TRANSACTIONS OF SECTION F. 583 
3. How far are Mathematical Methods really of Use in Economic 
Science? By A. J. Kenny, M.A. 
The object of this paper was to consider the methods and principles involved 
in the numerous applications of mathematics which have been made to economic 
science. A distinction was made between the algebraic method, with extension to 
calculus, as used by Cournot and others, and methods which are not wholly of 
a mathematical nature, but in which mathematics are used to support some 
particular doctrine, as, for example, that of marginal utility. In the latter 
group the question arises whether these abstract conceptions are adequately 
represented by the mathematical symbols used, and consequently whether the 
conclusions drawn are valid. 
It can be shown that on account of the restrictions imposed on the mathe- 
matical method, and the consequent lack of variety in the methods employed, 
many points are unnecessarily obscured. For instance, the principle of maximum 
and minimum is sometimes applied in the theory of demand and the conclusion 
arrived at that the price is in the ratio of the marginal utilities of the com- 
modity and money. This determines the quantity purchased, if the marginal 
utility of money be known, as is usually assumed. A general method, however, 
leads to the conclusion that the marginal utility of money depends essentially 
on its distribution in the purchase of all the commodities desired, so that the 
application of mathematics, subject to the hypothesis that the utility of money 
is known, leads to a result which is only true in a limited sense. 
Again, in support of the assertion that the problem of economic equilibrium 
is determinate, equations are found which are equal in number to the unknown 
quantities. As the equations so found are not in general of the first degree, there 
may be a large number of possible solutions. This shows the necessity of recog- 
nising conditions which are not capable of being expressed as relations between 
variables. 
The conclusion was that mathematical methods are capable of throwing light 
on economic problems in a manner impossible by any other means. But in order 
that valid results may be obtained it is necessary that the methods used should 
be of such a general character as to admit of the possibility of discussing various 
hypotheses. 
4. Some Effects of Compulsion on the Economics of Sickness 
Insurance. By Samuren F. Wiuson. 
The Insurance Act of 1911 has introduced many new and important elements 
into the economics of the State, the employer, and the wage-earner. The 
limited part of the general subject dealt with in this brief paper was the effects 
of compulsion on that part of the scheme—about one-third of the total contri- 
butions—which is devoted to the payment of sickness benefits. 
Regarded from an economic point of view, this part differs from the other 
portions of the scheme, inasmuch as a flat rate of contributions is fixed to 
meet contingent and gradually increasing benefits, thus necessitating large 
reserves of capital, and periodical valuations of the present values of contribu- 
tions and benefits. Into this part of the scheme, but more especially under 
compulsion, the great variety of human nature, as well as of circumstances, 
enter in many ways. 
Hitherto these valuations have affected voluntary members only, so that 
secession has always opened a safety valve for dissatisfaction. Under com- 
pulsion this valve is closed, and deficiencies when disclosed, as they certainly 
will be, will have a much more disastrous effect. 
It is submitted that a part of the task of unravelling the new and complex 
conditions affecting solvency might very well be undertaken by this Section of 
the British Association. In time the conditions imposed by compulsion become 
the normal field for voluntary effort, and it is highly desirable that such 
conditions should be thoroughly investigated. A strong critical element outside 
the Government actuarial office, and altogether apart from the make-believe of 
eae and political writers, gives promise of the best and most enduring 
results. 
