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And the community would gain or lose as
1–q-" + }. The common mode of calculating the annuity A has been used, but it does not appear to be strictly applicable; it makes no provision for paying machine makers in the first year after the machinery comes into use, and does provide for their payment in the (d+1) year: that is, after the machinery is finished.
To commence the manufacture of new machinery immediately an additional capital must be employed, to advance the wages of its makers; and if the same sum is paid every year in this way, the additional capital must equal that part of the annuity A which is available for a similar purpose.
Let Cy be the additional capital.
Cy is the annuity, commencing at the beginning of 1" year and ending at the beginning of d" year, which pays for the machine.
Hence, since at the beginning of d" year this amounts to d
Again, the produce must supply an annuity A, which pays the profits on C(1 + y), and accumulates by the end of d" year to C (1 + y).
As before, the condition necessary that the community shall gain by the use of machinery is
and since p' cannot be > p, the community cannot lose, unless q, be < q, or the capitalist also lose.
From the result of the above investigation it would seem that we are entitled to draw the following conclusions: Wol. VI, PART III, 3 U
If we assume that a capitalist will employ machinery or labour as the one or the other will procure for him the highest rate of profit, then the employment of machinery will always increase the wealth of the community. Not only is the capitalist unable to secure his own advantage at the expense of any other class, he cannot even prevent a general participation in the benefit.
The operation on the labourer is to abstract a fund which has been or would have been annually employed in the payment of wages, and annually renewed by the produce due to his exertions, and to supply a new fund, by increasing the wealth of the community, a portion of which will in general be paid as wages; this portion is at first smaller than the fund abstracted, but it increases without any assignable limit, the rapidity of increase depending on the proportion in which the new fund is divided between the labourer and the other classes of society. Speaking with reference to the formulae, the rapidity of increase depends on the values of the arbitrary quantities m, m, m, k, and these values can be assigned with greater or less exactness, as our statistical knowledge connected with the particular case is more or less accurate.
Comparison of two machines, one of which lasts one year the other ten years, the cost of each being £20000, and their produce the same, the ratio of profit 10 per cent.
When d = 10, let y and A become y' and AI,
If G now represent the gain to the community by employing the more durable machine,
Therefore if D, be the loss to the labour-fund at the end of the : p” year by employing the more durable machine, - *
If m = m, = m = k = 4; D, will be negative, and the labour-fund will be increased at the end of the 1* year.
Hence, after 38 years the amount spent in wages is greater than it would have been if the improvement had not taken place, and
increases beyond this period to an indefinite amount.