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If an individual has the monopoly of the supply of the 
commodity in the market, his immediate interest will, of course, 
lead him to determine w so that «{F (a) —f(a)} shall be a 
maximum. Let the curve y= F(x) —f (2) be traced, whether 
by direct inductions or otherwise, on a paper on which are 
already lithographed a series of rectangular hyperbolas having 
Ox and Oy for asymptotes. It will then be obvious by inspec- 
tion for which of two amounts that the monopolist may throw 
upon the market—or, which is the same thing, for which of two 
prices that he may demand—he will obtain the greatest total 
nett profit. Many striking results can thus be obtained in cases 
in which the curves cut one another more than once. 
This mode of representation of the problem of monopolies is 
elastic, and lends itself to the treatment of some complex 
hypotheses. Specially important results will present themselves, 
if the assumption be introduced that the monopolist is willing 
to undergo some abatement of his claims, when, by so doing, he 
can confer great benefit on the consumers. 
(3) A Machine for constructing a series of Rectangular 
Hyperbolas with the same Asymptotes. By Mr 
H. H. CunyneHame. 
This machine was intended for the purpose indicated in the 
last paper. 
