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Lecture 5 Environmental Cost - Benefit - Analysis under Irreversibility, Risk, and Uncertainty

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Option Value Value relates to the willingness to pay to guarantee the availability of the services of a good for future use by the individual. Concept was introduced by Weisbrod (1964) in considering a national park and the prospect of its closure. He argued the benefit of keeping the park open would be understated by just measuring current consumer surplus for visitors and that there should be added to that a measure of the benefit of future availability -> called option value.

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U(Y) U U(A) U(N) YNYN Y*Y* Y ** YAYA Y N A Figure 13.2 Risk aversion, option price and option value (Perman et al.: page 448) CY A -Y*: option price, OP, the maximum amount that the individual would be willing to pay for the option which would guarantee access to an open park. Y A -Y**: expected value of the individual’s compensating surplus 1), E[CS]. Option value, OV: OP - E[CS]=Y**-Y*. “Option value is a risk aversion premium” (Cicchetti and Freeman, 1971, p.536) Option Value (OV) 1) Compensating surplus: WTP for improvement of the environment to happen.

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Irreversibilities Examples: loss in biodiversity landscape changes GHG emissions several forms of pollution (pesticides, SO 2 ) sunk investment costs

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Irreversibility with future known. A: amenity value of wilderness area MC: marginal costs MB: marginal benefits NB: net benefits MNB: marginal net benefits

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Irreversibility with future known. A 1 : amenity value now, period 1 A 2 : amenity value in the future, period 2 MNB 2 > MNB 1 A 1 NI : MNB 1 = 0. A 2 NI : MNB 2 = 0. A 2 NI > A 1 NI

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Irreversibility with future known. Considering irreversibility: -Optimal preservation at A I 1, A I 2 Cost of irreversibility: - area abc in period 1 -area def in period 2 Cost of ignoring irreversibility: edhi – abc.

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Figure 13.5 Irreversibility and development with imperfect future knowledge (Perman et al.: page 454) Irreversibility with future unknown. MNB known in period 1, unknown in period 2 E[MNB 2 ]=p*MNB (1-p) MNB 2 2 Irreversibility implies: A 2 A 1 A I 1, A I 2 : outcome where there is irreversibility but no risk. If MNB 2 1, A 1 NI is chosen. If MNB 2 2, A 2 I is chosen If uncertainty about MNB 2, outcome A I 1, A I 2, if p = 0.5.

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Quasi Option Value. Notation and assumptions: D: development, P: preservation, R i : return from i-th option B pt : preservation benefits, B dt : development benefits C dt : development costs, only in the period development project is undertaken two periods t, 1 now and 2 the future, benefits, B, and costs, C, in period 2 are in present values (discounted) DM has complete knowledge of all period 1 conditions at the start of period 1, period 2 outcomes can be listed and probabilities attached to them at the end of period 1, complete knowledge about period 2 will become available to the DM decision to be taken at the start of period 1 is whether to permit development

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Quasi Option Value. Two-period development/preservation options. return immediate development: R 1 = (B d1 – C d1 ) + B d2 return preservation in period 1: either R 2 or R 3

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Quasi Option Value. return preservation in period 1: either R 2 or R 3 (Option 2 or 3) => if B p2 > (B d2 - C d2 ) => choose R 3, preservation period 2 returns from preservation in the first period, R p : R p = B p1 + max{B p2, (B d2 - C d2 )} Two-period development/preservation options.

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Quasi Option Value. assume complete knowledge over future circumstances => develop if R d > R p -> R d - R p > 0 => (B d1 - C d1 ) + B d2 - B p1 - max{B p2, (B d2 - C d2 )} > 0 (B d1 - C d1 ) - B p1 actually known to DM, other terms not, that’s why it is not an operational decision rule Two-period development/preservation options.

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Quasi Option Value. assume complete knowledge over future circumstances => develop if R d > R p -> R d - R p > 0 => (B d1 - C d1 ) + B d2 - B p1 - max{B p2, (B d2 - C d2 )} > 0 (B d1 - C d1 ) - B p1 actually known to DM, other terms not, that’s why it is not an operational decision rule Now, assume possible outcomes of B d2, B p2, (B d2 - C d2 ) are known and DM can assign probabilities to the mutually exclusive outcomes. => (B d1 - C d1 ) - B p1 +E[ B d2 ] - max{E[B p2 ],E[(B d2 - C d2 )]} > 0 ignores, more information are available at the start of period 2.

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Quasi Option Value. Now, assume possible outcomes of B d2, B p2, (B d2 - C d2 ) are known and DM can assign probabilities to the mutually exclusive outcomes. => (B d1 - C d1 ) - B p1 +E[ B d2 ] - max{E[B p2 ],E[(B d2 - C d2 )]} > 0 ignores, more information are available at the start of period 2. if area is developed in period 1, information cannot be used if area is preserved in period 1, information can be used whether or not to develop in period 2 but decision has to be made in period 1, but DM also knows the outcomes and the probabilities

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Quasi Option Value. Now, assume possible outcomes of B d2, B p2, (B d2 - C d2 ) are known and DM can assign probabilities to the mutually exclusive outcomes. => (B d1 - C d1 ) - B p1 +E[ B d2 ] - max{E[B p2 ],E[(B d2 - C d2 )]} > 0 but decision has to be made in period 1, but DM also knows the outcomes and the probabilities this leads to the following decision rule, develop if: R d = (B d1 - C d1 ) - B p1 +E[ B d2 ] - E[max{ B p2,(B d2 - C d2 )}] > 0

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Quasi Option Value. Develop if, (considering availability of future information): (B d1 - C d1 ) - B p1 +E[ B d2 ] - E[max{ B p2,(B d2 - C d2 )}] > 0 Develop if, (ignoring availability of future information): (B d1 - C d1 ) - B p1 +E[ B d2 ] - max{E[B p2 ],E[(B d2 - C d2 )]} > 0 Quasi option value: E[max{ B p2,(B d2 - C d2 )}] - max{E[B p2 ],E[(B d2 - C d2 )]} > 0 The amount by which the net benefits form development project that includes irreversible costs have to be reduced. => reflects the benefits of keeping the option alive for future preservation

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Quasi Option Value. max{E[B p2 ],E[(B d2 - C d2 )]} = max{E[0.5* * 5], E[0.5* * 6]} = max {7.5, 6}= 7.5 develop if : (B d1 - C d1 ) - B p1 +E[ B d2 ] > 0 result: = 0.25 > 0. Simple numerical example:

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Quasi Option Value. Now consider E[max{ B p2,(B d2 - C d2 )}], there are two outcomes A where B p2 > (B d2 - C d2 ), B p2 =10, p A = 0.5 B where B p2 < (B d2 - C d2 ), (B d2 - C d2 ) = 6, p B = 0.5 Hence: E[max{ B p2,(B d2 - C d2 )}] = (0.5 * 10) + (0.5 * 6) = 8 develop if : (B d1 - C d1 ) - B p1 +E[ B d2 ] - 8 > 0 result: = don’t develop first period Simple numerical example:

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Quasi Option Value. Simple numerical example: QOV= E[max{ B p2,(B d2 - C d2 )}] - max{E[B p2 ],E[(B d2 - C d2 )]} = = 0.5. The QOV is always positive, as it allows to reduce losses compared to the situation where the arrival of information is ignored.

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