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Example text

Again we consider three cases, the first of which is a generalization of Case 1, the second of Case 2 and the third of Case 3. Case 1 1 ( R 0 ~ Rs ): In this general outline, the optimal policy of the Ieader is the same as in Case 1. The resource-stock is purchased by the Ieader at a present-value price Po - k, with p 0 < pm (R 0 ), but is then withheld. Until pm (R) is reached, the leader's optimal selling price rises from p 0 according to formula (6) and thereafter falls with increases in R. Case 2 1 (R 0 k.

Recycling is considered to be the process of regaining material (homogeneous to the extracted material) from secondary material that is a waste product with positive material contents. e. 1 ) Helpful comments from two anonymaus referees are gratefully acknowledged. The author is, of course, responsible for the remaining errors. 2 ) See,forexample,FisherjPeterson (1977). PearcejWalter [1977]. Hoel [1978], Jaeger [1980] and Vogt [1980], andin particular the recycling Iiterature surveyed by Jaeger, and Fisher and Peterson.

2. 1 Assumptions We consider a world in which one and the same natural resource - called material can be produced by two different technologies: the virgin material technology or extraction technology and the recycling technology. 4 ) The extraction technology is described by a production function E: De-+ R+, De C Ri. Its image e = E (ae, a) is interpreted as the material that can be extracted when the labour input is ae and when a is the value of an efficiency parameter. E satisfies 5 ): Assumption E: AEi: Eisa twice differentiable concave function with domain De := {(ae, a) E Ri I a E [0, ä], ä ER++}, and it is strictly concave on the interior of De· AEii: E (O,a) =E (ael ä) = 0 andE0 ~ O,Ea < 0 andEaa < 0.

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