economy may however speak against such solutions: it would require that some regions take on mitigation burdens that are excessive (for the region in isolation), while other regions do little. Its political feasibility is, we argue, questionable.

# **4. The case of continuous increase in climate costs: Upward energy price drift**

In the previous section we assumed that the fuel price (combined with the emissions cost) stays constant, except when a “catastrophe” occurs, at which time it makes discrete jump upward.<sup>18</sup> More realistically, most global climate impacts take the form not of discrete, upward jumps but rather as an upward drift in the marginal impact of emissions over time. A simple way to represent this is through a fuel price (including an optimal emissions charge) that continuously increases over time. In a particularly simple case (considered here) q is deterministic and takes an exponential form:<sup>19</sup> where δ is a constant growth rate in the fuel price. One implication is clearly that whenever the infrastructure investment decision is incorrectly based on an energy price q0, given at the time of investment, t = 0 in (9), one moves gradually farther away from the optimal solution for the infrastructure investment, as long as the fuel price increases and infrastructure is given. Assume δ < r so that the rate of energy price increase is below the rate of interest (since otherwise there could not be an intertemporal equilibrium; arbitrage would always lead to postponement of energy resource extraction to reap capital gains).

In studying this case we simplify by assuming, mainly for analytical convenience, that all emissions arising from a given infrastructure project are fixed ex post. We consider first a deterministic solution (no “climate catastrophes”), with everlasting infrastructure.

We here first note that since the infrastructure investment in a project of type i implies given constant emissions F0i from then on, the cost of these emissions will also grow exponentially over time, and will at some future point of time eliminate any potential net value of the project. The project then always has a maximal economic operating time, which we denote _ti(M_ ). Ignoring now the net utility from variable energy consumption, his is found by first setting<sup>20</sup> Using (9), we find

> 18 This could be generalized in straightforward manner to cases with several “catastrophes”, and several upward jumps in the marginal damage cost of emissions.

> 19 That the exponential form is assumed here mainly for analytical convenience. Note however that such a path can be justified analytically in at least two contexts. First, it corresponds to the price path for a non-renewable natural resource with an economically limited supply (such as fossil fuels) in competitive equilibrium, as shown by Hotelling (1931); see also Dasgupta and Heal (1979). Secondly, it also corresponds to an optimal emissions price path when aggregate discounted mitigation costs are minimized; see e g U.S. Department of Energy (2007). 20 When counting also variable energy consumption, this will, in most cases (and always when the ex post utility function is log-linear), give rise to positive net utility at ti(M). This leads, in general, to an optimal closedown time somewhat in excess of this level.