THE THEORY OF INTEREST

represents the rate of growth, at any time, of the forest.The value at present (at the point of time A) of the for-est, in terms of cords of wood, will be represented, not bythe height AB, but in a different manner, as follows: Iffrom B' the discount curve 5 B' C' be drawn, the ordinateof which, at any time, will represent the discounted valuesof A' B' at that time, then AC' will represent the presentvalue of A' B', i.e., of the amount of the wood if cut infive years. Similarly, AC" will represent the presentvalue of A" B", the wood if cut in ten years. Wedraw in like manner a number of discount curvesuntil one is found, tT, which is tangent to the curveBN. At will then be the correct value of the youngforest, and D will represent the time at which it shouldbe cut. Clearly, At is quite different from AB, theamount of wood at the present time, and also from DT,the amount of wood at the time of cutting. At is the maxi-mum present value out of all possible choices as to thetime of cutting. If the forest is for some reason to be cutat once, its value will be only AB ; if it is to be cut at A'its present value will be AC; if at A", it will be AC";if at D, it will be At. At is the maximum, for if the forestwere cut at any other point of time on either side of Tthe discount curve passing through that point wouldevidently he below the curve tT.

At the time A, then, the wood in the forest is only ABbut, assuming proper foresting, the value of the forest interms of wood is At; the rate of growth of the forest is thepercentage-slope of BN at B, but the rate of interest is thepercentage-slope (the same at all points) of tT.

At the point of tangency alone, namely T, are the rateof growth and rate of interest (both in terms of wood)

5 The Nature oj Capital and Income, Chapter XIII.

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