74
Irving Fisher—Mathematical investigations
The inclination of the line AB is such that OA > OB that is A ischeaper than B, for OA and OB are the quantites of A and B pur-chasable for the same money. If the prices of A and B were equalso that OA = OB, it would not be tangent to an indifference curveunless on the B axis and A would go out of use.
Moreover it is evident that a slight variation in the relative pricesof A and B will change greatly the position of I for a poor man butwill not change materially that of I" for a rich man.
If the poor consumers predominate the line AB will follow thegeneral trend of the curves near the origin. If the rich consumerspredominate the line AB will become steeper (as in the dotted posi-tions). That is the two prices of the two qualities separate widely.
This interprets the fact that in a rich market like New York City a slight difference in quality will make an enormous divergence inprice while in some country towns different grades either do not existor sell for nearly the same price. In the country districts of “ thewest ” all cuts of beef sell for the same price (about 10 cts. per lb.).In the cities of the west two or three qualities are commonly dis-tinguished, while in New York a grocer will enumerate over a dozenprices in the same beef varying from 10 to 25 cts. per lb.
§ 14 -
In fig. 25 if the individual III attempts to change the position of2g III he may do so in many
different “ directions.” If hechanges in the direction IIIa,, he will increase his con-sumption of A without alter-ing that of B or if toward B,III (3, without altering A, ifin an intermediate direction,III 3, he will increase both Aand B and in the ratios ofthe components of that direc-tion (III a and III (3). Thedirection of maximum in-crease of utility is perpendicular to the indifference curve.* Wemay figure III 3 as a force. If III were in any other position theforce would evidently have a component along the line A, B s andwould move III back to the position of equilibrium III.
* For between two infinitesimally distant indifference curves the shortest routeis on their perpendicular.