September 26, 19 12] 



NATURE 



We may use similar diagrams in the exposition of 

 economic facts. It was, however, reservea for Cour- 

 not to show that the use of curves might go further 

 slill. Not onl)' might they be used to display statistical 

 facts, but they might also be used to solve problems. 

 I will endeavour to illustrate this very ingenious and 

 interesting development. 



It is a well-known fact that in certain departments 

 of industry the cost of making an article increases in 

 proportion to the number produced. The growth of 

 corn is a familiar example of this principle. The 

 principle depends on two facts : (i) that corn can be 

 grown in • some places with a less expenditure of 

 capital and labour than in others ; and (2) that the 

 quantity of the more favourable land is limited. 

 Whence it follows that growers will first have recourse 

 to the most fertile land ; afterwards to that which is 



Fig. 3- 



less fertile. If we were acquainted e.xactly with the 

 economics of corn-growing we could represent this 

 state of things in any country at any given time by 

 a curve like a barograph. 



.\long the line OX (Fig. 3), instead of the progres- 

 sive days of the week, we should mark off successive 

 quantities of corn, and the vertical height of the curve 

 above any given quality would represent the price 

 per quarter of production of that part which was 

 produced at greatest expense. Thus, the cost of pro- 

 duction of the first and most easily grown quarter 

 would be, say 185., of the next 185. lil., and so on. 

 .■\nd it would be evident that the total cost of the 

 whole of the wheat grown would be obtained by 

 adding all these prices together, that is to say, by the 

 area of the curve OMB.A; for an area is but the sum 



Y Money 



^X 



Z'c/ 



o 



of all its constituent parallel lines, just as the total 

 of a bill for goods is an addition of all its items. 



Let us now dismiss this corn-growing graph from 

 our minds and turn to another side of the question. 

 Let us consider the various prices which consumers 

 would give for various quantities of corn if they could 

 get these and no more. I do not mean the market 

 prices of the quantities, but what might be called the 

 famine prices, which they would give rather than not 

 have the corn. If we draw a corn-consumers' graph 

 it will obviously be a descending curve, for the more 

 thev can get the less they will value successive por- 

 tions. In fact, if the supply of corn were unlimited 

 the surplus would be used first to feed animals, then 

 to consume as fuel, then as manure, and at last have 

 to be destroyed as a nuisance. 



The curve would be of the form shown in Fig. 4. 



NO. 2239, VOL. 90] 



The contemplation of these curves of corn will no 

 doubt suggest the question whether if we had them 

 we could tell what the market price would be. For 

 it seems obvious that if we know all the conditions. 

 Doth of demand and supply, we ought to be able to 

 foretell the market price. This is the case and can 

 be easily done. All that is necessary is to superpose 

 the curves, as is done in Fig. 5. 



We then see at once that PM must represent the 

 market price of corn per quarter at a given epoch, 

 and OM the quantity produced in a standard time. 

 For if more than OM were grown it could only be 

 sold at a loss; if less the growing of corn would 

 produce an abnormal profit, which would soon cause 

 an expansion, so as to bring the quantity grown arc! 

 sold up to the maximum that could be profitablv 

 produced. 



These diagrams have therefore done more than 

 present a state of facts ; they have solved a problem, 

 just as could be done by a pair of algebraic equations. 



Moreover, other illustrations can be derived from 

 Fig. 5. By drawing the series of lines shown in 

 Fig. 6 meanings can be given to various parts of the 

 diagram. The area NPMO represents the total price 

 paid for the corn; the area APMO represents the 

 total cost of growing; the area APN, which is the 

 difference between them, represents the surplus profit 

 obtained froir^ the use of the better lands, or, in other 

 words, rent; the area BPMO represents the total 

 enjoyment the consumer derives from the corn, ex- 

 pressed in terms of money; and since NPMO is the 



price he pays for it, BNP is the surplus enjoyment 

 he gets by obtaining corn for less than he would have 

 given for it had there been a famine. 



Let us go a little further. Suppose that a tax were 

 laid on corn, and that all corn grown in a country 

 were subject to an excise duty like that now levied on 

 the manufacture of spirits. Suppose the duty were 5.';. 

 a quarter, and to simplify the problem suppose no corn 

 came in from the outside. Then the curve .^PS 

 (Fig. 7) would be pushed upwards all along its length 

 by ss., and assume a position A'P'S'. And notice that 

 the price would rise, not by 5«., but by some amount 

 rather less than 55. For "M'P'-MP must always be 

 less than the upward movement of the curve .APS. 

 Again, the rent would be decreased, for the area 



