question (for the analysis in Strand et al (2014), up to 2050); meaning that protection values and opportunity values are similar, and that saving or not saving this part of the forest will depend highly on its precise assessed value in relation to its opportunity value (and such that actual saving decisions are optimal contingent of available information).<sup>14</sup> Let us also assume that the parameter values are otherwise as in the last example presented; importantly in particular we assume that EB = EV. Then VOPI for this part of the forest would be 8% of its gross protection value.

How large could such values be for the Amazon rainforest? In a gross value sense, the numbers could be very large. Consider a gross (non-carbon) protection value of $5,000 per hectare; this can be viewed as conservative.<sup>15</sup> 8% of this value is $400 per hectare, which will then be the VOPI for the relevant forest area. With more than 500 million hectares of Amazon rainforest, 10% of the area means more than 50 million hectares of contested rainforest, leading to a VOPI of at least $20 billion. This would correspond to the (present discounted) value of providing perfect and comprehensive valuation data for this extent of the forest, for cases where decisions about saving and not saving the forest are taken optimally subject to given available information (which is improved in the VOPI case); and where the informational background for savings decisions must also be updated over time as various new areas become threatened with conversion. Even if only 1/10 of the area considered above is subject to explicit evaluation, then using the lower σB value, VOPI would still be $500 million.

There are several reasons why the actual value of providing more information about forest protection values will be lower in practice than this astronomical figure. First, information will not be used optimally in practice as assumed in the example above. Much forest conversion may take place with no detailed analysis of its value for any one particular piece of land. Secondly, the uncertainties to be resolved through valuation studies could be smaller than assumed here. If instead the standard deviation for the prior distribution of B was 1⁄4 EB, instead of 1⁄2 EB, this would by itself reduce the VOPI value by half, though $10 billion is still a very high number. Thirdly, no study will resolve all uncertainty; there will always be left some residual uncertainty. Fourthly, and quite importantly here, the protection values and opportunity values are often less similar. In Figure 1, the more dissimilar EB and EV are, the more will the VOPI curve be shifted (to the right or left), and the lower will VOPI be. In particular, when EB and EV differ by one instead of being equal (so that expectations differ by two standard deviations on either of the variables), the VOPI value from Figure 3 in this case is reduced by a factor of about three. We also see in the figure that if EB – EV is greater than 4, VOPI virtually vanishes.

> 14 This argument assumes that losses of value are roughly proportional to forest losses over this loss range; which presumes that no major tipping points are reached over such a range.

> 15 Note that a recent SP study of WTP for Amazon rainforest preservation in the US and Canada, Siikamäki et al (2015), indicates an annual (non‐carbon) WTP, in these countries alone, of about $10,000/ha. Note also that we may here think of separating out the carbon values as our hypothetical valuation studies, reducing uncertainty about B, would not be expected to resolve any significant uncertainty about the carbon values; only other sources of uncertainty.

21