The name is absent

composite market good. The consumer problem can
be modeled as an effort to minimize expenditures
subject to the constraint that utility is equal to the
reference utility level

(1) e(p_i,u) = min £ £ p_ix_i + y ∣ u(x_i,y) = u J

where e(∙) is the expenditure function, pi is the trip
cost for a visit to resource site i, and u is the reference
utility level. Trip costs include both money and time
costs.

To define use value, suppose the individual con-
templating a visit to the resource site is facing a trip
cost increase, such as an entrance fee, that makes the
trip a less attractive activity. If the increase in the
trip cost to site 1 is above the reservation price, pj,
no visit to resource site 1 will be made. Use value
for resource site 1 is

(2) UVi = e(pΓ,u)-e(pi,u)

where UV is the use value and pɪ* = (ρj,p2,-. ∙,p∏), pi
> pi. Use value is the amount of money that the
recreationist would be willing to pay to avoid the
price increase, holding utility constant. At the indi-
vidually determined use value, the potential recrea-
tionist is indifferent between paying the use value in
the form of higher entrance fees and taking trips or
not taking trips and leaving income intact. For
nonusers who already face their reservation (or a
greater) price, use value is equal to zero because
there is no observed price change. The nonuser faces
the reservation price before and after the entrance fee
increase.

Because ü = v(ρ_i,m), where v(∙) is the indirect
utility function and m is income, equation (2) can be
expressed as

UVi = e(p,*,v(pi,m)) - e(ρ_i,v(ρ_i,m))

(3) UVi = e(p*,v(p_i,m)) - m

UVi =∕(p⅛,m)

which simplifies since the expenditure function
evaluated at indirect utility is equal to income.' The
function /(∙) is the recreation valuation function.
Individuals will participate in recreation at site 1 if
the use value of recreation is greater than zero: Xi ≥ 1
if∕(p_i*,p_i,m) >0.

Measuring Use Value from Logistic Regression

Empirical estimates of use value must be consis-
tent with the theoretical definition of use value. The
recreation participation decision provides observ-
able behavior from which the determinants of the
behavior, such as trip costs and income, can be found
using logistic regression participation equations.
Estimates of use value that conform to the theoretical
definition of use value can be derived from empirical
recreation participation equations.

The recreation participation decision is a discrete
choice: whether or not to visit a natural resource site.
Single-site participation data is of the form

^{(4) Ilj=}

I 0 otherwise

where lŋ is a participation indicator variable and j
represents each individual in the sample, j ≡ l,...,m.
From equation (4), recreation participation will be
observed if the number of trips is greater than or
equal to one.

The recreation valuation function, and therefore
use value, depends on reservation prices, trip costs,
and income. Differences in recreation valuation will
also arise from differences in individual tastes and
unobservable differences in individuals. Acknow-
ledging these sources of differences in individual
valuations, the empirical recreation valuation func-
tion can be specified as the mean valuation function
with random error

(5) UVi =∕(pΓ, Pu m; τ) + ɛ

where ɛ is a mean zero error term. Subscripts for
individuals have been suppressed for simplicity.
Each individual is assumed to possess a common
valuation function with observable differences rep-
resented by τ and unobservable individual differ-
ences accounted for with the error term, ɛ. By
substitution, equation (4) becomes

{1 tf/( Pb Pi, m; τ ) + ɛ > 0

0 otherwise

Individuals will participate in recreation if the bene-
fits of participation outweigh the costs. That is, if

¹ An alternative, but equivalent, definition of UV is found using the indirect utility function. The implicit definition of UV is:
v(p,m) = v( pɪ*, m - UV). UV is the maximum willingness to pay to avoid the cost increase and leave the individual just as well off.
Using the implicit definition, it can be seen that UV leaves the individual indifferent between participation and nonparticipation.

114

<<   1   2   3   4   5   >>

More intriguing information