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Proceedings of the Pioyal Society 
3. On the Principles which regulate the Incidence of Taxes. 
By Professor Pleeming Jenkin. 
It is well known that many taxes do not fall ultimately on the 
person from whom they are in the first instance levied. The mer¬ 
chant advances the duties imposed on goods, but the tax ulti¬ 
mately falls on the consumer. The problem of discovering the 
ultimate or true incidence of each tax is one of great importance, 
and of considerable complexity. The following paper contains an 
investigation of the methods by which this incidence may in some 
cases be experimentally determined, and of the principles regulat¬ 
ing the incidence in all cases, these principles being stated in a 
mathematical form. 
The author, in a paper published in Recess Studies, expressed 
the law of supply and demand by representing what may be 
termed the demand and supply functions, as curves. The ordi¬ 
nates parallel to the axis OX, fig. 1, were prices—the co¬ 
ordinates parallel to the axis OY were the supplies at each 
price, and the demand at each price for the respective curves—the 
market price is then indicated by the ordinate X of the point at 
wdiicli the curves intersect, this being the only price at which 
buyers and sellers are agreed as to the quantity to be transferred. 
We might write the law algebraically as follows, calling y the 
quantity of goods in the market, at each price x , we have y — <p x ; 
and calling y ± the quantity of goods demanded at each price, we 
have y x — <p x x ; the market price is determined by the equation 
y = y L . There is, however, little or no advantage in adopting this 
algebraic form, because we cannot suppose that in any instance 
px or p x x will be any tolerably simple algebraic function, whereas 
the curve for given goods might be determined experimentally by 
observing from year to year variations of quantities bought or 
quantities supplied at various prices. 
Professor Jevons has since given a much more complex algebraic 
representation of the same law, which, however, reduces itself to 
the above simple form. 
The graphic method may also be employed to indicate the 
advantage gained by each party in trade, and to show how it may 
be estimated in money. Let the two curves indicate the demand 
