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(1 +r)r dAJt | dAjt dA"t dl)t + dA"t dl)t

for t = 0,...,T - s, where X\ is the shadow price giving the value of increasing / by a small increment.9 Eq. (4) simply says that at the optimum, the present value of the marginal increase in welfare of expenditure Ijt minus the shadow price of I must equal the present value of an additional dollar of investment. As the equation demonstrates, the value of an incremental increase in Ijt is sum of the returns from periods t + i to T1.'0 According to Eq. (4), the marginal value of an additional dollar of conservation is a function of the marginal change in varieties conserved per additional dollar of investment as well as being a direct function of the change in welfare due to a change in accessions.

If we explicitly acknowledge the stochastic aspects of the model, using expectations, Eq. (4) becomes

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