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Conclusions
This paper has introduced and illustrated a new empirical demand system that may be of
some use in measuring access values for recreation activities that are commonly price-
inelastic. Like the standard “semilog” demand system which relates demand covariates
to log-quantities, the “double semilog” or DS system generates finite access values, or
total consumer's surplus, estimates for own-price inelastic demands. This does not occur
with several other common and/or flexible demand forms, including the Almost Ideal
Demand System, the Linear Expenditure System, and the Cobb-Douglas demand models.
In addition, the DS model has somewhat greater flexibility than does the semilog system
to represent price, quality and income elasticities. Each demand has a separate income
coefficient in the DS model, while all income coefficients are the same in the semilog
model. Similarly, the price and quality elasticities in the DS model involve more
parameters, including the income elasticity in every case and, for own-quality effects,
additional parameters beyond that.
The model was developed initially for the standard single-constraint setting, then
extended to the case of two binding constraints on choice, as is often expected with
consumption of time-intensive goods such as recreation. The marginal value of time is a
parameter or function that can be estimated jointly within the model, provided it meets
certain homogeneity requirements implied by the two-constraint choice theory, or it can
be assumed to be predetermined as is common in many other recreation demand studies.
An illustration of the model is provided, using data on whalewatching in Northern
California at a system of 3 sites in relatively close proximity that one might expect act as
substitutes in consumption. The demand model satisfies the integrability conditions, and
estimates for two of the three sites, Point Reyes and Monterey, are highly significant with
the expected signs. The estimated marginal value of time is approximately $5.90 per
hour, with a range from $0.45/hr to $14/hr. Despite the fact that demands are highly