58

Irving Fisher—Mathematical investigations

changes possible are effected by change in the forms of the cisternsor by changing their number , that is by changing the “ cost” of pro-duction or the utility of consumption, or by changing the population(which changes, we may remark, go together). By making thecisterns removable and replaceable the effects of varied conditionscan be studied as in the preceding chapter.

However, this equilibrium is indeterminate in one respect. Unlikethe former it does not fix the unit of value. The sum of theincome-cistern-contents is arbitrary. If all duplicate income-and-expenditure-pistons are simultaneously depressed so as to increaseall incomes proportionately, the equilibrium will not be upset norwill the distribution of commodities be affected. The rear cisternswill simply dilate in uniform* ratio. The money standard has alonechanged.

This may be remedied by making the thicknesses of all back cis-terns for the commodity A equal to unity. A thus becomes the stand-ard of value, and henceforth all prices are in terms of this com-modity. This is what is done in the actual world.

§ 6. Analytical.

A *, l + A *.2 +

Ar,.+ A -

®k.1.+ B k , s +

m equations.

2 mn unknowns.

m k ,,+m k , 5 +

M„, 1 + M WI +

] (n — 1) inde-

A ir,i -P« +. • • • • + Mjt.i . p m — ,. p a + .... + M KI ,. p in j pendent equa-

► tions.

+-M

m new un-knowns (prices) _

f( a „,,);

F(M„)

F( A *,i);

2 mn equations.

F( A „.)

F( A „..);

2 mn new un-I knowns}■ (marg. ut.).

■- = J

* Cf,. Ch.- IV, § 8, number 7.