Suppose a landowner has a ‘balanced’ woodlot with one tree of ‘each’ age from 0 to t*. What is the value of this woodlot? Hint: It is the sum of the values of all trees in the lot.

If the value of the woodlot is V, show that the instantaneous interest on V (that is, r · V) is equal to the ‘proits’ earned at each instant by the landowner, where by proits we mean the difference between the revenue obtained from selling a fully matured tree [f (t*)] and the cost of planting a new one (w). This result shows there is no pure proit in borrowing to buy a woodlot, because one would have to pay in interest at each instant exactly what would be earned from cutting a fully matured tree.