Measurement, Quantification, and Economic Analysis: Numeracy in Economics

By Ingrid H. Rima | Go to book overview

NOTES
1
The lectures were delivered and published in 1857. But the present chapter quotes from the second edition that was published after Cairnes acquainted himself with Jevons’s works.
2
For instance, the table appeared in the celebrated book of Tooke (1838), A History of Prices, vol. l, p. 12.
3
Davenant did not disclose the empirical basis of the table, and it was even suspected that the table might not have been derived from actual observations at all. Whewell (1862) was among those who made such suggestion. See Greedy (1986).
4
Since we examine Cairnes’s view in order to offer a basis of comparison with Jevons’s statistical works, the following question may be raised. How could the former’s statement have been interpreted by the latter? According to Jevons’s theory of exchange, the quantity (x) of food demanded by a consumer, its price (m) and income (c) are such that ϕ(x)=mΨ(c) where ϕ and Ψ represent the marginal utilities of food and money, respectively. But Jevons was told like this: the marginal utility functions are not susceptible of arithmetic or mathematical expression because the marginal utilities are not to be weighed and measured; and hence numerical accuracy is not attainable for the price of food (cf. Cairnes 1875:109).
5
Cairnes also cited the multiplicity of causes and the intermixture of effects from Mill (1879: Book III, ch. 10), whose position he mostly adopted.
6
It was suggested that the situation would be different if the economist had the power of experimentation. But Cairnes also pointed out that the economist, whose subject matter of inquiry is human beings and their interests, is absolutely barred from controlled experiment.
7
Jevons continued to say: “These data would consist chiefly in accurate accounts of the quantities of goods possessed and consumed by the community, and the price at which they are exchanged. ”
8
The pamphlet was reproduced in Investigations in Currency and Finance.
9
The principle of inverse probability, first set forth by Thomas Bayes (1702-61) and further developed by Laplace (1749-1827), consists in computing the probability of an observed event resulting from each possible cause. The highest probability then is taken as the reason why the event should be attributed to a particular cause. To be more specific, “the probability of the existence of any of these causes is then a fraction of whose numerator is the probability of the event resulting from this cause and whose denominator is the sum of the similar probabilities relative to all the causes” (Laplace 1951:15-16). For the development of this principle, see Todhunter (1949) and Stigler (1986).
10
In such a case, Laplace said, “it is necessary, in place of the probability of the event resulting from each cause, to employ the product of this possibility by the possibility of the cause itself (1951:16).
11
The following is the most favorable interpretation that I can propose. Taking Jevons to consider a case where the value of an article has fallen at the same rate in its rate of exchange with each of the four other articles, let P(A) represent the probability that the demand or supply of an article A is so disturbed as to raise (drop) its rate of exchange with other articles during a given period of time. Apparently, he assumed such disturbances to be independent of each other: P(BC)=P(B)P(C) if P(BC) represents the probability that the disturbance occurs to both B and C. It also seems to be his assumption that P(A)=P(B)= P(C)=P(D)=P(E)=p. Then p(1−2p)4/p4(1−2p) should be the odds which

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