in the theory of value and prices. 



71 



to parallel straight lines whose intercepts on the A and B axes are 

 inversely proportional to the fixed ratio of their marginal utilities. 



The point M is indeterminate on the line 99. "Lehigh" and 



21. 







20. 



" Lackawanna " anthracite coal are nearty perfect substitutes. If it 

 cost nothing the individual would indifferentl}^ consume the quan- 



22. 



23. 

 A" ^/ ' ' 



B'B 



tity 09 (vertical) of one or 09 (horizontal) of the other or any 

 combination of the two on the straight line 99 inclined in this case 

 at 45°. 



For perfect completing articles the whole family of curves 

 reduces to a straight Ime passing through the origin (fig. 23). Let 

 us regard a pair of shoes as two distinct commodities : right shoes 

 and left shoes. For any point in the line OM (fig. 23), the desire 

 for right shoes vanishes as long as no new left shoes are admitted, 

 and yet the desire for a new pair may exist. The idea of marginal 

 utility for right shoes has no application though that for pairs of 

 shoes has. 



§11. 



There are endless points of view from which the primitive and its 

 derivatives may be approached and made to yield the economic 

 relations we seek.* Descriptions will be confined chicfiy to the 



* For instance we might take curves corresponding to the sections of the deriv- 

 ative surfaces at various heights, or curves orthogonal to the indifference curves 

 /these will he again referred to), or curves representing the locus of points at 

 whic h the marginal utilities of the two commodities have a given ratio. 



