76 



Irviiig Fisher — Mathematical mvestigatio7is 



Fig. 26 shows the usual sort of indifference production curves. 

 36. B is here laid off to the left and A downward ; 



the line AB is the locus of production combina- 

 tions of A and B which can be sold for the 

 same money, say $1,000. The point of tan- 

 gency* I is the point at which the individual can 

 produce the required $1,000 worth of A and B 

 with the minimum disutility. The curves are 

 such that the points of tangency will be gener- 

 ally at or near the axes, especially if the amount 

 of production is large i. e. if the line AB is far 

 from the origin. If B becomes cheaper (OB longer) the point of 

 tangency will change but slowly until presently there are tw^o points 

 of tangency and if B becomes still cheaper the individual will change 

 his profession suddenly from the position I to a position in or near 

 the A axis. 



The numbers on the indifference curves for production increase in- 

 detinitely negatively. There is usually no maximum or minimum 

 point. 



§17. 



Finally an article consumed may be competing or completing to 

 another produced. A blacksmith finds small utility in dumb bells; 

 the production of horseshoes " competes " with the consumption of 

 dumb-bells. 



The relations between competing articles and completing articles 

 are not alwa^^s so simple, for articles may be competing at some 

 combinations and completing at others. Statistical inquiries along 

 these lines might be made with profit, and have apparently attracted 

 little attention.! 



CHAPTER II. 



THREE OR MORE COMMODITIES. 



§1. 



The foregoing methods extend very readily to three dimensions. 



Suppose the whole market to attain equilibrium. As before, let us 



as it were, freeze this equilibrium except for three commodities A, B, 



and C. Then as before, we obtain a fixed sum of money disposable 



* The tangency must be such that the curve is on that side of the straight line 

 toward the origin. The other kind of tangency represents an unstable equilib- 

 rium, t See Jevons, p. 135. 



