The trees in Forest ? (another unusual forest - both biologically and in its nom

Question

The trees in Forest ? (another unusual forest - both biologically and in its nomenclature) grow such that the volume of timber at time t can be represented as f(t) = et - 2t. The annual real interest rate is 0.07, and the per-year opportunity cost of using the forest land to grow timber is 36000 platinum hexagons (PH). Each unit of timber can be sold at a price of 900 PH. Tlaloc becomes the owner of the forest at t = 7 years. What is his marginal cost of waiting another year to cut the trees? Should he wait another year to cut down the trees?

Explanation / Answer

Here, the per-period cost of waiting is rpf(t) + R, where R = 36000. Thus, MC(waiting) = 0.07*900*f(7) + 36000 = 0.07*900*968.633158429 + 36000 = MC = 97023.88898 PH. Here, MB > MC, so Tlaloc should wait another year to harvest the trees.

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