 3000 feet. If George moves to
the 1000-foot mark, he will gain 1000 feet of new territory,
and he will lose only 500 feet to Henry. At the 1000-foot
mark, he will sell to all people from 0 to 1000 feet. He
will also sell to those people between him and Henry who are
closer to him. Because Henry did not move, but stayed at the
2000-foot mark, George will get all the customers up to the
1500-foot mark. Equilibrium in this case will occur only
when Henry moves to the 3000-foot mark.
In Hotelling's original model with small traveling costs,
location decisions were not economically efficient. By
increasing traveling costs, it seems that we can have
location decisions that are economically efficient. However,
the next section shows that
adding transport costs results in new efficiency problems.
Copyright Robert Schenk