has been discussed e g by Goulder and Schneider (1999), Goulder and Mathai (2000), Bonanno et al (2003), and Greaker and Pade (2008). A separate issue is that while it may be very difficult to reach an international agreement to effectively reduce GHG emissions, using policy instruments such as emissions taxes and caps, some analysts claim that reaching an agreement to support emissions-reducing technological progress may be easier.<sup>20</sup> Here we simply assume that the “decision unit” that carries out the initial infrastructure investment, may also carry out R&D activity to affect the options, and costs, of retrofitting this particular infrastructure in period 2. Assume that such investment only affects retrofit costs for this particular infrastructure, and not for other units nor more generally. We assume that the entire distribution function for period 2 retrofit costs can be given a constant vertical shift (in similar fashion as in section 4 below) through additional R&D effort in period 1.21 This upward shift in distribution is the same as a downward cost shift, as in section 4, and was there given from (23), as a result of changes in a shift parameter _β_ for this distribution.

Here, consider the following modified discounted utility as viewed from period 1: where _EW(2)_ is given from (7), _R_ is the first-period R&D cost, the G function is shifted, with shift parameter _β,_ and where the size of _β_ is a positive function of _R_ . We then derive the following general optimality condition with respect to _R_ : (26) where _βR_ is the derivative of _β_ with respect to _R_ .<sup>22</sup> The partial derivatives in (26) are found from (20)-(23) plus (11) differentiated. While (26) looks complicated, its essence is that the total derivative of _EW(1)_ with respect to _R_ consists of three marginal benefit terms inside the curled bracket, classified by how model variables are affected: 1) effects via the increase in _H_ ; 2) via increase in the joint probability of period 2 operation, _P(1)+P(2);_ and 3) via operation costs (energy costs plus retrofit costs) in period 2. These three terms are traded off against, and at the optimum set equal to, the unit cost of R&D investment.

An important parameter here is _βR._ Presumably, the marginal effect of R&D costs diminishes with greater costs (as will, rather generally, be required for a unique internal optimum to be found under the problem (26)).23 Consider here again a standard second-order Taylor expansion (and thus quadratic formulation)

> 20 See in particular Barrett (2006, 2009).

> 21 This is of course highly unrealistic. In practice, R&D efforts will affect retrofit costs more generally, and also for other projects, and thus imply positive externality effects for the latter. This issue is not discussed fully here. For further discussion see e g Golombek and Hoel (2005, 2006).

> 22 A second-order condition here also needs to be fulfilled. A sufficient condition here is that _βR_ is decreasing in _R_ .

> 23 One way to visualize this is to consider R&D projects carried out in sequence by their likelihood of success; when only a few projects are funded these are the most promising.

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