¹ Foresters' rules for determining the age at which trees should be cut may be classed into those based on physical production and those determined by financial considerations. There are a number of variations of each of these classifications. The rule for cutting forests described in this article—maximum sustained yield—is in the first class and is, I feel, widely accepted in Canada as “the rule.” Moore, Milton, in his Forestry Tenures and Taxes in Canada (Toronto, 1957), 243–6Google Scholar, compares the physical optimum (maximum sustained yield) with an economic optimum based on discounted net revenue maximization, and has suggested that maximum sustained yield is not the generally accepted rule for cutting. Professor Scott, too, has suggested in correspondence that maximum sustained yield is not the sustained yield that many royal commissions and governments thought they were talking about. I would say that, in general, when royal commissions and governments are advised by foresters about sustained yield cutting, the foresters adopt maximum sustained yield in giving their advice. In practice, the long rotation determined by maximum sustained yield has frequently been rejected (e.g. by the late Chief Justice Sloan in his reports).

² See: Keirstead, B. S. and Lamontagne, M. in Murray, E. G. D., ed., Our Debt to the Future (Toronto, 1958), 90–4 and 94–101 respectivelyGoogle Scholar; Scott, A. D., Natural Resources (Toronto, 1955), and elsewhereGoogle Scholar; Keenleyside, H. L., “Problems in the Administration of Canadian Resources,” this Journal, XVI, no. 3, Aug., 1950, 327–33.Google Scholar

³ Economics of Forest Management, Dept. of Northern Affairs and National Resources, Forestry Branch Bulletin 112 (Ottawa, 1954).Google Scholar

⁴ This is the standard definition; see the writer's “Economics of Forestry,” Forestry Chronicle, spring, 1954. It should be noted that there will be a different yield for each level of management. More intensive management, such as thinning, spraying, limbing, planting, etc., would result in a higher yield. This paper is not concerned with the problem of how much management to use.

⁵ Not all rotation periods, or periods between cuttings, can be sustained. In practice there are problems of regenerating the stand which may make it extremely costly to cut a stand when it is either too young or too old. This difficulty will be ignored in this paper; it is assumed that any rotation period can be sustained. Not only is there a question of the costs of regeneration, but the costs of cutting, hauling, driving, etc., are likely to be excessive if yield per acre is very low. Very short rotation periods are therefore not normally feasible. In our example the costs for very short rotation periods are probably too low, and actual costs, if they could be obtained, would probably result in a longer rotation period than that calculated.

⁶ Best, Economics of Forest Management, 10. In the actual management plan, Best allowed ten years for the stand to be re-established, and added ten years to the 80 given by the intersection to arrive at the rotation period of 90 years. The re-establishment factor is neglected, and it is assumed in what follows that regeneration is instantaneous (or that there is sufficient advance growth to give a well-stocked stand at any year of cutting). It should, however, be pointed out that the M.A.I. curve in Figure 1 appears to be displaced to the right by nearly five years. It should have been plotted at the mid-point (approximately) of the discrete points in time from which it is computed. This was apparently not done in the original study, nor is it done in Figure 1. It should also be noted that Best showed that his management plan would pay; but not that it was the “best” from the firm's point of view.

⁷ Scott points out that “the particular analysis applied to the output of factories and shops in ordinary economic theory is not of much use here” and argues that recourse must be had to capital theory (Natural Resources, 4–5). Timber-growing is used as an example by Wicksell, Scitovsky, Boulding, Kaldor, Metzler, Scott, and Fisher, to name but a few.

⁸ Assuming a given and constant price per cord of wood does not make volume and value figures equivalent for planning. Harvesting costs vary with output but not proportionately.

⁹ With the exception noted in n. 5 above. Cf. Best, Economics of Forest Management, and the example used by Moore (n. 1 above).

¹⁰ This is the procedure used by Boulding, K. in “The Theory of a Single Investment,” Quarterly Journal of Economics, XLIX, 05, 1935, 475–94.CrossRefGoogle Scholar

¹¹ The assumption of regular annual production merely eases the calculation of the internal rate of return. This procedure is used by Scitovsky, T., Welfare and Competition (Chicago, 1951), chap, IXGoogle Scholar, and by Kaldor, N., “Annual Survey of Economic Theory: The Recent Controversy in the Theory of Capital,” Econometrica, V, 1937, 201–33.CrossRefGoogle Scholar

¹² Boulding, K., Economic Analysis (3rd ed., New York, 1955), 868.Google Scholar See also Malinvaud, C., Capital Accumulation and Efficient Allocation of Resources (Chicago, 1953), 253.Google Scholar

¹³ Scott, , Natural Resources, 95 and 138 Google Scholar (with example); Moore, Forestry Tenures (with example); also Metzler, L. A., “The Rate of Interest and the Marginal Product of Capital,” Journal of Political Economy, LVIII, no. 4, Aug., 1950, 289 CrossRefGoogle Scholar: “If the capital market is competitive the business man will be faced with a given interest rate at which he can borrow or lend, and he will accordingly adjust his production plans so as to maximize the present value of this expected future income at this given interest rate … the business man will purchase and use additional machines [capital] up to the point where the marginal income derived from each machine …, is equal to the amount of interest that would have to be paid, at the prevailing rate, on the private capital invested in each machine.” See also Boulding, Economic Analysis, 868.

¹⁴ The continuous chain case is discussed by F. A., and Lutz, Vera, The Theory of Investment of the Firm (Princeton, 1951), chap. III.Google Scholar

¹⁵ Scitovsky, , Welfare and Competition, 210 Google Scholar; Boulding, , Economic Analysis, 872 Google Scholar; Wicksell, K., Lectures on Political Economy, ed. Robbins, L., I, General Theory (London, 1934), 184.Google Scholar

¹⁶ “The Rate of Interest and the Marginal Product of Capital,” 289.

¹⁷ Economic Analysis, 870–1.

¹⁸ Welfare and Competition, 213.

¹⁹ See, in this connection, Papandreou, A. G., “Some Problems in the Theory of the Firm” in Haley, B. F., ed., A Survey of Contemporary Economics (Homewood, Ill., 1952), II, 183–222.Google Scholar

²⁰ “The Equilibrium of the Firm,” Economic Journal,XLIV, 1934, 60–74 Google Scholar; also Shove, G., “Increasing Returns and the Representative Firm,” Economic Journal, XL, 1930, 94–116.Google Scholar

²¹ Welfare and Competition, 193; see also Reder, M. W., “A Reconsideration of Marginal Productivity Theory,” Journal of Political Economy, LV, 1947, 450–8CrossRefGoogle Scholar; Cooper, W. W., “Theory ol the Firm: Suggestions for Revision,” American Economic Review, XXXIV, 1949, 1204–22Google Scholar; Kalecki, M., Theory of Economic Dynamics (New York, 1954), chaps. VII, IX.Google Scholar

²² Cf. Marshall, Alfred, Principles of Economics (8th ed.), 583 Google Scholar, on the “law of round-aboutness.”

²³ This might not be true in a sawlog case, such as that referred to in Table II, if the increase in value with the increased size of the individual trees pushed the value curve far to the right. Another possibility should also be noted. A number of foresters have suggested to me, in private discussions, that the C.A.I.–M.A.I. curves of Figure 1 are not representative, and that in fact both curves tend to the horizontal after intersecting. If such is a common case, and the curves do in fact take such a form, the position is radically changed. It may be true that because the cordage per acre continues to increase for some years, firms may operate with rotation periods longer than the physical optimum. Firms may not be able to cut until after C.A.I. = M.A.I, because the sparse cordage per acre makes harvesting costs too onerous. Under these circumstances the financial “optimum” and the physical “optimum” may have similar rotation periods.

²⁴ Scott has also supported this contention: “I would argue that, in situations where the whole economy has not come to equilibrium, the owners of capital should be maximizing its internal rate of return in each use, even though this rate of return may not be the same everywhere” (“Taxation as a Tool for Accomplishing Social Objectives in Forest Management” in Taxation and Conservation of Privately Owned Timber, proceedings of conferences held at the University of Oregon, Jan., 1959 (Eugene, Ore.: University of Oregon, Bureau of Business Research, n.d.), 25).

²⁵ This has been clearly recognized by foresters and economists for some time. For example, in 1935, the Royal Forest Service was instructed by the Swedish government that “the general policy … is that forestry should be practiced on the basis of sustained yield, with, if possible, regular fellings, and that production, in terms of money, shall be high.” Quoted in Algvere, K. V., “Historika Kostnader för Virkesproduktion inom ett revir i norra Sverige” / “Historical Costs of Timber-growing Operations in a Permanently Established Forest Enterprise,” Sartryck ur Svenska Skogsvardsforeningens Tidskrift, I, 1958, 70 Google Scholar, who goes on to point out that “this meant that the management goal in the forest enterprise is to obtain … highest possible operating profit … and not the highest possible profitability of the forest capital. …”

²⁶ It is not intended to assert anything about the desirability of a maximum sustained yield policy. But, whatever the rationale of such a policy, it must be remembered that it (or some variant of it) has been adopted by almost every province in Canada and state in the United States as the way in which forests should be managed, that it has been accepted by both the Canadian and the United States federal government, and that it is supported in the expressed policies of many of the major forest-using firms in Canada and the United States. It should also be understood that the conflict between maximum revenue from and maximum sustained yield of forests is only one of many conflicts facing a government. Other goals, such as larger populations, industrialization, and so forth, may also conflict with resource management.