Estimating the Recreational-Use Value for Hiking in Bellenden Ker National Park, Australia

Abstract

The recreational-use value of hiking in the Bellenden Ker National Park, Australia has been estimated using a zonal travel cost model. Multiple destination visitors have been accounted for by converting visitors’ own ordinal ranking of the various sites visited to numerical weights, using an expected-value approach. The value of hiking and camping in this national park was found to be $AUS 250,825 per year, or $AUS 144,45 per visitor per year, which is similar to findings from other studies valuing recreational benefits. The management of the park can use these estimates when considering the introduction of a system of user pays fees. In addition, they might be important when decisions need to be made about the allocation of resources for maintenance or upgrade of tracks and facilities.

Appendix: The Expected Value Approach to Ranked Criteria Adopted from Nijkamp and others (1990)

Assuming that J criteria need to be ranked in increasing order of importance and that weights are nonnegative and add up to 1, the set of feasible weights is

$$ S=\{ (\gamma _1 , \ldots ,\gamma _j )|0 \le \gamma _1 \le \gamma _2 \le \cdots \le \gamma _j ;\sum\limits_j {\gamma _j } = 1\} $$

(A1)

It is assumed that the probability density function of the weights is equal for all values in S. Thus, a uniform distribution of the weights in S is derived:

$$ \eqalign{ {g(\gamma _1 , \ldots ,\gamma _{J - 1} )} &= c {\rm \ if \ } :0 \le \gamma_1 \le {1 \over J} \cr &\quad {\gamma_1 \le \gamma_2 \le {1 \over {(J - 1)}} - {{\gamma _1 } \over {(J - 1)}}} \cr &\quad {\vdots } \cr &\quad {\gamma _{J - 2} \le \gamma _{J - 1} \le {1 \over 2} - {{\gamma _1 } \over 2} - \cdots {{\gamma _{J - 2} } \over 2}} \cr & =0 {\rm \ elsewhere}} $$

(A2)

In Rietveld (1989), it is shown that c = (J−1)!J !. Once the values γ₁,...,γ_J-1 are known, the value of γ_J can be found as

$$ 1 - \gamma _1 - \cdots - \gamma _{J - 1} $$

The expected values of γ₁,...,γ_J−1 are the cardinalized values of rank numbers of 1,...,J. The expected value of an arbitrary γ _j is given by:

$$ E(\gamma _j ) = \int_0^{1/J} \int_{\gamma _{1} }^{q_ {1}} \cdots \int_{\gamma _{J - 2} }^{q_ {J - 2} } {(J - 1)!J!\gamma _j } d_{\gamma_{J - 1}} \cdots d_{\gamma_{1}} $$

(A3)

where

$$ q_k = {1 \over {(J - K)}} - {{\gamma _1 } \over {(J - K)}} - \cdots {{\gamma _k } \over {J - K}}(k = 1, \ldots ,J - 2) $$

(A4)

After integrating out γ_J−1, γ_J−2,. γ_J+1 in Equation A3, the following is obtained:

$$ \eqalign{E(\gamma _j ) &= \int_0^{1/J} \cdots \int_{\gamma_{j-1} }^{q_{j-1}}{(j-1)!J! \over (J-j-1)!(J-j)!} \cr &\quad (J-j+1)^{J-j+1_{\gamma_j}}\left(q_{j-1-\gamma j}\right)^{J-j-1} d_{\gamma j}\cdots d_{\gamma 1}}$$

(A5)

Integrating out r_j in Equation in A5 and making use of the fact that the primitive function of x(a-x)ⁿ equals

$$ {{ - 1} \over {n + 1}}(a - x)^{n + 1} x - {1 \over {(n + 1)(n + 2)}}(a - x)^{n + 2} $$

the following results can be obtained after the appropriate integrations (Rietveld, 1989):

$$ \eqalign{ E(\gamma_1 ) &= {1 \over {J^2 }} \cr E(\gamma _2 ) &= {1 \over {J^2 }} + {1 \over {J(J - 1)}} \cr &\qquad\qquad{\vdots} \cr E(\gamma _{J - 1} ) &= {1 \over {J^2 }} + {1 \over {J(J - 1)}} + \cdots + {1 \over {J \times 2}} \cr E(\gamma _J ) &= {1 \over {J^2 }} + {1 \over {J(J - 1)}} + \cdots + {1 \over {J \times 2}} + {1 \over {J \times 1}} } $$

({\rm A}6)