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Part II. —Utility of on* commodity a function of th!e
QUANTITIES OF ALL COMMODITIES.
CHAPTER I.
TWO COMMODITIES.
§ 1 -
Hitherto it has been assumed that the utility of a commodity is afunction of the quantity of that commodity alone. It is true thatit depends upon that quantity more than any other and the analysisof Part I is a necessary first approximation. In astronomy theattraction of the sun on the earth is first studied alone to determinethe earth’s motion; next the moon’s influence is admitted, then theoccasional “perturbations” due to planets and comets. Absoluteaccuracy is never attained for the earth’s motion is a function ofthe mass and position of every body in the universe.
So also the utility of the 100th lb. of butter (100 lbs. per year)depends mostly on ihat 100 lbs. It would not be perceptibly in-fluenced by a change in the quantity of clothing, but it would beperceptibly reduced if the amount of bread consumed were reducedfrom 300 loaves to 200, for bread and butter go together.
It is needful here to distinguish carefully between two ways inwhich the quantity of one commodity can affect the utility of others.Even under the supposition of Part I, a change in the price ofclothes effected a change in the individual valuation of money andso changed the quantity of bread consumed and so in turn changedthe marginal utility and price of bread. But under onr new sup-position, a change in the price of butter directly changes the utilityof the same quantity of bread. In the first case marginal utility ofbread can change only after a change in its quantity. In the secondthe marginal utility of the same amount of bread changes; the firstcontemplates a variation in the quantity of water in a cistern, thesecond contemplates a variation in the cistern wall itself.
In Part I we assumed: z= F(A t ) > but now we must write:
^=F(A„ B„ C„ . . . M,).