The recreation travel-cost model is really a simple type of household production model: households spend money and time to produce recreation trips, where Q is an unpriced input to trip quality. Assuming trip costs are incurred to access the site (and don't generate any utility directly), the trip cost serves as a proxy for a site price.

Consider a really simple hypothetical case. Suppose there are three concentric zones (A, B and C) around a recreation site with no entry fee:

Zone    Population      Visit Rate      Total Trips     Cost/Trip
  A       10,000           2.5            25,000           $2
  B       20,000           1.0            20,000           $4
  C       30,000           0.5            15,000           $6

We assume visitation rates are solely determined by trip cost. Suppose the site started charging a $2 entry fee. Residents of zone A would then have a cost of $4 per trip, equivalent to the current trip cost for residents of zone B. So they would cut back their visitation rates equivalently to zone B's current rate of 1.0. And residents of zone B, facing an increased trip cost of $6, would cut back their visitation rates to 0.5, equivalent to the current visistation rate from zone C. We assume there would be no visits from zone C, so under a $2 entry fee there would be 10,000 trips from zone A and 10,000 trips from zone B, or 20,000 trips total.

Following the same logic, if the site entry fee were set at $4, you would expect 5,000 trips from zone A only. And since we don't see any visitors with trip costs of $6, we'll assume that's the site demand choke price. So the site demand schedule would pass through these points:

Can you calculate the economic value (consumer surplus) of this site?

There are a number of variations on this method:

1. We can analyze the relationship between visitation rate and cost/trip via regression analysis, and use the predicted regression equation to calculate aggregate site demand under any site price.
2. We can analyze probabilities of individual trips rather than aggregate trip frequencies from geographic zones. This usually requires the use of discrete-choice regression procedures. Total site visits is determined by both individuals' binary decisions (visit/don't visit) and individuals' trip frequencies which are conditional on the decision to visit.
3. An extension of this discrete-choice approach is the random-utility model (RUM), in which observed site choices are treated as indexing the relative utilities individuals derive from alternative sites. The analyst estimates a discrete-choice model for each site as a function of site characteristics and trip expenditures. The marginal rate of substitution between a site quality index and trip expenditures represents a WTP measure for site quality.
4. A hedonic travel-cost method decomposes trip expenditures into implicit WTP measures for component attributes of sites.

1. Trip costs should account for both money and time costs, but the valuation (opportunity cost) of travel time is typically ill-defined. Researchers often simply assume the value of travel time is some fraction of the recreationist's wage rate.
2. Some zones may have substitute sites which reduce visitation rates to the site being analyzed.
3. If the site is congested, a site fee will reduce visitation by less than the model would predict, since any reduction in visitors improves site quality (by reducing congestion) for the remaining users.
4. Trips are assumed to be homogeneous, but may not be. How do we account for multi-purpose or multi-day trips?