Appendix E

Economic Feasibility of Adopting Alternative Technologies

E.1 DE NOVO TECHNOLOGY CHOICE WITH IDENTICAL SERVICE

Most radioactive sources have multi-year lifetimes. For example, cesium-137-blood irradiators are generally operable for 30 years as opposed to x-ray machines, which are generally operable for half that time. Assessment of radioactive sources and their possible replacements requires a holistic accounting of costs and benefits over their operational life cycles: from purchase and installation, through operation over the useful life of the technology, and ending with disposal. To illustrate, consider a radioactive source that is purchased at time zero (today), operates during the following T years, and is disposed of at the end of T years. The present value of social cost of using this device over its useful life is given by the following equation:

(Eq. 1)

where PVSCrs is the present value of social cost of use of the radiation source technology over its useful life of T years; CC₀^rs is the purchase and private installation cost; EX₀^rs is any externality cost associated with the manufacture, transportation, and installation of the technology; OC_t^rs is the operating cost of the technology during year t including labor, maintenance, opportunity cost of the space used, and any other costs required to keep the technology operational; EX_t^rs is the external cost associated with use of the technology during year t, including the monetized accident and illicit use risks; PC_D^rs is the costs of disposal of the technology borne by the owner of the technology; EX_D^rsis the costs of disposal not borne by the owner; and d is the social discount rate.

From the perspective of the private entity, however, the present value of private cost of the technology is given by the following equation:

(Eq. 2)

where i is the rate of interest at which the entity can borrow or the rate at which it assesses capital investments funded internally from its own revenue sources.

For a replacement technology that does not use a radioisotope, has a useful life of M years, provides comparable service to the radioactive source, and does not impose externalities on the broader society, the social cost is given by the following equation:

(Eq. 3)

where PVSC_ns is the present value of social cost of use of the replacement technology over its useful life of M years; CC^ns is the purchase and private installation cost; OC_m^ns is the operating cost of the technology during year m including labor, maintenance, opportunity cost of the space used, and any other costs required to keep the technology operational; and PC_D^ns is the cost of disposal of the technology borne by the owner of the technology. The present value of private cost of the alternative technology replaces the social discount rate (d) with the adopter’s borrowing rate (t) in Equation 3.

From the social perspective, the entity should choose the alternative technology if

(Eq. 4)

where a_d^M and a_d^T are the respective annuity factors¹ to annualize each present value so that the comparison is valid if M ≠ T (see Boardman et al., 2018, ch. 9). For example, at a 5 percent discount rate, the annuity factors are 7.72 and 12.46 for 10-year and 20-year devices, respectively.

However, the private entity is more likely to adopt the alternative technology if

(Eq. 5)

The larger the external costs of the radioactive source, the more likely it is that the inequality in Equation 4 will be satisfied but the inequality in Equation 5 will not be satisfied. That is, choosing the alternative technology is socially desirable but the entity will choose the radioactive source technology to minimize its internalized costs. Depending on the time patterns of costs, this divergence between private and social maximizing could also occur in the absence of externalities if d ≠ i. Various tax distortions and other market imperfections suggest that the social discount rate may be lower than market rate of interest (see, e.g., Moore et al., 2013).

The following sections discuss some general observations about the relevant externalities.

E.1.1 Externalities Prior to and During Installation (EX₀^rs)

For most technologies that do not involve radioactive sources, regulations, taxes, and insurance premiums tend to internalize social costs into the installation price. Similar factors will also internalize much of the social cost of radioactive sources into their installation prices so that any remaining external costs are likely to be small. However, some cost may be external because insurance and provider liability may not cover the full social costs, including those borne by workers, first responders, and the public. For example, first responders and the public may suffer uncompensated costs if a device that has a radioactive source is compromised during transportation to the installation site.

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¹a_iⁿ = 1 – (1+i)^–n/i, where n is the number of years and i is the discount rate.

E.1.2 Externalities During Operation (EX_t^rs)

The risks of accident and diversion of radioactive sources by a terrorist or a criminal group motivate public policies to enhance safety and security, including replacement of these sources with alternative technologies. Regulatory agencies regulate the use of radioactive material in order to protect people and the environment and reduce safety and security risks. Remaining risk, particularly that associated with an accident that causes injuries, death, or the denial of facility use, may not be fully internalized. Private entities may avoid liability through bankruptcy, and large nonprofit and public organizations such as hospitals and universities may not fully assess risks in allowing organizational subunits, such as a specific department within a hospital or a research group within a university, to make decisions regarding use of radioactive sources or alternative technologies. Although many of the regulatory and organizational protections that seek to reduce the risk of accident also reduce the risk of malevolent use, the possibility that a terrorist or a criminal group will seek ways to circumvent these protections means that some external (but generally unknown) risk remains. A simple conceptualization of this risk follows:

where Risk_j is the annual risk associated with use of a radioactive source j, p is the overall average probability across all radioactive sources of a representative terrorist act that imposes a present value of cost on society of L, and OR_j is the odds ratio that captures an adjustment to p to reflect the relative risk of j. As discussed in Chapter 2, radiological events and hypothetical scenarios that involve detonation of a radiological dispersal device (RDD) suggest that L could be very large, perhaps in the billions or even trillions of dollars. The analytical problem is the absence of a plausible way to estimate p. However, interpreting pL as an average expected loss, then OR_j can be thought of as the adjustment to the unknown probability, and therefore to the risk, that results from taking account of all the factors that make source j more or less likely to contribute to the average risk. For example, cesium-137 blood irradiators are likely to pose a larger relative risk than cobalt-60 blood irradiators because they contain cesium chloride in highly dispersible powder form, which makes it attractive for use in an RDD. While assessing OR_j does not allow monetization of the risk associated with device j, it does provide a basis for identifying the radioactive sources that pose the greatest relative risk and therefore the largest relative external costs. The radioactive source characteristics contributing to risk are discussed in Section 2.2 of this report.

E.1.3 Externalities of Disposal (EX_D^rs)

Disposal of radioactive sources may involve two externalities. First, the institutional arrangements may not require disposing of the radioactive source, which by itself increases safety and security risks, if the sources do not receive the same level of protection and monitoring as sources in use. Second, the disposing entity (typically the owner and user of the radioactive sources) may not pay the full costs of disposal. This is often the case in the United States and elsewhere as discussed in Section 2.8.

E.2 IMPLICATION OF SUNK COSTS FOR REPLACEMENT

As noted earlier, many radioactive sources allow devices to operate for many years after installation. Therefore, in any particular year, only a few of these devices will have reached the end of their useful life. Entities currently operating these devices will not assess the present value of continued use based on Equation 2 because the installation cost of the device, CC^rs, is a sunk cost that is not relevant to the decision about whether to continue using the radioactive source or replace it with an alternative technology. This reduces the right-hand side of Equation 5, making it less likely that the inequality will be satisfied. Consequently, other things equal, it will be less likely that the alternative technology will be adopted.

Sunk costs may also affect decisions when a device containing a radioactive source is at the end of its useful life. Training and expertise relevant to the device may carry over to a new radioactive source but may not be relevant to an alternative technology. Consequently, the private costs associated with a new device that contains a radioactive source would be lower than they would be in a truly de novo choice of technology so that the inequality in Equation 5 is less likely to hold.

E.3 NONIDENTICAL SERVICES: LIMITATIONS IN LOW- AND MIDDLE-INCOME COUNTRIES

The assessment of an alternative technology has so far assumed that it provides the same services as the radioactive source. When the entity has flexibility in resource use, this assumption is likely to be reasonable for technologies that provide similar but not identical services because differences can be made up by making operating adjustments, such as using the technology more intensely, or temporarily purchasing alternative technologies during downtimes. These adjustments can be factored into the operating cost, OC_m^ns, to facilitate a valid comparison. However, when the entity has little flexibility in resource use, as may be the case in low- and middle-income countries, it may not be possible to adjust operating cost to achieve the comparable service. In such cases, Equation 3 should be modified to take account of foregone services. For example, replacing a cobalt-60 teletherapy machine with a linear accelerator (linac) may result in periods of unavailability of the linac due to maintenance, repairs, or other reasons that cannot be temporarily replaced by services using a different machine that can provide the same service (a cobalt-60 teletherapy machine or a different linac) in the same or at another hospital. As described in the case studies (see Section 4.3.3), these downtimes have direct consequences in terms of patients not receiving treatment. Consequently, another component of operating cost would be the value of the foregone services, for example, an estimated monetized value of increased mortality or morbidity risk for patients who do not receive a timely treatment.

E.4 REPLACEMENT FEASIBILITY

In economic systems in which entities choose which technologies to employ, an alternative technology is feasible if it satisfies Equation 5. As noted earlier, within this framework, feasibility has institutional as well as technical determinants. For example, more stringent security regulations both internalize some of the externalities (moving some cost from EX_i^rs to OC_t^rs) and further reduce the magnitude of externality by reducing the odds ratio (OR_j). Alternative technologies that do not currently satisfy Equation 5 may do so if economies of scale in manufacturing can be realized to reduce the installation (CC^ns). Wider use may also increase the availability of expertise that reduces operating costs (OC_m^ns). Public policy may contribute toward increasing feasibility of adopting alternative technologies by affecting the costs of either the replacement of radioactive sources or the acquisition of the replacement technology, by influencing institutional policies, and through investment in research and development. As discussed in Sidebar 1.2 and Section 3.6, the U.S. government increases the feasibility of adopting alternative technologies by doing all of the above.