to the mountain lake for fishing. The utility function is assumed to have the normal properties of being concave with respect to its individual arguments.
The number of visits by the household is its internal “production function” for recreational fishing at the mountain lake. These visits may depend on the total time l that the household spends traveling to and fishing at the site, the various goods and services v (e.g., mode of travel, expenditures during traveling, and lodging, fishing gear) that the household uses in these activities, and the overall environmental quality of the lake q that makes it particularly suitable for fishing. Thus, the household’s “production” of the number of fishing visits z to the mountain lake is
Production of z is concave with respect to l and v and will shift with changes in environmental quality of the lake q.
Finally, one assumes that the household has an income based on wage earnings and uses that income to purchase all of its expenditures, including money spent on traveling to and from the lake. Given market prices px and pv for commodities x and v, respectively, and representing the market wage rate earned by the household as w, the household’s budget constraint is expressed as
with L being the total labor time available to the household and M representing any nonlabor income of the household (e.g., property rents, interest income, dividends). Equation (3) indicates that the total expenditures of the household must equal its total income.
By assuming that the household maximizes its utility from Equation (1) subject to Equations (2) and (3), one can derive the optimal demands for the time and purchased inputs, l* and v*, respectively, that the household spends on recreational fishing. These input demands will depend on the prices faced by the household px, pv, and w, its nonlabor income level M; and the environmental quality of the lake q. By substituting l* and v* into Equation (2), the household’s demand for the optimal number of visits z* to the lake for recreational fishing can be expressed as
Since the number of visits for recreational fishing is observable for all households that engage in this activity, the demand function in Equation (4) can be estimated empirically across households. Moreover, it is a common practice in many travel-cost models to determine whether households would vary their number of visits if any fees for recreational fishing f also changed. As a result,