Box 3. Calculation of User Benefits Using Compensating Variation

As discussed by Johnston, Rodier, Choy, and Abraham (2000), Small and Rosen (1981) show how a consumer benefit measure known as compensating variation (CV) can be obtained from discrete choice models:

where l is the individual's marginal utility of income, V_m is the individual's indirect utility of all m choices, p⁰ indicates the initial point (before the policy change), and p^f indicates the final point (after the policy change). The change in indirect utility is converted to dollars by the factor, 1/l, or the inverse of the individual's marginal utility of income.

The compensating variation formula (1) above is adapted to work with the SACMET96 mode choice models. In these models, households are segmented into income/worker categories and person trips are generated for those categories. To obtain compensating variation for each income/worker category h, the following formula is applied for all modes m and for all trips Q between all origins i and all destinations j:

where l is provided by the coefficient of the cost variable in the mode choice equations. Total compensating variation is obtained by summing the compensating variation obtained from each income/worker group. Compensating variation is also obtained from the non-home-based mode choice models, which are not stratified by household/income classes.

Compensating variation can easily be calculated by extracting the required information from the travel model and manipulating it in a spreadsheet. The specific steps are as follows:

1. Write a program within the travel model (in this case, MinUTP) to output the logsum (denominator) of the mode choice equation for each trip type and household/income category, as well as the number of trips in each category.

2. Import these data into a spreadsheet, and calculate CV for each category. Summing this value would provide the total user benefits, without including project costs.

3. Determine the estimated annualized capital and operating costs of each alternative.

4. Determine the proportion of VMT attributable to each trip category, based on number of trips and average trip length by type.

5. Allocate the annualized capital and operating costs to trip category based on the proportion of VMT in that trip category.

6. For each trip category, subtract the allocated costs from the CV to produce the net economic benefit. Sum across trip types to get net benefits by income group.

Based on a review of the literature, the authors assumed total operating costs of $0.40 per mile. Capital and operation and maintenance (O&M) costs of the new facilities were estimated based on cost figures provided in the Sacramento region's 1996 metropolitan transportation plan.

Commercial Vehicle Travel

Economic benefits for commercial vehicles are calculated based simply on travel time and operating cost savings. Benefits are obtained from the trip distribution model in SACMET96, which distributes commercial vehicle trips as a function of zone-to-zone travel times. As reported in Johnston, Rodier, Choy, and Abraham (2000), the following formula was applied:

where B is equal to the net benefits to commercial vehicle travel, including travel time costs, O&M costs, and revenue benefits. Travel time and VMT changes for commercial vehicles are obtained from the travel model for each scenario. Travel time is converted to dollars using the average wage rate of truck drivers in the region ($12 per hour). Total O&M costs and revenue benefits for the scenarios, excluding wages, are obtained by multiplying the average per mile costs for the region ($0.90 for O&M and $0.95 for revenues) by VMT. (Truck wages, O&M costs, and revenues were developed based on national data and in consultation with the California Trucking Association; very little local data were available.)

User benefits were calculated using SACMET96 but not MEPLAN. There are differences of opinion over whether consumer surplus measures, such as the Small-Rosen traveler welfare model described above, are valid when land use demand shifts. Using the Portland statewide model (a TRANUS application), Dr. Jonathan Hunt at the University of Calgary is currently testing methods to obtain measures of consumer welfare from MEPLAN, TRANUS, or a similar transportation-land use model.

For additional discussion of this measure, see Rodier, Johnston, and Shabazian (1998).