# Cost–Benefit Analysis of Investments in Air Traffic Management Infrastructures: A Behavioral Economics Approach

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Background: How the Evaluation of Airside Investments Can Evolve from a Neoclassical to a Behavioral Approach

- Propose a preliminary model for the CBA of investments in ATM infrastructures that evolves from the traditional approach to consider behavioral economics inputs.
- Apply this model to a case study—a CBA for the implementation of ADS–B technology aimed at improving airport operations and increasing available capacity, thus reducing delays and alleviating congestion.
- Obtain information on how investment decisions in airport airside facilities would be modified by including behavioral considerations.

## 3. A Methodological Framework for Classic Cost–Benefit Analysis

_{t}

_{0}is the generalized cost in year t without the investment; g

_{t}

_{1}is the generalized cost in year t with the investment; q

_{t}

_{0}is the volume of airport users in year t without the investment; q

_{t}

_{1}is the volume of airport users in year t with the investment; p is the price per trip including airport charges, airline ticket, and access and egress money costs; and τ is the value of total trip time (flying, access, egress, and waiting).

_{1}− τ

_{0}) and assume that prices remain unchanged (Section 7 presents a case of investment in ADS–B technology, which follows these assumptions). This kind of investment, which ultimately results in higher capacity [11,32], is illustrated in Figure 5. The vertical axis measures the generalized costs of passengers and their willingness to pay for airport services, while the horizontal axis measures the number of passengers per unit of time. Curve D represents demand conditions for air traffic at a period of time, and curve C represents the cost to the average passenger.

_{a}, g

_{0}), meaning that when the conditions faced by the airport are as described by curve D

_{0}, a maximum of q

_{a}passengers can be attended to over a period, at a constant generalized cost equal to g

_{0}. The average generalized cost function C implies that if the critical point q

_{a}is reached, at this capacity level there can only be an increase in traffic at a higher average cost. According to this initial situation, demand in a period (D

_{0}) has an imperfect substitute (e.g., another less convenient flight, airport, or mode of transportation) available at a generalized cost of g

_{1}that is higher than that of g

_{0}. However, with demand D

_{0}, all passengers willing to pay g

_{0}will be served. From that point onwards, further demand growth will cause congestion in the airport, creating time costs and delays, forcing passengers to travel at less preferred times if there are no investments in capacity. This is represented in Figure 5 by curve C, which provides a higher cost to the average passenger when demand grows. If the airport decides not to add capacity as demand increases, pushing the demand curve to the right, the airport throughput would exceed q

_{a}, resulting in increased congestion. Eventually, congestion and the corresponding generalized cost to passengers would reach a level where the average passenger would not have a preference between using the airport or the alternative means of transportation. The intersection of curves C and ‘Alternative’ represents this situation. At that moment, the generalized cost incurred by the average passenger would be g

_{1}, which is the generalized cost to passengers (for whom the airport is the preferred mode of transit) of diverting to the alternative mode of transportation. Let us presume that the growth in demand in the following period t leads to D

_{t}. Depending on which cost (g

_{0}or g

_{1}) applies, D

_{t}would be fully served by the airport if the project is implemented (q

_{d}), but would only be partially satisfied by the existing airport facilities if the project is not carried out (q

_{b}). In the latter case, there will be some deviated traffic to the second-best alternative (q

_{c}− q

_{b}), and some ‘discouraged’ or deterred traffic (q

_{d}− q

_{c}) that cannot be attended to at these costs. The project leads to higher capacity, so the situation with the project is illustrated by the possibility of maintaining a generalized cost of g

_{0}as demand changes to D

_{t}(q

_{d}). At a demand level equal to D

_{t}, without the project, the equilibrium point in the airport would be q

_{b}< q

_{d}. Therefore, the equilibrium level for demand D

_{t}with and without the project has been determined (q

_{d}and q

_{b}, respectively), and we can evaluate the economic benefit of the investment project.

_{b}); (ii) benefits from avoided diversion costs (q

_{c}− q

_{b}); and (iii) benefits from new generated traffic (q

_{d}− q

_{c}). These benefits can be measured as follows. The benefits to current users are given by (g

_{1}− g

_{0})·q

_{b}, since the alternative travel option now determines the maximum number of passengers (q

_{b}). The benefits from avoided diversion costs are given by (g

_{1}− g

_{0}) · (q

_{c}− q

_{b}), since passengers in the portion (q

_{c}− q

_{b}) will deviate to a less desirable alternative. The diversion could be ‘in time’ if passengers are compelled to depart at less convenient times or ‘in mode’ if they must choose an alternative airport or mode of transportation. The ‘rule of a half’, as shown in Equation (2) and Figure 4, applies equally to both diverted and generated traffic. The benefits of diverted traffic are given by the difference (g

_{1}− g

_{0}) in Figure 5. This amount should be understood as the average, which is equal to half of the time savings interval. The benefits from new generated traffic due to the project are given by 0.5·(g

_{1}− g

_{0})·(q

_{d}− q

_{c}). This benefit can also be read as the amount of deterred traffic that is avoided as a result of the investment, given a future demand prediction equal to Dt. Note that additional benefits (taxes and revenues above incremental costs) may be linked to deviated and generated traffic.

- First, an expansion in airside capacity will allow for an increase in both departure frequency and the number of routes available from the airport. This will reduce the frequency delay and perhaps even the duration of the trip, both of which help to lower the generalized cost of transportation. The frequency delay represents the difference between the preferred departure time for an average passenger and the closest actual flight departure that is acceptable to the passenger [32]. Other things being equal, the higher the departure frequency, the lower the frequency delay, and, consequently, the time cost of travel for the passenger.
- Second, airside investments might shorten the process time for aircraft, saving operating costs for airlines. These projects improve flight efficiency and, for instance, would reduce fuel consumption (internal benefit). The greater number of efficient procedures would, in some cases, enhance air transportation sustainability (external benefit) by lowering harmful emissions for the environment (reducing air pollution) or limiting noise in the airport vicinity.

## 4. Behavioral Economics Inputs

#### 4.1. Inconsistency in Time Adjustment When Evaluating Future Monetary Flows

- Exponential time discounting: ${\delta}_{E}=(1+{i}_{E}{)}^{-t}$, where ${i}_{E}$ is the exponential discount rate. This is the traditional approach for CBA (neoclassic framework), as illustrated in Equation (1).
- Hyperbolic time discounting: ${\delta}_{H}=(1+{i}_{H}\xb7t{)}^{-1}$, where ${i}_{H}$ is the hyperbolic discount rate. It considers time inconsistencies in valuations where impatience arises (much larger discounts in near-term decisions than in longer-run comparisons).
- Quasi-hyperbolic time discounting: ${\delta}_{QH}=\beta \xb7{\gamma}^{t},t\ge 1;{\delta}_{QH}=1,t=0$, where 0 < β < 1 captures the degree of immediate impatience (a smaller β shows greater impatience), and $\gamma ={(1+{i}_{QH})}^{-1}$ depends on the quasi-hyperbolic discount rate ${i}_{QH}.$

[PGL 1] To incorporate recent work in behavioral economics, which explores inconsistencies in time adjustments related to decision-making processes, we propose including non-exponential discounting in the airport capacity expansion problem. This can be achieved by using a discount factor that reflects the decision maker’s ‘real’ time perception.

#### 4.2. Risk Perception and Loss Aversion That Imply Expected Utility Deviations

- When faced with a risky decision that could result in gains, people are risk-averse and prefer options that have a higher likelihood of success but lower expected utility (concave value function).
- When faced with a risky decision that could result in losses, people tend to be risk-seekers, choosing options that have a lower expected utility if they have the potential to prevent losses (convex value function).

_{0}(an adaptation level or ‘anchoring’) and not only on the absolute value of revenues. This parameter r

_{0}depends on the expected direct revenues from passengers and airlines, as well as on costs related to the operation. It needs to be calibrated using empirical data.

[PGL 2] To incorporate recent work in behavioral economics, which explores the psychological aspects of decision-making, we propose including risk perception/aversion and expected utility deviations from neoclassical welfare economics in the airport capacity expansion problem. This can be achieved by using Prospect theory when reflecting the expected utility of the airport and the referent group (including society) in the analysis.

^{θ}and has been widely used for modeling risk aversion.

^{θ}if α ≥ 0, and

U (α) = λ u (α) = −λ (−α)

^{θ*}if α < 0

_{0}, the utility function can be expressed as Equation (6), and outcomes are evaluated relative to the reference point α

_{0}:

_{0})

^{θ}if α ≥ α

_{0}, and

U (α) = λ u (α) = −λ (α

_{0}− α)

^{θ*}if α < α

_{0}

_{0}) and losses (α < α

_{0}).

_{0}, then the function depends on the difference, α − α

_{0}. In fact, the valuation function itself differs depending on the sign of this difference. In more complicated versions of Prospect theory, the reference point may differ from current wealth or be randomly determined, such as by the circumstances of choice.

_{1}, α

_{2}, …, α

_{k}(e.g., annual cash flows in the evaluated project) ordered from smallest to largest with respective probabilities p

_{1}, p

_{2}, …, p

_{k}. These probabilities can be considered as ‘objective’ in the sense of being based on either logical analysis of relative frequencies or scientifically sound empirical evidence. Prospect theory allows decision makers to have decision weights, w

_{k}(p

_{k}), that may depend on the objective probabilities. Cumulative Prospect theory constructs decision weights for the ordered outcomes so that they are all positive and sum to one. These rank-dependent decision weights allow for the introduction of pessimism, the overweighting of extremely negative outcomes, and optimism, the overweighting of extremely positive outcomes, as well as other deviations from objective probabilities, while preserving the properties of a proper cumulative probability distribution [19,64]. Putting the decision weights and outcome valuation function together gives the following Equation (7):

_{A}is the valuation of prospect A. If the decision maker is choosing between two prospects, A and B, then Prospect theory predicts that the decision maker will choose A over B if V

_{A}> V

_{B}, choose B over A if V

_{B}> V

_{A}, and be indifferent between A and B if V

_{A}= V

_{B}.

_{k}(p

_{k}) = p

_{k}. Therefore, the decision maker must use objective probabilities as decision weights in Equation (7). For the differences in valuations of the alternatives to correspond to those from expected utility (neoclassical approach), the reference outcome must be set to zero so that valuation depends on outcomes rather than on gains and losses. When these conditions do not hold, policies proven to be efficient under the assumption that individuals are maximizing expected utility may not be efficient. Deviations of decision weights from objective probabilities and implications of non-zero reference outcomes (large differences between willingness to pay and willingness to accept) are addressed through a behavioral economics approach.

## 5. Problem Statement: Investments in Air Traffic Management Infrastructures

_{1}, and the ‘Movements 2’ curve represents the F capacity when adding ADS–B technology, which is higher and equal to f

_{2}. Therefore, the ‘Movement’ curves represent two levels of airside capacity, before and after equipment enhancement. When the airside capacity of the airport is given by ‘Movements 1’ and F is limited at f

_{1}(point a, and a capacity for aircraft movements of f

_{1}), the vertical axis on the left side indicates that the marginal benefit of adding a departure frequency is f

_{d}

_{1}. This value is higher than the marginal cost of decreasing AS, given by c

_{1}(point d). Expanding airside capacity to ‘Movements 2’ increases F to f

_{2}, which is accompanied by a decrease in AS. This can be explained by the fact that in f

_{1}the passenger costs due to FD are f

_{d}

_{1}, higher than the marginal operating costs, which are equal to c

_{1}. Then, the willingness of passengers to pay for an additional frequency is greater than the marginal cost associated with reducing AS (f

_{d}

_{1}> c

_{1}), and thus airlines have an incentive to increase F, implying a decrease in AS. Therefore, flight frequency increases to equilibrium at f′ (point b), resulting in a decrease in AS. At this point b, the marginal benefit of improving FD is equal to the marginal cost of decreasing AS (f

_{d}′ = c′). The benefit of expanding airside capacity from ‘Movements 1’ to Movements 2’, allowing for an increase in F, is equal to the area ‘abd’. There would be, at least initially, excess airside capacity (f

_{2}> f′). The provision of facilities operating at less than full capacity is due to technological invisibility in production functions (although this may well be the welfare-maximizing option; traffic growth generally means that capacity is ultimately covered).

## 6. ADS–B as an Investment for Airport Operations Enhancement

- Automatic—Position and velocity information is automatically transmitted periodically (at least once every second) without flight crew or operator input. Other parameters in the transmission are preselected and static.
- Dependent—The transmission is dependent on the proper operation of on-board equipment that determines position and velocity and the availability of a sending system.
- Surveillance—Position, velocity, and other aircraft information are transmitted as surveillance data.
- Broadcast—The information is broadcast to any aircraft or ground station with an ADS–B receiver. Current mode S Air Traffic Control (ATC) transponders are interrogated and then send a reply.

- Safety—ADS–B offers more precise and commonly shared traffic information. All participants have a common operational picture in real time. Therefore, ADS–B significantly improves the situational awareness of flight crews and air traffic controllers. Moreover, ADS–B provides more accurate and timely surveillance information than radar, with more frequent updates; it allows for a much greater margin in which to implement conflict detection and resolution measures. Additionally, ADS–B displays both airborne and ground traffic.
- Capacity—ADS–B can provide a substantial increase in the number of flights that the ATC system can accommodate. More aircraft can occupy a given airspace simultaneously if separation standards are reduced, and the increased precision of ADS–B enables the reduction of separation standards while maintaining safety. ADS–B not only enhances the accuracy and integrity of position reports, but also increases the frequency of these reports for a better understanding of the air traffic environment in the air and on the ground. Therefore, unwanted waiting times and delays are reduced, which releases capacity. ADS–B also (i) increases runway capacity with improved arrival accuracy to the metering fix; (ii) helps maintain runway approaches using cockpit display of traffic information in marginal visual weather conditions; (iii) enhances visibility of all aircraft in the area to allow more aircraft to use the same runway; and (iv) potentially allows for a reduction in separation.
- Efficiency—ADS–B allows substantial improvement in the accuracy of surveillance data within the ATC system. This helps ATC understand the actual separation between aircraft and allows controllers to avoid inefficient vectoring commands to maintain separation assurance, therefore improving efficiency both for flights and for ground movement. Then, the amount of fuel consumed is reduced because aircraft follow a more efficient path. With the implementation of ADS–B, there is affordable and effective surveillance of all air and ground traffic, even on airport taxiways and runways and in airspace where radar is ineffective or unavailable. Airlines can reduce the cost per passenger kilometer by flying more direct routes at more efficient altitudes and speeds with uninterrupted climbs and descents. Finally, airport operations increase their efficiency with the use of ADS–B data, because more accurate and timely surveillance information reduces unnecessary waiting times on ground movement and limits traffic delays.
- Environmental impact—ADS–B allows for more efficient movement of aircraft on the ground, which implies fewer waiting times, better routing and monitoring, and optimized paths. This results in fewer polluting emissions. Moreover, engine emissions and aircraft noise are reduced through continuous descent and curved approaches.

## 7. A Practical Example for the New Cost–Benefit Analysis Framework

- Financial CBA. The financial appraisal of an investment project involves estimating revenues and costs (market prices), including financing costs.
- Economic (social) CBA. The result of an economic appraisal informs the public sector investor about the economic viability of a project for society, independently of its financial returns.

#### 7.1. Traditional CBA for the Adoption of ADS–B Infrastructure

#### 7.1.1. Identification of the Project Objectives and Relevant Alternatives (Problem Statement)

#### 7.1.2. Identification of the Time Horizon for the Evaluation

#### 7.1.3. Identification of Costs and Benefits

#### 7.1.4. Assessment of the Distribution of Costs and Benefits throughout the Evaluation Horizon

- Project investment costs and replacement expenditures are obtained from previous ADS–B implementations and studies [74,78,82,93,94], with price adjustments based on the Consumer Price Index (CPI), calculated by the US Bureau of Labor Statistics [95], and the Harmonized Index of Consumer Prices (HICP), calculated by Eurostat [96]. Those indexes account for inflation and deflation. We consider both the equipment costs (ADS–B, Controller Working Positions, software, Human Machine Interfaces, and communication facilities) and the technical training for the technology use.
- As depicted in Figure 16, the main operational benefits arise from improved monitoring and surveillance data that allow for a reduction in delays due to shorter waiting times on the ground. A reduction in delays is reflected in an increase in capacity, which represents new benefits due to ‘non-diverted’ and ‘induced’ traffic in the project scenario according to the differential approach (see Section 3 and Section 5). The theoretical relationship between capacity and delay is illustrated in Figure 10a (see Section 5), which shows that delay is not a phenomenon that occurs only at the limit of capacity. Some amount of delay will be experienced long before capacity is reached (leading to the formation of queues), and it grows exponentially as demand increases. The term congestion describes a situation where demand is high in relation to capacity, and normal operations are accordingly compromised. Following this graphical theoretical model, an exponential relationship is proposed between delay and capacity utilization [34,38,97], resulting in the following Equation (8):

_{t}= φ

_{o}· (exp(U) − γ)

_{T}, DEP is the number of departures per hour, C

_{T}is the throughput capacity, φ

_{t}(in minutes) is the average delay at departure, and γ is a parameter related to the delay generated when traffic is extremely low. A calibration of Equation (8) with departure delay data from the EUROCONTROL’s Central Office for Delays Analysis [98] provides us with the fitting values of φ

_{o}= 115 min and γ = 1, which validates the findings of previous studies [38]. Following Equation (8) and using the reference data presented in Table 2, we can estimate the monetary benefits derived from an increase in capacity (induced traffic) due to delay reductions.

_{2}and NO

_{x}), because of the decrease in fuel consumption. This last benefit can be expressed in monetary values using data from Table 2. The computed benefits are of a financial and social nature, since they not only generate income for the referent group, but also include externalities that increase well-being and sustainability.

#### 7.2. Inclusion of PGL 1: Non-Exponential Discounting

#### 7.3. Inclusion of PGL 2: Utility Considerations

_{0})

^{θ}if α ≥ α

_{0}, and U (α) = λ u (α) = −λ (α

_{0}− α)

^{θ*}if α < α

_{0}.

_{1}, α

_{2}, …, α

_{k}). This provides us with the utility value of each year’s result. However, when performing CBA, we want to evaluate the utility of the whole project. Following Equation (7), ${V}_{A}={\sum}_{k=1}^{K}{w}_{k}\left({p}_{k}\right)U\left({\mathsf{\alpha}}_{k}\right),$ considering all the yearly wealth outcomes and weighting all of them equally, we can obtain the overall utility value. The results are shown in Table 4. Adding partial (yearly) utilities to obtain the overall prospect valuation is in line with behavioral principles and has been proven mathematically sound [19]. As discussed in Section 4, each element could be weighted according to probabilities or importance in the choice process.

_{0}= 0. Sometimes, this reference point can be understood as the ‘initial wealth’ considered by the decision maker and, therefore, may differ from zero. This accounts for the behavioral notion related to individuals valuing gains and losses from reference points rather than valuing outcomes. A reference point different from zero represents one of the main deviations from traditional neoclassical methods and explains the gap between willingness to pay and willingness to accept. It is certainly a major breakaway from final-wealth models. In more complicated versions of Prospect theory, the reference point may differ from current wealth or be randomly determined, for instance, by the circumstances of choice.

## 8. Discussion: Insights Regarding the Incorporation of Behavioral Notions to the Traditional Cost–Benefit Analysis Framework

_{1}(α

_{0}= 0, λ = 5, θ = 0.4, θ* = 0.5). Then, the subsequent rows display the sensitivity of the final outcome when the defining parameters are modified from the initial combination (U

_{1}): U

_{2}includes a change in θ (from 0.4 to 0.5), U

_{3}includes a change in θ* (from 0.5 to 0.6), and U

_{4}includes a change in λ (from 5 to 3). Therefore, taking U

_{1}as the baseline arrangement of parameters, changing θ (U

_{2}versus U

_{1}) influences years with positive outcomes, while changing θ* (U

_{3}versus U

_{1}) or λ (U

_{4}versus U

_{1}) has an effect on years with negative outcomes. Note that results in year 12 account for the equipment replacement costs and represent a disturbance in the project’s utility evolution.

_{0}will not modify the shape of the power utility curve, but will help decision makers evaluate the project in terms of gains and losses from a fixed level (‘initial wealth’) rather than valuing pure outcomes. A reference point different from zero explains the gap between willingness to pay and willingness to accept and characterizes how individuals make decisions. To represent the real behavior of airport operators and policy makers, who evaluate wealth with respect to certain anchors, the initial level α

_{0}should be calibrated according to the initial situation of the airport. Then, investment decisions are adjusted to reflect actual behavior in relation to this ‘anchor’ after introducing behavioral economic notions in the analysis, particularly loss aversion and actual willingness to pay. Therefore, the utility of airport expansion projects will depend not only on their absolute associated revenues, but also on a reference point that can be predetermined. While projects whose net present value is far from the reference point can be more easily accepted or rejected because of the diminishing sensitivity toward losses and gains, those projects whose net present value is close to the reference point region will require clearer gains to be accepted, as the evaluation is influenced by the fact that losses are overweight relative to gains.

_{1}reflects values for the power utility curve parameters (θ, θ*, and λ) that are consistent with past reflections from decision makers with moderate perceptions of diminishing sensitivity and loss aversion. The cumulative result for U

_{1}(V < 0) shows that even for a relatively small investment such as the one registered in the example, a moderate perception of risk and losses can draw a negative utility. In fact, this reticent behavior is intensified when projects require strong capital investments in the initial years, yet are slow to generate positive cash flows. Therefore, the behavioral model better explains the short-terminist thinking of some decision makers and their real aversion to risk and losses.

_{1}is the baseline scenario. Figure 20a shows that when θ is increased from 0.4 to 0.5 (enhancing sensitivity to gains), the cumulative utility curve (U

_{2}) shifts its slope upward (the closer θ is to one, the power curve depicted in Figure 9 is closer to linear, which represents the traditional neoclassical model of utility). In this situation, the project reaches a positive cumulative utility in year 8 (2025). This is the break-even point when the project begins to be not only profitable in the traditional way (NPV > 0), but also viable even considering risk and loss aversion (if no additional capital investments reduce the cumulative utility during the project time frame). Note that when diminishing sensitivity and aversion to losses are considered, the break-even point of the project is delayed from year 2 to year 8. Therefore, even if the behavioral inputs still provide a positive decision for the project’s development, it will be a less ‘strong’ decision than one with only the traditional approach. Increasing θ* (boosting sensitivity to losses) from 0.5 to 0.6 shifts the cumulative utility curve (U

_{3}) downward, as depicted in Figure 20a. The sensitivity to losses increases, and they are felt more intensely, making the final valuation even more negative. Figure 20b shows that lowering λ (reducing loss aversion) from five to three has the opposite effect and shifts the cumulative utility curve (U

_{4}) upward. In this situation, with a smaller aversion to losses, the project reaches a positive cumulative utility in year 14 (2037). Therefore, changes in θ modify the slope of the cumulative utility curve, while changes in θ* and λ shift the curve itself (this is because, in our example, there are only negative outcomes in the first year, so acting on θ and λ represents a change in origin).

- Using non-exponential discounting (PGL 1), the proposed method introduces risk in time value, obtaining lower-than-expected cash flows, and thus represents an investors’ penalty for bearing with risks associated with time value of money.
- Incorporating a utility approach in the analysis (PGL 2) allows capturing the behavioral notions described by Prospect theory, such as loss-aversion attitudes, decreasing sensitivity for gains and losses, and a potential anchoring of the decision with respect to a reference point.

## 9. Conclusions

#### 9.1. Managing Airport Capacity and Demand

#### 9.2. Evaluating Airport Investment Projects and Introducing Behavioral Economics in the Framework

[PGL 1] To incorporate recent work in behavioral economics, which explores inconsistencies in time adjustments related to decision-making processes, we propose including non-exponential discounting in the airport capacity expansion problem. This can be achieved by using a discount factor that reflects the decision maker’s ‘real’ time perception.

[PGL 2] To incorporate recent work in behavioral economics, which explores the psychological aspects of decision-making, we propose including risk perception/aversion and expected utility deviations from neoclassical welfare economics in the airport capacity expansion problem. This can be achieved by using Prospect theory when reflecting the expected utility of the airport and the referent group (including society) in the analysis.

#### 9.3. Findings and Limitations of the Study

- Performing a sensitivity analysis to determine which variables may cause project profitability to deviate from the estimated base case.
- Adopting a probabilistic approach when dealing with the uncertainties that exist in airport development projects.
- Estimating the likelihood that a project will perform below the profitability threshold and then no longer be desirable (adopting a probabilistic approach). The minimum acceptable level of profitability and the maximum tolerated probability of returns falling below the threshold are managerial decisions influenced by the project’s performance relative to the risk–reward profile of other investments in the sector and the broader economy.
- Performing additional airport capacity/demand assumptions to test and generalize the results concerning the CBA of ATM infrastructure investments.
- Expanding the new framework to the analysis of investments in other airport facilities and transportation areas.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Simplified overview of Cost–Benefit Analysis [14].

**Figure 4.**Consumer surplus $\mathsf{\Delta}C{S}_{t}=\frac{1}{2}({g}_{t0}-{g}_{t1})({q}_{t0}+{q}_{t1})$, with $g=p+\tau $ and $\tau =V\xb7t$, where V is the value of time per time unit; (

**a**) price reduction: $\frac{1}{2}({p}_{t0}-{p}_{t1})({q}_{t0}+{q}_{t1})$; (

**b**) time saving: $\frac{1}{2}({\tau}_{t0}-{\tau}_{t1})({q}_{t0}+{q}_{t1})$.

**Figure 5.**User benefits, derived from [32].

**Figure 8.**A hypothetical value function, derived from [61], with the reference point at zero.

**Figure 9.**Power utility curves, where θ represents perception of risk and diminishing sensitivity and λ reflects loss aversion.

**Figure 10.**Dynamics of capacity and delay [55]; (

**a**) relationship between demand, practical capacity, and throughput capacity; (

**b**) typical probability distribution of aircraft delay.

**Figure 12.**Benefits and costs in airside capacity provision [11]; (

**a**) effect of an increase in capacity (Movements 1 → Movements 2); (

**b**) effect of an increase in income on the investment case for airside infrastructure.

**Figure 13.**ADS–B operation diagram, derived from [20].

**Figure 14.**The ‘with and without’ approach to cost–benefit analysis [12].

**Figure 15.**The difference between the financial and social cost–benefit approaches, derived from [85].

**Figure 17.**Discount functions, illustrating exponential discounting with ${i}_{E}=0.05$, hyperbolic discounting with ${i}_{H}=0.08$, and hyperbolic discounting with ${i}_{H}=0.05$.

**Figure 18.**Monetary flows for the project (differential approach); (

**a**) benefits, costs, and investment; (

**b**) free cash flow and discounted cash flow (traditional exponential discounting with ${i}_{E}=0.05$).

**Figure 19.**CBA results; (

**a**) free cash flows and discounted cash flows (DCF): traditional exponential discounting with ${i}_{E}=0.05$, hyperbolic discounting with ${i}_{H}=0.08$, and hyperbolic discounting with ${i}_{H}=0.05$; (

**b**) cumulative NPV for the different discounting approaches.

**Figure 20.**Valuation prospect for different combinations of diminishing sensitivity to gains and losses, and loss aversion; (

**a**) baseline valuation (U

_{1}) and sensitivity to diminishing sensitivity to gains (U

_{2}) and to losses (U

_{3}); (

**b**) baseline valuation (U

_{1}) and sensitivity to loss aversion (U

_{4}).

Row | Differential Scenario | Concept | Units | Total | Year 0 (2023) | Year 1 (2024) | Year 12 (2035) | Year 20 (2043) |
---|---|---|---|---|---|---|---|---|

1 | Project operating benefits (1) | (EUR k) | 2627.4 | 0.0 | 96.8 | 135.4 | 172.9 | |

2 | Capacity | (EUR k) | 343.7 | 0.0 | 12.7 | 17.7 | 22.6 | |

3 | Benefits associated with a reduction in waiting times and path optimization—induced traffic | (EUR k) | 343.7 | 0.0 | 12.7 | 17.7 | 22.6 | |

4 | Efficiency (internal effects) | (EUR k) | 2256.0 | 0.0 | 83.1 | 116.3 | 148.4 | |

5 | Reduction in operating costs | (EUR k) | 149.1 | 0.0 | 5.5 | 7.7 | 9.8 | |

6 | Reduction in passengers’ waiting time | (EUR k) | 2079.0 | 0.0 | 76.6 | 107.2 | 136.8 | |

7 | Reduction in fuel consumption | (EUR k) | 27.8 | 0.0 | 1.0 | 1.4 | 1.8 | |

8 | Environment (external effects) | (EUR k) | 40.2 | 0.0 | 1.5 | 2.1 | 2.6 | |

9 | Reduction in CO_{2} and NO_{x} emissions | (EUR k) | 40.2 | 0.0 | 1.5 | 2.1 | 2.6 | |

10 | Project capital investment costs (and replacement expenditure) (2) | (EUR k) | 288.0 | 238.0 | 0.0 | 50.0 | 0.0 | |

11 | ADS–B equipment | (EUR k) | 150.0 | 125.0 | 0.0 | 25.0 | 0.0 | |

12 | Controller Working Position (CWP) | (EUR k) | 30.0 | 15.0 | 0.0 | 15.0 | 0.0 | |

13 | Software actualization | (EUR k) | 20.0 | 10.0 | 0.0 | 10.0 | 0.0 | |

14 | Human Machine Interface (HMI) | (EUR k) | 75.0 | 75.0 | 0.0 | 0.0 | 0.0 | |

15 | Communications equipment | (EUR k) | 5.0 | 5.0 | 0.0 | 0.0 | 0.0 | |

16 | Training of technical staff | (EUR k) | 8.0 | 8.0 | 0.0 | 0.0 | 0.0 | |

17 | Project operating costs (3) | (EUR k) | 177.8 | 0.0 | 8.0 | 9.0 | 9.8 | |

18 | ADS–B equipment maintenance | (EUR k) | 54.3 | 0.0 | 2.0 | 2.8 | 3.6 | |

19 | Maintenance staff | (EUR k) | 123.5 | 0.0 | 6.0 | 6.2 | 6.2 | |

20 | Benefits (1)–Investments (2)–Costs (3) (project cash flow) | (EUR k) | 2161.6 | −238.0 | 88.8 | 76.4 | 163.1 | |

21 | Net Present Value (NPV) with traditional exponential discounting | (EUR k) | 1199.0 | −238.0 | 84.6 | 42.6 | 61.5 |

Variable | Value |
---|---|

Minute of delay (EUR)—cost | 100.0 |

Fuel price/ton (EUR) | 515.2 |

Damage from CO_{2} emissions (EUR/ton)—cost | 135.1 |

Damage from NO_{x} emissions (EUR/ton)—cost | 20.6 |

Value of passenger time (EUR/hour per passenger) | 53.5 |

Air traffic growth rate 2023–2043 (EU)—annual rate (%) | 3.1 |

Passengers per movement (arrival or departure) | 120.0 |

Average time taxi-in and taxi-out (min/operation) | 18.0 |

Airline operating costs—taxi (EUR/min) | 65.8 |

Average fuel burnt in taxi (kg/min) | 15.7 |

CO_{2} emissions in 1 min of taxi (kg) | 86.6 |

NO_{x} emissions in 1 min of taxi (kg) | 0.4 |

Discounting Approach (PGL 1) | Units | NPV | Year 0 (2023) | Year 1 (2024) | Year 12 (2035) | Year 20 (2043) |
---|---|---|---|---|---|---|

Traditional exponential discounting ${\delta}_{E}=(1+{i}_{E}{)}^{-t}$; ${i}_{E}=0.05$ | (EUR k) | 1199.0 | −238.0 | 84.6 | 42.6 | 61.5 |

Hyperbolic discounting ${\delta}_{H}=(1+{i}_{H}\xb7t{)}^{-1}$; ${i}_{H}=0.08$ | (EUR k) | 1109.3 | −238.0 | 82.2 | 39.0 | 62.7 |

Hyperbolic discounting ${\delta}_{H}=(1+{i}_{H}\xb7t{)}^{-1}$; ${i}_{H}=0.05$ | (EUR k) | 1355.8 | −238.0 | 84.6 | 47.8 | 81.6 |

Utility Consideration (PGL 2) | Units | NPV | Year 0 (2023) | Year 1 (2024) | Year 12 (2035) | Year 20 (2043) |
---|---|---|---|---|---|---|

Hyperbolic discounting ${\delta}_{H}=(1+{i}_{H}\xb7t{)}^{-1}$; ${i}_{H}=0.08$ | (EUR k) | 1109.3 | −238.0 | 82.2 | 39.0 | 62.7 |

Utility—U (Equation (6) with α_{0} = 0, λ = 5, θ = 0.4, θ* = 0.5) | −294.7 * | −2439.3 ** | 95.6 ** | 90.1 ** | 121.9 ** |

Utility Consideration (PGL 2)—Prospect Valuation | Value | Year 0 (2023) | Year 1 (2024) | Year 12 (2035) | Year 20 (2043) |
---|---|---|---|---|---|

Utility 1—U_{1} (α_{0} = 0, λ = 5, θ = 0.4, θ* = 0.5) | −294.7 * | −2439.3 ** | 95.6 ** | 90.1 ** | 121.9 ** |

Utility 2—U_{2} (α_{0} = 0, λ = 5, θ = 0.5, θ* = 0.5) | 4469.3 * | −2439.3 ** | 298.7 ** | 277.6 ** | 404.9 ** |

Utility 3—U_{3} (α_{0} = 0, λ = 5, θ = 0.4, θ* = 0.6) | −6267.8 * | −8412.3 ** | 95.6 ** | 90.1 ** | 121.9 ** |

Utility 4—U_{4} (α_{0} = 0, λ = 3, θ = 0.4, θ* = 0.5) | 681.0 * | −1463.6 ** | 95.6 ** | 90.1 ** | 121.9 ** |

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**MDPI and ACS Style**

Rodríguez-Sanz, Á.; Rubio Andrada, L.
Cost–Benefit Analysis of Investments in Air Traffic Management Infrastructures: A Behavioral Economics Approach. *Aerospace* **2023**, *10*, 383.
https://doi.org/10.3390/aerospace10040383

**AMA Style**

Rodríguez-Sanz Á, Rubio Andrada L.
Cost–Benefit Analysis of Investments in Air Traffic Management Infrastructures: A Behavioral Economics Approach. *Aerospace*. 2023; 10(4):383.
https://doi.org/10.3390/aerospace10040383

**Chicago/Turabian Style**

Rodríguez-Sanz, Álvaro, and Luis Rubio Andrada.
2023. "Cost–Benefit Analysis of Investments in Air Traffic Management Infrastructures: A Behavioral Economics Approach" *Aerospace* 10, no. 4: 383.
https://doi.org/10.3390/aerospace10040383