74 



Irving Fisher — Mathematical investigations 



The inclination of the line AB is such that OA ^ OB that is A is 

 cheaper 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 equal 

 so that OA ■=: OB, it would not be tangent to an indifference curve 

 unless on the B axis and A would go out of use. 



MoreoA'er it is evident that a slight variation in the relative prices 

 of A and B will change greatly the position of I for a poor man but 

 will not change materially that of I'' for a rich man. 



If the poor consumers predominate the line AB will follow the 

 general trend of the curves near the origin. If the rich consumers 

 predominate 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 Xew York City 

 a slight difference in quality will make an enormous divergence in 

 price while in some country towns different grades either do not exist 

 or sell for nearly the same price. In the country districts of " the 

 west " 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 Xew York a grocer will enumerate over a dozen 

 prices 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 of 



III he may do so in many 

 different " directions^ If he 

 changes in the direction III 

 a, he will increase his con- 

 sumption of A without alter- 

 ing that of B or if toward B, 

 III f3, without altering A, if 

 in an intermediate direction, 

 III 6^ he will increase both A 

 and B and in the ratios of 

 the componentB of that direc- 

 tion (III a and III (5). The 

 direction of maximum in- 

 crease of utility is perpendicular to the indifference curve.* AVe 

 may figure III c^ as a force. If III were in any other position the 

 force would evidently have a component along the line A3 Bg and 

 would move III back to the position of equilibrium III. 



* For between two infinitesimally distant indifference curves the shortest route 

 is on their perpendicular. 



25. 



