WHAT MAKES THE PRICE OF OATS 9 
accurately the relation between production and price, but that better 
results might be obtained through the use of curvilinear functions 
such as those employed by Moore 5 and Working. 6 A curvilinear 
relation suggests, that, for example, the addition of 50 million bushels 
of oats to a 1,400 million bushel crop may lower the price per bushel 
less than the addition of the same amount to a crop of only 800 
million bushels. 
In Figure 3 curves of the type referred to are fitted to the scatter 
diagram of production ratio and price ratio of oats. A curve of the 
type used by Working described by the equation Y= _ ^ 
coincides approximately with a curve of the type used by Moore 
described by the equation Y=X~ 1A12 e • 229 (^~ 1 ) where Y and X are 
price ratio and production ratio, respectively, and e is a constant. 7 
A curve described by either formula fits the data somewhat more 
closely than a straight line; that is, the sum of the squares of the 
deviations or residuals from the curves is less than the sum of the 
squares of the deviations from a best fitting straight line fitted by 
the method of least squares. Several other curves were tried and 
found not to fit the data as well as those illustrated. 8 
COMPARISON OF THE VALUES OF LARGE AND OF SMALL CROPS 
The fact that the relation between production and price is found to 
be represented by a curved line of the type illustrated in Figure 3 
suggests an interesting problem regarding the values of oat crops of 
various sizes. It is commonly said that a large crop may often be 
worth less than a small crop. This idea is borne out by a study of 
Figure 3. Here it is found that a decrease of 10 per cent from normal, 
from 1.0 on the scale to 0.9, is accompanied by an increase of 13 
per cent in price, whereas an increase of 10 per cent above normal 
is accompanied by a decrease of 11 per cent in price. The values 
of production multiplied by price in both cases are illustrated in 
Table 2. 
Table 2. 
■Product of 'price multiplied by production when production is below 
and when production is above normal 
Produc- 
tion in 
terms of 
normal 
Corre- 
sponding 
price in 
terms of 
normal 
Product 
of pro- 
duction 
and price 
0.90 
1.10 
1.13 
.89 
1.017 
.979 
These conclusions may be applied to actual data by comparing 
the values of the large crops of 1902, 1904, 1905, and 1906, with the 
values of the small crops of 1901, 1903, 1907, and 1908. Table 3 
5 H. L. Moore. Elasticity of demand and flexibility of prices. In Jour. Amer. Statis. Assoc, March, 
1922. 
6 Holbrook Working. Factors determining the price of potatoes in St. Paul and Minneapolis. Minn. 
Agr. Exp. Sta. Tech. Bui. 10. 1922. 
7 The value of e, the base of the Naperian system of logarithms, is 2.7182818. The common logarithm 
of e is 0.4343. 
8 A suggestion has been made that these coincident curves do not exactly correspond to the economic 
concept of a demand curve and that the terminology used here may not be of the best. See Appendix B, 
p. 39, for reference on the subject of demand curves. 
47438°— 25t— Bull. 1351 2 
