in order to prevent displacement of
labor. If we get on with two thirds of the labor which the making of
the commodity out of raw materials formerly required, we do not save
two thirds of the total expense of making the finished article; and
yet to retain all the labor that is now in the business we must sell
one and a half times the former number of the goods produced.[1]

[1] The mathematical problem stands thus: If all the
subgroups of the _A_ series have the same amounts of labor
and a machine enables a half of the force now in _A''_ to do
all that is required in transmuting the usual supply of _A'_
into the usual amount of _A''_, then some of the labor in
_A''_ would in most cases betake itself to entirely different
industries. The superfluous labor at _A''_ would amount to an
eighth of all the labor required for the complete creation of
_A'''_. If wages constituted the only cost which the
_entrepreneur_ must defray, the price of _A'''_ would be
reduced to seven eighths of the former price, and this might,
in the case of some goods, enlarge the demand to eight
sevenths of its former amount and so keep all the labor in
the general group. Since there are outlays to be met besides
wages, this reducing of wages by an eighth would not usually
reduce total cost by more than about a twelfth, and even if
price quickly went down to eleven twelfths of its former
amount, it would be too much to expect that the consumption
of the _A'''_ should increase by a seventh, except in cases
in which this amount of reduction of price caused _A'''_ to
take the place of _B'''_, _C'''_, etc., in the purchase lists
of many consumers. The enlargement of consumption would have
to take place in a ratio greater than that which represents
the saving in cost. Costing eleven twelfths as much as
before, the article must sell eight sevenths as freely--which
is possible only when it thrusts itself extensively into the
place of other consumers' goods. Even then some labor would
have to move from _A''_ to other subgroups of the series. One
half of the amount of labor formerly at _A''_ does the whole
work formerly done there, and to keep it all at work at that
point would require that the output from the whole group be
doubled. Saving one twelfth in cost could not well insure
selling double the amount of goods. In this v