'^6 Irving Fisher — 3Iatheniatical investigations 



14. 



In Fig. 14 the stoppers* or pistons S and S' which regulate the 

 quantities in the cisterns for production and consumption, respect- 

 ively, are so connected as to move together, keeping the quantities 

 in the two cisterns equal. Furthermore the water pressure on them 

 from the tank keeps the level of all three liquids the same — that in 

 the tank and those in the two cisterns. The lever keeps the mar- 

 ginal utility equal to the marginal disutility, for its pivot is a fixed 

 one and is placed midway between the axes of ordinates. The 

 resulting determinate equilibrium is subject to three sets of condi- 

 tions : 



(1) The quantity consumed equals that produced — a condition pro- 



vided for by the duplicate pistons, 



(2) There must be a relation between the quantity produced and 



its marginal disutility and between the quantity consumed 

 and its marginal utility — the character of the cisterns. 



(3) Marginal utility and disutility are equal^the lever, 



§ 4. AXALYTICAL. 



If A^ and A^ be the quantities of A produced and consumed, 

 respectively, the conditions of equilibrium are : 

 , ^ / 1 equation. 





2 unknowns. 



1 



2 equations. 

 j 2 new unknowns. 



J 



dTj _ d\^ ]^ 1 equation. 



d A^ dA^ J no new unknown. 



No. equations : 1 -|- 2 + 1=:4. 

 No, unknowns : 2 + 2 + 0=:4. 



dV 

 d\ 

 dV^ 



dA. 



In practice a more intricate frictionless bellows would be used. 



