CHAPTER 18 • Management of Tokyo Bay
341
For a zone which is farther from the site, the assumption is that fewer individuals are
likely to visit, all other factors being the same.
The relationship between number of visitors and the time-distance to the site can
be plotted, as shown in Fig. IS. sa. Suppose the distance from the given zone is tl, and
the number of visitors to the site is V,. What the diagram indicates is that all visitors
up to V, visitors would actually be willing to spend more time travelling to the site. If t
is now translated into cost of travel (travel expenditures plus opportunity cost), then
the ordinate represents the willingness of the individuals to pay for the recreational
experience. However, all individuals to the left of V, have to pay less than they are really willing to pay, so that there is, in real terms, a "consumer's surplus". The total amount
of that surplus is represented by the hatched area in Fig. IS. sa.
FigtJfe IS.Sb illustrates the effect of improving the quality of the site. If the distance
remains the same, i.e., t" the improved quality will induce more visitors to the site, as
reflected by V2• This increases the consumer's surplus, the additional consumer's surplus being represented by the trapezoidal area in the figure. The increment in
consumer's surplus represents the benefits of the actions taken to improve quality.
However, the increase in consumer's surplus mayor may not be larger than the costs
to improve the quality of the site.
A monetary estimate of Potential Consumer's Surplus (PCS) is hence derived from
the physical demand function of a recreational activity combined with an estimate of
unit travel cost and the population of the area from which recreationists come. Thus,
to
PCSijk = 2mp J fk(t, Qj)dt ,
tij
where
• PCSijk = potential consumer's surplus associated with visitors from i residential
zone to j recreational area for k recreational activity;
• m
= cost per hour of travel;
• to
= longest possible time distance for a day recreation trip, assumed as four
hours.
The unit demand function for activity k at site j, Le., potential visits per
looooo-population of residential zone i to recreational area j, is V ijk = A(tii'Q/ A
coefficient, 2, reflects the fact that each recreational visit requires a round trip consisting of two trips, Le., one each way.
The expression after the integral is the nUDlber of visits in a year to zone j, for
activity k, per 100 000 persons of population in residential zone i. This rate, multiplied by the population, Pi' yields the estimated number of visits to zone j for
activity k. The number of visits multiplied by the cost of a round trip yields the
potential consumer's surplus in monetary terms. The integral with respect to time
indicates that all zones with to:S; 4 hours each way are included in the estimate of
PCS. SUDlming up PCS with respect to all i's yields total PCS expected in zone j for
activity k.
to
PCSjk = 2m'4,Pi J fk(t, Qj)dt
1
tij
341
For a zone which is farther from the site, the assumption is that fewer individuals are
likely to visit, all other factors being the same.
The relationship between number of visitors and the time-distance to the site can
be plotted, as shown in Fig. IS. sa. Suppose the distance from the given zone is tl, and
the number of visitors to the site is V,. What the diagram indicates is that all visitors
up to V, visitors would actually be willing to spend more time travelling to the site. If t
is now translated into cost of travel (travel expenditures plus opportunity cost), then
the ordinate represents the willingness of the individuals to pay for the recreational
experience. However, all individuals to the left of V, have to pay less than they are really willing to pay, so that there is, in real terms, a "consumer's surplus". The total amount
of that surplus is represented by the hatched area in Fig. IS. sa.
FigtJfe IS.Sb illustrates the effect of improving the quality of the site. If the distance
remains the same, i.e., t" the improved quality will induce more visitors to the site, as
reflected by V2• This increases the consumer's surplus, the additional consumer's surplus being represented by the trapezoidal area in the figure. The increment in
consumer's surplus represents the benefits of the actions taken to improve quality.
However, the increase in consumer's surplus mayor may not be larger than the costs
to improve the quality of the site.
A monetary estimate of Potential Consumer's Surplus (PCS) is hence derived from
the physical demand function of a recreational activity combined with an estimate of
unit travel cost and the population of the area from which recreationists come. Thus,
to
PCSijk = 2mp J fk(t, Qj)dt ,
tij
where
• PCSijk = potential consumer's surplus associated with visitors from i residential
zone to j recreational area for k recreational activity;
• m
= cost per hour of travel;
• to
= longest possible time distance for a day recreation trip, assumed as four
hours.
The unit demand function for activity k at site j, Le., potential visits per
looooo-population of residential zone i to recreational area j, is V ijk = A(tii'Q/ A
coefficient, 2, reflects the fact that each recreational visit requires a round trip consisting of two trips, Le., one each way.
The expression after the integral is the nUDlber of visits in a year to zone j, for
activity k, per 100 000 persons of population in residential zone i. This rate, multiplied by the population, Pi' yields the estimated number of visits to zone j for
activity k. The number of visits multiplied by the cost of a round trip yields the
potential consumer's surplus in monetary terms. The integral with respect to time
indicates that all zones with to:S; 4 hours each way are included in the estimate of
PCS. SUDlming up PCS with respect to all i's yields total PCS expected in zone j for
activity k.
to
PCSjk = 2m'4,Pi J fk(t, Qj)dt
1
tij