136 Dr. WHEWELL, ON THE MATHEMATICAL EXPOSITION OF 



28. It is not pretended that the law of the increased cost of increased quantity is exactly 

 represented, for agricultural or any other produce, by the formula just given; but only that 

 such a formula may serve to exemplify a dependance having such a character as has been 

 described. 



29- In commodities of the first of the three classes above-mentioned, (a), (commodities of 

 Fixed Supply,) the price depends entirely upon the intensity of the demand. As the amount 

 of supply is invariable, the price can vary only from some variation in the demand ; and this 

 must arise from changes not expressed in our formulae. 



In commodities of the second class, (/3), (commodities of Fixed Cost) the quantity supplied 

 will depend upon the amount of capital, labour and skill employed in the production. When this 

 quantity varies for a unit of the commodity, the price will vary. And the relation will be given by 

 the equation of demand and supply (23). If p, the selling price, be greater than the cost price 

 with the usual rate of profits, capital and labour will flow into the employment, till p is reduced 

 down to cost price. If by any cause, for instance, improvement in the process of manufacture, 

 the cost price is diminished, the diminution may be expressed by x, in that equation ; and (m 

 being known) the equation will give the quantity which will be sold at the new price. 



In commodities of the third class, (y), (commodities of Increasing Cost) the quantity sup- 

 plied will be determined by the cost price which purchasers are willing to give. The selling 

 price, in the long run and on the large scale, will be the cost price with the ordinary profit. 

 If the purchasers are willing to give a higher price, (as for instance, in consequence of the 

 increase of wealth and population) the quantity produced will be increased by extended or 

 more expensive cultivation. And the amount of increase will be given by the equation of 

 increased cost (27). (If by improved methods of cultivation the cost price p be diminished, 

 this equation no longer applies to that change. The case then comes into the second class 

 and the equation of demand and supply is to be used). 



30. For example ; let the price which purchasers are willing to pay rise from 9 to 



10 shillings, and let n = 1. Then ny 2 = -, and y = -. Therefore q will be increased in the 



. 4 

 ratio - . 

 3 



An increase of - in the population, with a proportional increase in the means of living, 

 3 



would on these suppositions, correspond to an increase of price from 9 to 10. 



On the same suppositions, what rise of price would take place on the next equal increase 



of population, under the like conditions ? 



2 / 4A 



Herey = -, whence p' = p I 1 +-) . Hence the price would be nearly half as much 



again as at first. 



If the original population be doubled under the like conditions, y m l t p' = 2p, and the 



price is doubled, though for the increase of - in the population, the price was only increased-. 



3 9 



