Spatial demand functions describe the relationship between distance of
consumers' homes to the place where a good is produced or
traded and the demand after this single good or group of goods.
Basis for the delineation of such spatial demand functions are the convex
downward-sloping
individual demand curves. One example for such a demand curve is shown
in
Figure 1 below.
Figure 1: Individual demand curve
(J.B. Parr and
Denike, K.G., H.S. 1970, p.
569)
This function can be modified for a given f.o.b. price of a product to
consider the manner in which individual demand varies with the distance of
the consumer's location to the point at which the good is produced or
offered.
Away from this location the real price is greater than the f.o.b. price
(as transport costs occur) so that the individual demand is reduced with
increasing distance. Figure 2 shows an example of a resulting individual
spatial demand function for three different f.o.b. prices.
Figure 2: Distance-demand relationship for given fob-prices
(J. Parr and
Denike, K.G., H.S. 1970, p.
569)
Aggregation of all individual spatial demand functions for a given
product leads to a
general spatial demand function for that product.
To measure the responsiveness of quantities demanded to changes in
distance to the place where a good is produced and/or traded we use the
slope of this general spatial demand function. As measure we can take the
distance elasticity of demand, which is defined as the negative of the
percentage change in quantity demanded divided by the percentage change
in distance or
Figure 3 shows an example of an demand curve for jogging
shoes with
a
constant distance elasticity of demand of one.
Figure 3: Distance-Demand Curve with Constant Elasticity of One
(M.J. Katz and
Rosen, H.S. 1991, p. 91)
As the curve of the function of aggregated spatial demand will in most
cases not be
of such a shape, the distance elasticity of demand can be different for
changing
distances so that we have to determine the distance elasticity of demand
for a given point on the spatial demand curve. At the point on a
demand curve where the distance is d and the associated quantity
demanded is X, the distance point elasticity of demand is defined as
Cross distance elasticity of demand
In analogy to the cross price elasticity of demand for a good X with
respect to the price of good Y it is possible to delineate a cross
distance elasticity of demand.
The cross price elasticity of demand for a good X with respect to the
price of good Y is defined as the percentage change in the demand for X
induced by a percentage change in the price of Y.
A positive cross price elasticity of demand would mean that X and Y are
substitutes, and when the price of Y goes up, the consumption of X
increases.
Complementary goods would show a negative cross price elasticity of
demand, a price increase of Y would lead to a lower demand of X.
Accordingly a positive cross distance elasticity of demand for a good X
with respect to the distance which has to be overcome to acquire a good Y
would mean that an increasing distance between the consumer of Y and the
"market" of Y would result in a increasing demand after X. In this case X
and Y would be substitutes, instead of carrying the costs of overcoming
the increased distance to acquire Y consumers tend to substitute Y by
X.
If X and Y had a complementary relationship, consumers would demand less
of X with a higher distance to the market of Y, as Y is needed to make use
of X. A negative cross distance elasticity of demand would express this
relationship.
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