6. Step 6: Estimate user benefits

Chapters 6 and 7 show how to calculate the user benefits of proposed initiatives. This is done by gradually building up the level of complexity of the transport setting and associated analytical method, as follows:

Chapter 6 introduces the general concepts and their application to the simpler case where there are no cross-modal or network effects.
Sections 7.1 to 7.2 extend the concepts and methods to cases where cross-modal and network effects apply. The content can be directly applied to relatively simple cross-modal and network situations.
Sections 7.3 and 8.4 address the application of the principles and concepts to the complex case of urban transport networks in cities.
Section 8.5 completes the discussion by addressing the issue of deferred future investments, and its effects on user benefits.

Box 5 introduces some key concepts used throughout Chapters 6 and 7. The detailed foundations underlying these two chapters can be found in NGTSM06 Volume 5, Sections 2.6 and 2.7. Those sections of Volume 5 discuss three methods for benefit estimation: the social welfare approach; the gainers and losers approach; and the consumers’ surplus with resource correction approach. The social welfare approach is used here because it is the simplest, together with the consumers’ surplus with resource correction approach because it used in some of the mode specific guidance sections. Volume 5 shows the application of these methods to a wider range of settings.

Steps

6.1 Determine methodologies for estimating impacts of the initiative on user costs.

6.2 For existing traffic, take the difference between total social generalised costs for the Base and Project Cases.

6.3 For induced (diverted and generated) traffic, calculate user benefit as the difference between the increase in willingness-to-pay and the increase in social generalised costs for the Project Case

6.4 If the consumers' surplus method is used to measure user benefits, a resource correction factor may be required.

Table 2 provides a summary of the formulas to be used for calculating user benefits for existing and induced (diverted + generated) traffic.

Box 5: User benefit estimation: key concepts

User benefits arise from transport improvements. They are measured by comparing key outcomes in the Base Case versus the Project Case (denoted by subscripts 1 and 2 respectively).

The above figure shows a travel demand curve, where the level of traffic (Q) is a function of the user’s perceived cost (P), where perceived cost is the sum of all monetary and non-monetary travel costs that the user considers in making transport decisions, all expressed in equivalent monetary units. A standard assumption is to assume the demand curve is linear, allowing the ‘rule of half’ to be used (see Section 6.3).

The transport improvement lowers the perceived cost from P₁ to P₂, resulting in an increase in traffic from Q₁ to Q₂ (a move along the demand curve).

At any given traffic level, the marginal benefit of travel is the height of the demand curve, reflecting the marginal willingness-to-pay (WTP) for a given quantity. The area under the demand curve measures the total WTP (TWTP). The word ‘total’ here means for all units of traffic being considered added together. In the Base Case, TWTP = areas a + b + c. In the Project Case, TWTP = areas a + b + c + d + e. The increase in TWTP for the project case compared with the base case is areas d + e.

Consumer surplus (CS) is the TWTP above P. In the Base Case CS = area a . In the Project Case CS = areas a + b + d. The increase in consumers’ surplus for the project case compared with the base case is areas b + d.

The above figure shows the resource user cost situation. It shows the average social generalised cost (AC) curve for the Base and Project Cases. The constant AC case is shown here. (NGTSM06 Vol 5 Part 2 also discusses the increasing cost case.) Total social generalised cost (TC) is measured as the product of AC and Q. For the Base Case TC = areas f + g. For the Project Case TC = areas g + h. The increase resource user costs for the project case compared with the base case is areas h – f.

Sections 6.2, 6.3, 6.4 and Chapter 7 apply these concepts to generate user benefit formulas in various situations.

Table 2: Summary of formulas for calculating user benefits for existing and induced traffic
	ExistingTraffic(1)	InducedTraffic(2)	All TrafficCombined(3 = 1+2)
Method 1: Increase in Social Welfare
a: Increase in willingness-to-pay	0	0.5 (P₁ + P₂) (Q₂ – Q₁)	0.5 (P₁ + P₂) (Q₂ – Q₁)
b: Increase in social cost	(AC₂ – AC₁) Q₁	AC₂ (Q₂ – Q₁)	AC₂Q₂ – AC₁Q₁
c = a – b: User Benefit	(AC₁ – AC₂) Q₁	0.5 (P₁ + P₂) (Q₂ – Q₁) – AC₂ (Q₂ – Q₁)	0.5 (P₁ + P₂) (Q₂ – Q₁) – (AC₂Q₂ – AC₁Q₁)
Method 2: Increase in Consumer Surplus + Resource Correction
d: Increase in Consumer Surplus	(P₁ – P₂) Q₁	0.5 (P₁ – P₂) (Q₂ – Q₁)	0.5 (P₁ – P₂)(Q₂ + Q₁)
e: Resource correction	(P₂ – AC₂) Q₁ – (P₁ – AC₁) Q₁	(P₂ – AC₂)(Q₂ – Q₁)	(P₂ – AC₂) Q₂ – (P₁ – AC₁) Q₁
f = d + e: User Benefit	(AC₁ – AC₂) Q₁	0.5 (P₁ + P₂) (Q₂ – Q₁) – AC₂ (Q₂ – Q₁)	0.5 (P₁ + P₂)(Q₂ – Q₁) - (AC₂Q₂ – AC₁Q₁)

_{Note: P is perceived cost; AC is average generalised cost; Q is traffic level; subscript 1 denotes Base Case; subscript 2 denotes Project Case.}

6.1 Determine methodologies for estimating impacts of the initiative on user costs

For most transport initiatives, the bulk of the benefits accrue (at least in the first instance) to users of the infrastructure. Trains, trucks and cars save operating costs; passengers and freight save time. There may be other benefits to transport users such as improved reliability or greater comfort for passengers, or less damage to freight. Both reductions in costs and improvements in service quality can lead to increases in usage – diverted demand, sourced from other routes or modes, and generated demand, which is altogether new traffic.

Estimates of vehicle or train operating costs and times taken for the Base and Project Cases for each year of the initiative’s life are also needed. For detailed CBAs, use computer models to derive these estimates. The computer models may estimate benefits and costs for selected years, for example, at five- or 10-year intervals, and interpolate for the intervening years. For rapid CBAs, a greater level of interpolation and extrapolation is acceptable.

Computer models require data on the infrastructure and on the vehicles or trains using the infrastructure (quality and quantity). For improvements to road and rail line-haul infrastructure, there is a four-step process:

Estimate free speeds (the speeds and times taken in the absence of any interference from other vehicles or trains)
Adjust speeds downward and travel times upward to allow for congestion (including time lost at intersections for urban traffic and in passing loops for trains)
Estimate levels of consumption of inputs (fuel, time)
Multiply input consumption levels by unit costs.

Here, the term ‘unit costs’ refers to the average price, cost or value of inputs; for example, fuel per litre, time per hour, hourly wage rates for drivers and crew, lubricating oil per litre, cost per tyre and so on. For some inputs, private and resource unit costs differ. For example, the resource unit cost of fuel will exclude excise causing it to be less than the private cost, which is the market price. Ensure the correct unit costs for estimating a financial cost or a resource cost are used (see Boxes 2 and 3 for explanations of financial and resource costs).

Calculations may be needed for a number of different categories of user (e.g. for road: private cars, business cars, rigid trucks, articulated trucks, B-doubles, road trains) and for multiple origin–destination pairs.

Since infrastructure utilisation fluctuates by time of day, day of week and season, and costs to users change with the level of infrastructure use when there is congestion, the computer model may have to loop around many times to cover the full range of utilisation levels. A simpler approach is to model only morning peak and apply an expansion factor to obtain whole-year impacts. Unrealistic expansion factors can lead to major errors in benefit estimation. It is better to model at least the peak and a representative off-peak time of day.

It is acceptable to index unit costs over the appraisal period where resource costs or users’ willingness-to-pay are expected to rise over time. For labour costs, value of work time, and human capital-based safety and externality values, use a forecast for real wages growth. For willingness-to-pay values such as non-work time, and willingness-to-pay-based safety and externality values, use a forecast for per capita GDP growth multiplied by an income elasticity of 0.5. Fuel consumption by vehicles and trains may be indexed to fall with time due to technological improvements.

6.2 For existing traffic, calculate user benefit as the difference between total social generalised costs for the Base and Project Cases

The social welfare approach to benefit estimation is used in Sections 7.2 and 7.3. In this method, net user benefit is the increase in the total gross benefit users' gain from travel (as measured by TWTP), less the increase in total resource cost borne by the user from that travel (time, fuel use and so on).

Existing traffic’ is traffic (referring to all units of throughput - people, vehicles, freight) that uses the relevant infrastructure in both the Base and Project Cases (not diverted or generated traffic). The quantity of existing traffic is, by definition, the same in the Base and Project Cases.

For existing traffic, TWTP does not change (see Box 5). So to calculate user benefit, estimate the total social generalised costs (TC) for the Base and Project Cases and take the difference where:

total social generalised cost = level of existing traffic × average social generalised cost

i.e. TC = Q x AC

The user benefit for existing traffic is therefore:

(AC₁ – AC₂) Q₁ [formula 1]

where Q₁ is the level of existing traffic, and AC₁ and AC₂ are the average social generalised costs for the Base and Project Cases respectively.

Note that changes in money and perceived costs are irrelevant for existing traffic (but are relevant for new traffic - see Section 7.3).

6.3 For induced (diverted and generated) traffic, calculate user benefit as the difference between the increase in willingness-to-pay and the increase in social generalised costs for the Project Case

If demand is assumed to be perfectly inelastic (no diverted or generated traffic), skip this section. Note that the term ‘induced traffic’ here refers to traffic not the number of users. Any increase in usage by existing users is treated as generated traffic.

Boxes 5, 6, 7 and 8 provide diagrammatic explanations and a numerical example that will assist readers in understanding the text below. It is suggested they be read concurrently.

The gross benefit to diverted and generated traffic from using the infrastructure affected by the new initiative is given by the increase in TWTP - the area under the demand curve between the Base Case and Project Case traffic levels.

The increase in TWTP can be estimated using the rule-of-a-half^[1] as:

increase in TWTP = (P₁+P₂)(Q₂–Q₁)/2 [formula 2]

where Q₁ and Q₂ are the respective Base Case and Project Case quantities and P₁ and P₂ are the respective Base Case and Project Case perceived costs paid or incurred by users. If there is no diverted or generated traffic, Q₁ = Q₂, and there is no WTP benefit (as in section 6.2).

To obtain the net user benefit arising from the diverted and generated traffic, deduct from equation (2) the increase in social generalised costs incurred by users.

Hence the net user benefit for diverted and generated traffic is:

(P₁ + P₂)(Q₂ – Q₁)/2 – AC₂(Q₂ – Q₁) [formula 3].

If diverted traffic is present, there may be additional benefits or costs to consider on the mode or route from which the traffic diverts. See Chapter 7.

Combining formulas (1) and (3) above for existing traffic and for diverted and generated traffic, the formula for net user benefit across all traffic is:

(AC₁ – AC₂)Q₁ + (P₁ + P₂)(Q₂ – Q₁)/2 – AC₂(Q₂ – Q₁)

which simplifies to

(P₁ + P₂)(Q₂ – Q₁)/2 – (Q₂ AC₂ – Q₁ AC₁) [formula 4].

6.4 If consumers' surplus is used to estimate user benefits, a resource correction factor may be required

Sections 6.2 and 6.3 calculated user benefits using the social welfare approach based on changes in total willingness-to-pay and total user resources costs. As noted at the start of this chapter, the alternative method is to estimate the user benefit using the gainers and losers approach in which gains and losses to users (consumers) are measured as consumer surplus changes. This approach is widely used in transport economics, including in urban transport assessments using urban travel demand models.

Consumers’ surplus is the area under the demand curve above the perceived price (perceived user cost). When there is a change in perceived cost from P₁ to P₂, the change in consumers’ surplus is measured as:

(P₁ – P₂)(Q₂ + Q₁)/2 [formula 5].

Note that the consumers’ surplus formula (5) matches the correct net user benefit result given by formula (3) in Section 6.2 only in the special case where perceived costs and average social generalised costs are equal; that is, P₁ = AC₁ and P₂ = AC₂. In practice, that may not be the case because:

Perceived cost may include taxes, charges and subsidies
Users may fail to perceive some of the resource costs they incur.

An adjustment or ‘resource correction’ is required whenever P₁ ≠ AC₁ and P₂ ≠ AC₂.The resource correction adjusts for the differences between perceived and social generalised costs. Details of the resource correction are discussed below. As in Section 6.3, references to Boxes 5, 6, 7 and 8 will assist readers in understanding the text below. It is suggested the text and the boxes be read concurrently.

For existing traffic, the consumer surplus change is (P₁ – P₂)Q₁ whereas the true benefit to society is (AC₁ – AC₂)Q₁ (see Section 7.2). The required adjustment is to add a resource correction equal to the increase in the gap between perceived price and social generalised cost (P₂ – AC₂)Q₁ – (P₁ – AC₁)Q₁. That is

(P₁ – P₂)Q₁ + [(P₂ – AC₂)Q₁ – (P₁ – AC₁)Q₁] = (AC₁ – AC₂)Q₁

For diverted and generated traffic, the resource correction is the difference between perceived and social generalised costs, that is, (P₂ – AC₂) (Q₂ – Q₁).

The resource correction formula for diverted and generated traffic can be expressed as

resource correction = (perceived [average] cost – average social generated cost ) ×
quantity of diverted and generated traffic

The total user benefit for diverted and generated traffic is then the consumers’ surplus change (P₁ – P₂) (Q₂ – Q₁)/2 plus the resource correction (P₂ – AC₂) (Q₂ – Q₁), which simplifies to

(P₁+P₂)(Q₂–Q₁)/2 - AC₂(Q₂–Q₁)

the same as formula (3) in Section 6.3.

Note that if social generalised costs exceed perceived costs, the resource correction will be a negative amount.

In the case of road infrastructure, where fuel excise causes perceived cost to exceed the resource cost of driving, the resource correction for additional diverted and generated traffic on the initiative infrastructure will equal the gain in fuel excise to the government (assuming all other costs are fully perceived). Even though the fuel excise is a transfer from road users to the government, it is still part of users’ increased WTP and so is a benefit.

Box 6: Diagrammatic explanation of user benefit estimation: price > cost

The diagram shows the case where perceived cost exceeds social generalised cost, for example, due to the fuel excise. The initiative reduces both perceived cost and social generalised cost, with subscript 1 indicating the Base Case and subscript 2 the Project Case. Infrastructure use is determined by the intersection of perceived cost with the demand curve (expressed as a function of perceived cost). The benefit, with respect to existing use, is the area of the rectangle between the Base and Project Case levels of social generalised costs up to the level of existing traffic, Q₁. For diverted and generated traffic (Q₁ to Q₂), the increase in WTP is the area under the demand curve between Q₁ and Q₂, while the benefit for this traffic is the WTP area minus Project Case social generalised costs.

Applying the consumers' surplus with resource correction approach (see Section 6.4), provided P₁ – AC₁ = P₂ – AC₂, no resource correction is needed for existing traffic. The resource correction for the diverted and generated traffic, that is, the rectangular area (P₂ – AC₂) × (Q₂ – Q₁). The total benefit can be measured as the consumers’ surplus change (P₁ – P₂) × (Q₂ + Q₁) / 2 plus the resource correction.

Box 7 provides a numerical illustration.

Box 7: Numerical example of user benefit estimation: price > cost

In this numerical example, the initiative results in a reduction in perceived costs from $2.00 to $1.80. Existing traffic is 10 000 units. The fall in perceived costs induces additional diverted and generated traffic of 2000 units. Social generalised costs per user fall from $1.40 to $1.20.

Existing traffic: Total social generalised costs fall from $14 000 = 10 000 × $1.40 to $12 000 = 10 000 × $1.20, leading to a benefit to society of $2000.

Diverted and generated traffic: The gross benefit to users (or the WTP) is $3800 = 2000 × ($2.00 + $1.80)/2. The social generalised cost to society of creating this benefit is $2400 = 2000 × $1.20. The net benefit from the increased WTP is therefore $1400 = $3800 – $2400.

Total benefit: The total benefit to society is the sum of benefits for existing traffic and for diverted and generated traffic, i.e. $3400 = $2000 + $1400.

Consumers’ surplus with resource correction approach (see section 6.4): Since, P₁ – AC₁ = P₂ – AC₂, that is, $2.00 – $1.40 = $1.80 – $1.20 = $0.6, no resource correction is needed for existing traffic. The resource correction applies to the diverted and generated traffic: 2 000 × $0.6 = $1200. The total benefit is the consumers’ surplus change ($2.00 – $1.80) × (12 000 units + 10,000 units) / 2 = $2200 plus the resource correction, $2200 + $1200 = $3400.

Box 8: Diagrammatic explanation of user benefit estimation: cost > price

The diagram shows the case where social generalised cost exceeds perceived cost, due to either a subsidy or users failing to perceive some of the costs they incur. The initiative reduces both perceived cost and social generalised cost, subscript 1 indicating the Base Case and subscript the Project Case.

Infrastructure usage is determined by the intersection of perceived cost with the demand curve (expressed as a function of perceived cost). The benefit in respect of existing users is the area of the rectangle between the Base and Project Case levels of social generalised costs up to the level of existing traffic, Q₁. For diverted and generated traffic (Q₁ to Q₂), the increase in WTP is the area under the demand curve between Q₁ and Q₂. The benefit for this traffic is the WTP area minus Project Case social generalised costs. The result is a triangle of positive benefit for traffic for which WTP exceeds social generalised cost, minus a triangle of disbenefit for traffic for which the social generalised cost exceeds WTP. The resource correction (see Section 6.4) for the diverted and generated traffic is the rectangular area (P₂ – AC₂) (Q₂ – Q₁). With social generalised cost exceeding perceived cost, the resource correction is a negative amount.

[1] The rule-of-a-half says that if we assume the demand curve to be linear over the relevant traffic range (here between Q₁ and Q₂), the area d in Box 5 can be estimated as half the rectangular area (Q₂ – Q₁)(P₁ – P₂).