The total loss to the labour-fund while the machinery is in progress is

And in the 1st year of its employment the whole capital C is abstracted.

Let the machinery be made to last d years by the expenditure of a1, az, az...... a, in the 1st, 2nd, d years respectively and be worth when rejected: also let the expenditure and profit be equivalent when the machine continues d years unimpaired, and then becomes

a

Let V be the exchangeable value of the machinery,

A the annuity necessary to pay the profit on C and provide new machinery at the end of d' years, paying also for the necessary repairs during this interval,

r1, the produce due to the use of the machinery,

r

..... to the labour it displaces,

P, P1, prices of produce before and after its employment,

G the whole annual gain to the community occasioned by its

uses,

D1, D2, ................ D, sums by which labour-fund is diminished at the end of 1st, 2nd pth years after it comes into operation,

Also, since the gain to the community may be measured by the price that would have been paid for the producer, minus the price that is actually paid for it when the profits of the capitalist have reached the average rate,

G=Cq=Cq (-1).

A

Or, this gain may be measured by the saving in expenditure, added to the cost of the additional produce enjoyed, reckoning that cost at the original price;

G

=

Cq − A +

A + "1 = ". Cq = C q. 2 - A as before.
"=" . = Cq, 2/

This will be an annuity in money or other produce, of which a th part may be consumed for immediate enjoyment and a (1 – k)th part used as capital, also of the former an mth part, and of the latter an mth part may go to the labourer, whilst an mth part of the annuity A after deducting the profit C(q-1) is employed in the same way. Before the use of the machinery the expenditure was C.

Hence, DC,

D1

= C-m {A - (q − 1) C} - {m, k + m2 (1 − k)} G,

D2 = C -m {A-(q-1) C} - {m, k + 2 m. (1 − k)} G,

2

D1 = C

-m {A-(q-1) C} − {m1k + pm2 (1 − k)} G

= C{1− m 2 − 1 − {m,k + pm; (1 − k)} q ( - )}.

When this becomes negative, the fund for the employment of labour will have become greater than it would have been if the machinery had not been constructed, that is, when

annually, and will continue to increase indefinitely.

We may in these formulæ, substitute for the produce in terms of the price.

1 - 1

1

1 - q-1
1-q-d'

-

-q

Dp=C{1 - m2 - - {m,k + m2 (1 - k) p} q. (2-1) = (-)

q⋅

It may be observed that p, cannot be >p; if it were, more than the ordinary profit would arise from employing labour, and the machine would be superseded.

In general the motive of the capitalist in supplanting labour by machinery, is to procure for his capital more than the ordinary profit.

If, then, he can raise his rate of profit to q, A1= C.

q' -1 1-qi

will be the

annuity which the produce must realize. The above values of G, however, are correct whatever q may become, since the gains of the capitalist are included in those of the community at large.

In a State where there is any number of machines at work, and also any number in progress, wealth will be increasing more rapidly than it would have been if all the capital had been employed in paying wages if ZG be positive, and less rapidly if EG be negative, that is, more or less rapidly as,

If in any case the machinery lower prices, the community must gain by its use, for if p<p, G is positive.

This supposes p, to give the capitalist no additional profit, à fortiori, therefore the community will gain, if, when the rate of profit is raised to q'-1, p, be <p.

Let p" be the price that would pay ordinary profits q-1.

The community will gain by the use of machinery, if

If a portion of the dispossessed labourers, whose wages were paid by a part 1.C of the capital, become dependent on society for support, there will result the equation

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 1st year and ending at the beginning of dth year, which pays for the machine.

Hence, since at the beginning of dth year this amounts to

and at the end of dth year this is worth Cy.q.

Again, the produce must supply an annuity A, which pays the profits on C(1+y), and accumulates by the end of dth year to C(1+y).

The accumulation is therefore worth

at end of 1st year A-C(1+ y) (q − 1),