SOME DOCTRINES OF POLITICAL ECONOMY. 129 



in a mathematical manner, we must define with precision the quantities which enter into the 

 relation. 



4. Let p be the price of a commodity 0, and q the quantity effectually demanded, that is, 

 bought, at that price ; p being of course expressed in units of money, and q in terms of some 

 unit which measures the commodity C. 



The demand for C depends (cwteris paribus) upon the price : q depends upon p. Let p 



increase in any ratio : the demand, that is, the quantity which buyers are willing to purchase, 



will commonly diminish : but it may diminish either in the same ratio in which the price 



increases, or less rapidly. If the price of corn be increased by one-fourth, the consumption may 



be diminished by one-fifth, one-eighth, or one-tenth. In the first case, the money demand, 



that is, the money expended on the commodity, would be unaltered : (for it would be 



5 4 5 7 35 7 



= price x quantity = - x - = l). In the second case, it would become =-x- = — = 1-| — , 



T) {} T* O O 4 \J/i 



or would be increased between one-fourth and one-fifth. In the third case, the money demand 



5 9 9 1 



would become =-x — = - = 1 + -, and would be increased by one-eighth. 

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5. In order to express such a relation generally, let p become p' = p (l + x), and let 

 q become q , such that p q = pq (l + moo), where m is a certain coefficient. This expresses the 



cases iust mentioned according as m = 0, m = -, or m = -. 

 J & 8 2 



6. But the price may also be considered as depending on the supply, that is, on the 

 quantity supplied for sale : and the quantity supplied to buyers at a given price is the same as 

 the quantity bought at that price; therefore the equation just given, p q =pq (l + mx), 

 expresses the relation between supply (q) and price (p'). 



If the quantity supplied of any given commodity be diminished by one-fourth (for example), 



the price may increase by one-third, or it may increase one-fifth, or it may increase one-half. 



3 4 

 In these cases the money demand respectively becomes = - x - = 1, that is, remains unaltered ; 



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becomes = - x - = — =1 , or diminishes by one-tenth ; becomes = — x- = -=l+-, or 



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increases by one-eighth. And since a is in these cases = -,-,- respectively, and mx = 0, — -,- 



1 1 



respectively ; we have in the three cases, m = 0, m = , m = -, respectively. 



If the quantity supplied be increased by one-fourth (for example), the price may be 



diminished by one-fifth, or one-tenth, or one-half. In these cases, the money demand becomes 



5 4 5 9 9 1,. 



respectively = - x - = 1, that is, remains unaltered ; becomes =-x — =-=1+-, that is, 

 4 5 4 10 8 8 



increases by one-eighth ; — becomes = -x-=- = l , that is, diminishes by three-eighths. 



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Vol. IX. Paht I. 17 



