**Table 1: Relative policy error, in the form of excessive carbon emissions over the lifetime of the infrastructure, in percent as a result of incorrect a) ex ante expected energy/environmental cost (=2); and b) ex post expected realized energy/environmental cost (=2), for different correct Eq, based on simulations in figures 7 and 10.**

|Type of<br>li|Utility<br>fti|Low v<br>|ariances<br>||Mediu<br>|m varianc<br>|es<br>|High v<br>|ariances<br>||
|---|---|---|---|---|---|---|---|---|---|---|
|pocy<br>error|uncon<br>specification|Eq=<br>2.5|Eq=3|Eq=4|Eq=<br>2.5|Eq=3|Eq=4|Eq=<br>2.5|Eq=3|Eq=4|
|Policy<br>error ex|Cobb-<br>Douglas|39|75|124|40|79|146|40|81|158|
|ante only|Logarithmic|18|32|50|18|34|57|18|35|61|
||Exponential|12|21|31|12|21|35|12|22|37|
|Policy<br>error|Cobb-<br>Douglas|68|177|693|64|154|446|62|147|403|
|both ex<br>|Logarithmic|42|109|430|39|90|248|37|84|213|
|ante and<br>expost|Exponential|34|91|363|31|72|199|30|66|168|

A main objective of this paper has been to study impacts of options to retrofit an established infrastructure on total expected costs, expected energy (including environmental) costs, and initial energy intensity of infrastructure. Our simulations provide a rich set of examples of how overall realized (conditional) expected costs vary in response to variations of certain key parameters (expectations and variances), and given that ex post energy and retrofit costs are both log-normally distributed (and independent). They indicate that some fraction of expected future energy use related to infrastructure can always be avoided by optimally exercising either the retrofit or close-down option at a later stage, given that exercising such options is ex ante optimal. This degree of cost avoidance can be large, under plausible assumptions; and larger when there is more uncertainty about energy and retrofit costs. In certain parametric cases more than half of the (ex ante expected) potential energy consumption is avoided through optimally exercising the retrofit alternative ex post. Expected total (energy plus retrofit) costs are then reduced, in some cases substantially.

Note that with a long expected time from infrastructure investment to availability of a relevant alternative option (retrofit, or closedown), and when the decision maker discounts too heavily (excessively), the options will also be discounted too heavily and given too little weight in the infrastructure decision problem. This factor would then serve as a partial counterweight to those emphasized here, that tend to reduce energy (and climate) cost below socially efficient levels, and lead to too energy intensive infrastructure choices.

Several limitations of our analysis must be pointed out. First, it is based on ex ante distributions of energy and retrofit costs that are both log-normal and known. Secondly, we assume only two periods, “the present”, and “the future”, which allows for only one decision point beyond that of infrastructure investment (at the start of period 2). Our choice of assumptions here was guided by a concern for generality in the distributional assumptions, while still permitting a tractable analysis. An extension of the current framework to three or more periods would make the analysis less tractable, but ought to be pursued in follow-up work. Relevant costs (of energy, emissions, and related to the retrofit technology), as well as benefits (the current utility value of the infrastructure technology), all in reality evolve 32