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Ore extraction with constant price
A firm owns an ore deposit of initial stock size S0 which must be extracted over a finite number T of periods. The per-period total cost of extraction depends on the extraction rate only as per function C(Rt), where Rt is the period-t extraction level, t â {0, 1, 2, ..., T}, and function C is increasing and convex. The unit selling price of the ore, p, is given and constant through time, as so is the firmâs discount rate r.
1. Solve for the extraction path that maximizes the present value of profits. Illustrate the extraction path with a graphic.
2. Discuss the case of a non-binding resource constraint.
3. Solve for an infinite time horizon T = â.
4. Discuss the case of a constant marginal cost of extraction.
PLEASE HELPP
Ore extraction with constant price
A firm owns an ore deposit of initial stock size S0 which must be extracted over a finite number T of periods. The per-period total cost of extraction depends on the extraction rate only as per function C(Rt), where Rt is the period-t extraction level, t â {0, 1, 2, ..., T}, and function C is increasing and convex. The unit selling price of the ore, p, is given and constant through time, as so is the firmâs discount rate r.
1. Solve for the extraction path that maximizes the present value of profits. Illustrate the extraction path with a graphic.
2. Discuss the case of a non-binding resource constraint.
3. Solve for an infinite time horizon T = â.
4. Discuss the case of a constant marginal cost of extraction.
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