in the theory of value and prices.
85
CHAPTER III.
MECHANICAL ANALOGIES.
§ 1 -
For each individual situated in the “economic world,” supposea vector drawn along each axis to indicate the marginal utility inthat “ direction.” The marginal utility of consuming (a) is a vectorpositive along the A axis, the marginal disutility of producing (a)(or the disutility of paying money for a) is an equal vector in theopposite direction. In like manner the marginal utilities anddisutilities along all axes are equal and opposite.
This corresponds to the mechanical equilibrium of a particle thecondition of which is that the component forces along all perpen-dicular axes should be equal and opposite.
Moreover we may combine all the marginal utilities and obtain avector whose direction signifies the direction in which an individualwould most increase his utility. The disutility vector which indi-cates the direction in which an individual would most increase thedisutility of producing. These two vectors are (by evident geo-metry) equal and opposite.
The above is completely analogous to the laws of composition andresolution of forces.
If marginal utilities and disutilities are thus in equilibrium “gain”- must be a maximum. This is the mere application of the calculusand corresponds exactly to the physical application of the calculuswhich shows that at equilibrium the balancing of forces implies thatenergy is a maximum. Now energy is force times space, just asgain is marginal utility times commodity.
In Mechanics.
A particleSpaceForceWorkEnergy
Work or Energy = force x space.Force is a vector (directed in space).Forces are added by vector addition(“parallelogram of forces.”)Work and Energy are scalars.
An individual.Commodity.
Marg. ut. or disutility.Disutility.
Utility.
Disut. or Ut. r= marg. ut. x commod.Marg. ut. is a vector (directed in com.)Marg. ut. are added by vector addition.
(parallelogram of marg. ut.)Disut. and ut. are scalars.
§ 2 .
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(4 4 .
(4 U
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