73. F. Y. Edgeworth to Harrod , 4 May  [a]
[Replies to a letter not found; follows on from 71 , continues at 76 ]
All Souls [College, Oxford]
4 May 
There is much truth in what you say about the conditions which determine the terms of trade and about the significance of "elasticity". Truths of this kind lend themselves [b] to representation by diagram. In using diagrams, or <reasoning> without them, we must often I think in economics take account of probabilities, [c] dwell on cases which general experience--"old experience doth alter" something like the character in history--teaches us to regard as typical. Thus Marshall is dealing with our present subject being properly described as the general case of demand- and supply-curves in international trade. Shapes of the sort here shown. This in his text: he relegates to an appendix freaks which behave otherwise as of comparatively little practical importance (Money Commerce etc. 1923  ). [fig. 1]
The magnitude of the effect on the Dominions produced by the introduction of the competition, the extent to which the index of exchange which was originally at P will move backward (on the D curve) to (such retrogressing spelling disadvantage) will depend on the nature of the yellow curve which compounded with OD produces the compound curve OC.
I have supposed this constituent curve to be of an ordinary kind (after Marshall Money Commerce etc. cited above) say like OJ [fig. 2]. Given this sort of shape, the further to the right OJ bends and the more deleterious will be the competition. Ceteris paribus the size of the yellow population makes the compet[ition]. worse. E.g. OJ would be <damped> to by a mere <+> of the trading population without any change in their disposition (their individual demand & supply curves).
All this on the supposition that OJ is of an ordinary character. Conceivably it might be perfectly inelastic [fig. 3] in such wise that however the rate of exchange turned in favour of the yellow country, however much of <commod[ity]> y was offered for a unit of x the competitive country would only offer OJ of exports. In that case no doubt the disturbance would be a minimum. But the man in the street is quite right in not basing a practical conclusion on an extreme supposition. The argument for free-trade requires some such assumption as I am now making--some premise based on Probabilities. I have put that view in a passage (cited Economic Journal 1915 p. 195 note  ) which Pigou has endorsed with reference to the elasticity of demand for labour (in his Economics of Welfare  ).
In short it is practically certain that the introduction of competition will be to the disadvantage of the Dominions as defined. But how great the detriment will be will depend on the consideration which you mention under your A & B.
You will observe that I dont entertain your conception that "before trade opens wages & profits per unit agency of standard effic[iency]. are equal in the two countries". I suppose the yellow men to have a virtue the contrary of the fault ascribed to the Dutch "giving too little and asking too much". For the same amount of exported (e.g.) wheat may cost the same quantity of effort and sacrifice they were willing before the removal of the barrier to take in exchange a smaller amount of things in general such as are purchasable on the international market. Your conception is more appropriate to a state like that represented by E in my figure, when the trade has settled down to a new equilibrium. If then an "expansion of trade is pending"--e.g. corresponding to the pushing up of the curve OE--it no doubt depends on conditions A & B how much or how little the Dominions would gain by the expansion.
Let us suppose then that the curves representing conditions of demand and supply and elasticity <thereof> in an assigned neighbourhood are of the general shape shown; and let us take as an illustrative problem a supposed Empire in which the Dominions trade with the mother country (both white) under a preferential agreement which excludes say the fellow <+>. Let OE be the demand- and supply-curve for the mother country; its shape is explained by Marshall indicating the circumstances which you describe as relevant. Let OD be the corresponding curve for the dominions. Now suppose a free trade government prevailing in the mother country removes the barrier established by the preference and allows the excluded yellow men to deal with the mother country in competition with the dominions. The consequence will be that the "nation" with which the mother country deals will now, as explained in my card,  be represented by a compound curve, say OC which must be to the right of D; since at any assigned rate of exchange (between exports and imports to the mother country) the imports will be greater than under preference (namely what they would have been under preference plus the offer of the yellows at said rate of exchange).
Altogether while agreeing with your premisses, as to elasticity and so forth, I dont find my conclusion against Cairnes and Mill & in favour of the man in the street much shaken. 
As to Lloyd the locus classicus is in an article by Prof. Seligman in the Economic Journal for 1903 (on some forgotten economists, or some such title).  Of course you have referred to Lloyd's lectures in your own library. It is not an easy subject to joke about. Hyndman in an attack upon Marshall tried to make fun of the doctrine by entitling his pamphlet "The final futility of final utility"--But he could not maintain that racy style.  The nearest approach to a joke on the subject was made by one who said that my name was suited to an experiment of marginal utility. The pun would go better in German in which language "Grenzwert" is almost the equivalent of your correspondent's surname.
F Y Edgeworth
2. F. Y. Edgeworth, "Recent Contributions to Mathematical Economics" (Part II), Economic Journal XXV, June 1915, pp. 189-203.
3. A. C. Pigou, The Economics of Welfare (1920), part V, chapter III, pp. 711-12, where Pigou refers to Edgeworth's "On the Use of the Differential Calculus in Economics to Determine Conditions of Maximum Advantage", Scientia VII: 13, 1910, pp. 80-103.
4. Edgeworth refers to the note appended to letter 71 ( [jump to page] ).
5. F. Y. Edgeworth, "Theory of International Values", Economic Journal 4, 1894, pp. 35-50, 424-43 and 605-38, in particular pp. 607-19.
6. E. R. A. Seligman, "On some Neglected British Economists", Economic Journal XIII, part I in September 1903, pp. 335-63, part II in December 1903, pp. 511-35. See in particular pp. 356-63 on William Forster Lloyd (1794-1852), Student of Christ Church (1812-37) and Drummond professor of political economy at Oxford from 1832 to 1837.
7. H. M. Hyndman, "The Final Futility of Final Utility", lecture delivered before the Political Economy Circle of the National Liberal Club. Reprinted as chapter 7 of The Economics of Socialism, London: The Twentieth Century Press Ltd, 1896.
- a. ALS, ten pages on three sheets (two of which folded and written on four sides), in HP IV-307.
b. Ms: «themselves».
c. Ms: «probabilities dwell».
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