counteracted by the fact that the present value of the return from future removal is lessened by the discount on the future. The net return from each ton removed in the present, even at an increased expense, may be greater than the present value of the same coal removed The basis of com at minimum expense in the future. parison, of course, beyond the point of maximum average net returns must be the net return from the removal of an additional quantity of coal (columns six and seven of table one), not the average net return. TABLE II Present Values of the Net Returns Derived from the Removal of Various Quantities of Coal at Different Future Periods with Interest at The maximum average net return per 100 tons 400 $50 $45.45 $41.66 +$38.46 +$35.71 +$33.33 +$31.25 + $29.41+ .90+ .83+ .76+ .71+ 40 36.36+ 33.33+ 30.76 +28.57 + 26.66+ 25.00 23.52 + 17.64 + 900 0 0 0 0 .58 + 0 Table II illustrates the theoretical method of determining the rate of utilization as a resultant of the two antagonistic factors: diminishing productivity and the discount on the returns from future removal (assumed to be ten per cent). If the total quantity of coal to be removed under the assumed conditions is only twelve hundred tons, there is no reason for the mine owner to remove more than four hundred tons a year; for the present value of the net return of the last four hundred tons removed in the third year is $41.66, whereas the removal of an additional one hundred tons in the first year will yield a net return of only forty dollars. If the entire quantity of coal is 3,700 tons, the owner of the mine will find it desirable to remove six hundred tons in the present; for the sixth hundred tons could not be removed at any time in the future so as to yield a greater net return than thirty dollars. If postponed until the eighth year, the present value of the net return is only $29.41. In the theory thus far presented, certain conditions have been left out of account for the sake of simplicity. In the first place, it is assumed, with Ricardo, that the landlord has the option of leasing the land to others or of using it himself. This assumes, of course, that the landlord will so adjust the contract in case of a lease that the mine will yield the maximum rent which might be derived from his own utilization. The limitations of this assumption need not be further considered here. In the second place, the ideal rate of utilization illustrated above implies operation on a large scale in the first year, with a decline in the magnitude of operation in successive years. It will be necessary to employ a larger amount of fixed capital in the first year than in successive years. A part of this fixed capital provided for the larger scale of operation in the first year will be wasted. It will, therefore, pay for the entrepreneur to adjust his rate of removal so that the rate of utilization will be more nearly uniform. This rate will be somewhere between the two extremes represented by the maximum rate of utilization in the first year and the minimum utilization of the last year. A third modification is made necessary by the fact that in the above consideration of the economic rate of utilization substantially constant returns were assumed. No allowance was made for the possibility that the removal of coal in the first year may change entirely the condi tions of removal in the second year. The removal of the 400 tons may have exposed coal which is not only of a better quality but also capable of being removed at less expense per ton than the coal removed during the first year. On the other hand, the deposit made accessible by the removal of the 400 tons may be of an inferior quality and so situated that the average expense of removal per ton will be greater than for removal in the first year. This may be true because of greater depth or special difficulties encountered, such as water or gas or the thinness of the vein of coal. In short, mining is subject either to the law of increasing returns or to the law of diminishing returns or to both tendencies alternately according to conditions.1 The assumption of decreasing returns would not affect the above conclusions. The owner of the mine would have no motive to accelerate the rate of removal of his coal simply to get access to the less profitable coal at lower depths. Under the assumption of increasing returns, however, a more rapid removal in the present might be justified by the fact that the larger net returns from the mine are in the future and are subject to the discount. With this modification the principles of utilization as above outlined will continue applicable. The influence of differences in the price of the product has thus far been disregarded. In an earlier part of this paper the effect of changing prices was discussed. The influence of higher or lower price levels must now be considered. It should be noted that, were there no discount on the future, a higher price level would not necessarily change the economic rate of utilization. It might still 1 Ricardo believed the law of diminishing return is normally characteristic of mining. Principles of Political Economy, chap. iii. On the possibility of increasing returns, cf. Taussig, Principles of Economics, vol. ii, p. 95. be economical to extract the coal at the point of maximum average net returns per unit of coal, as determined by the physical conditions of appropriation and the expense of the other factors. TABLE III Variations in the Net Return of Varying Quantities of Coal in a This point is illustrated in Table III, which is similar to Table I, except that the price of coal is doubled. The difference between the average net returns per hundred tons remains the same. The effect of the rise of price is merely to add one hundred dollars to the net return per hundred tons in every case no matter what the quantity removed. The point of maximum net returns is not changed. Altho a higher level of prices does not necessarily compel a change in the rate of utilization when there is no discount on the future, such a discount will affect the relative merits of present and future removal, and, therefore, the rate of utilization. For under the higher prices the magnitude of the net return per hundred tons, both in present and in future, is increased by the same amount. Because of the increase in the amount of the net return the discount of the net return for a future use will result in a larger deduction in arriving at present value than before the rise of price. Consequently the future use will be relatively less desirable than its competing present use. TABLE IV Present Values of the Net Returns derived from the Removal of Various Present Value of The maximum average net returns per 100 tons Present value of the net return from each additional 100 tons.. 400 $150 $136.36 +$125.00 $115.38 +$107.14+ $100.00 $93.75 $88.23+ This point is illustrated in Table IV, in which all the conditions are the same as in Table II except that the price of the product is doubled. At the original price of one dollar per ton the difference in the net return of the fifth one hundred tons in the present, as compared with the present value of the net return per hundred tons when four hundred tons is removed one year from the present, amounts to $5.45 in favor of the latter. |