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Estimating The Opportunity Cost of Recreation Time in An
Integrable 2-Constraint Count Demand Model

Introduction

The value of natural assets is often assessed, in part, using models of consumer behavior
relating to the asset that reflect an individual's constraints on choice and opportunities for
consumption. When the behavior of interest is recreational use, often the substitution
between sites is important to measuring the value of the asset and any given site. A
common approach used is the random utility model, which predicts the probability of a
site being chosen on a given choice occasion. As an alternative, the demand systems
popularized in the literature on demands for market goods have been recently been
applied to the recreation demand and nonmarket valuation setting (e.g., Fugii et al.;
Shaikh and Larson).

While the flexible functional forms often used in market demand analysis are
attractive for their ease of use and familiarity to economists working with market goods,
some interesting nuances arise in their application to the nonmarket setting. One of these
is in the measurement of the total worth, or “access value,” of the activity being
consumed. It is not uncommon for recreation demands to be price-inelastic at the
observed levels of consumption. Depending on the demand system being used, this can
lead to problems with measuring access value.

For example, in the Almost Ideal Demand System (Deaton and Muellbauer),
whose focus is explaining budget shares and elasticities, some ranges of parameter values
imply that budget share increases with price, which leads to to an infinite Hicksian choke
price (not, by itself, necessarily a problem) and an infinite willingness to pay for access.

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