346. R. L. Hall to Harrod , 17 February  [a]
Trinity College, Oxford #
17 February 
My dear Harrod,
We shall be very pleased to lunch with you on Feb. 25 th .
I must apologise for an elementary mistake--economists seem prone to make them in the mathematics of International Trade.  I read the book rather quickly and observed in passing that while wheat costs fell .2x, coal costs rose .14x: Table VI. The next step was that while wheat costs fell .55x, coal costs rose .02x. I naïvely thought that this rate of progression was somewhat discontinuous especially as you assume an even rate on p. 27. But of course my error is that it is the value and not the physical costs which matter and that if the value of wheat in terms of coal is falling rapidly, a large change in production of one is equivalent to a small increase in the other.
I have now looked at the methods and checked your figures: your formula is simple and I do not remember to have seen it before. But I still feel a more academic objection to Table VI, which is perhaps best expressed by Edgeworth "the equations of exchange enable us at best to determine the final position, not the steps by which it is reached."  You use an equilibrium formula to calculate a position which could only be stable if the position abroad were different. This would be avoided if you said (which [b] I suppose is all you need) "If the English production of coal rises to 1.14x the only rate of exchange which gives full employment to the resources is .8/1.14. But as this is different from the price ruling (since foreign wheat is coming in) this ratio cannot be established and England cannot stop at 1.14 as the marginal coal rise."  I hope this is not captious: I have enjoyed your formula now that I have been driven to examining it but you would agree that it could not be used inside a country without examining the demand functions.
R. L. H.
2. F. Y. Edgeworth, "Theory of International Values", part III, Economic Journal 4, December 1894, p.634.
3. In the 2nd edition of his book Harrod admitted the difficulty and pointed out that "in the changeover the relative values of the factors of production in England (and abroad) change" ( 1939:3 , p. 26). He did not, however, introduce the wording suggested by Hall.
- a. ALI, four pages on a single folded sheet, in HP IV-1238-1254/3, with envelope addressed to Christ Church. Year not specified.
b. Ms: «what».
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