675. Joan Robinson to Harrod , 8 June  [a]
[Replies to a letter not found; follows on from 672 , continues at 677 ]
3, Trumpington Street, Cambridge
8 June 
My dear Roy
I quite sympathise with your exasperation as I have been feeling just the same about you. Long ago I told you how I measure capital, i.e. in units of cost at the base date, this being the nearest possible approach to a physical measure, which is the ideal, 1 & said that your way of always measuring it per unit of something causes confusion. 
What I have been trying to get at all along is this--there are two factors to be considered a) the nature of the change in technique b) the change in proportions of the factors required to give equilibrium with a given rate of interest.
You have tried to boil these two into one.
You say in case of neutral invention & constant rate of interest if prices fall in proportion to increase of productivity money value of capital per man remains constant. This involves an increase in physical capital per man. Money capital per man is constant, money income of capital is constant, real income of capital has increased in proportion of increase in productivity. The capital goods purchased by a sum of money have increased in proportion to productivity and m[arginal ].p[roductivity]. of capital in both money terms and real terms is the same as before, i.e. equal to the rate of interest.
Well, all right. But this situation cannot be fully described merely by referring to the nature of the invention. It also brings in the m.p. of capital curve--i.e. you have to take into account how much physical capital per man changes to give equilibrium (see end, P.S. 3). Your picture would correspond to a case where, in my language the invention is neutral (Hicks) and h = 1.  But equally it would correspond to [b] a whole range of cases in which the invention is capital or labour saving (Hicks) and h correspondingly greater or less than 1.
Your initial objection to my method was 1) I did not state whether I measure capital per unit of labour or per unit of product. My answer to this is why the hell should I? I measure the stock of capital i.e. the total amount, not the average per something. Then I can average it as required, without having to stand on my head. Therefore your initial objection to the Hicks division of inventions does not seem to me to have any force. An invention is neutral (Hicks) when it increases mp of capital & of labour in the same proportion, the stock of capital & the amount of labour remaining the same. For equilibrium in this situation a rise in the rate of interest is required which measures the increase in m.p. of capital (this was the point of my question to you  ). If the rate of interest is constant an increase in capital per man (physical, i.e. cost at <+>, [c] units) is required. 2) That it is illegitimate to use h in this connection. But you yourself ululate at h as soon as the rate of interest alters (tho' actually this is precisely the case in which h does not come in) so that objection also seems to be fragile.
My objections to your method are 1) that it mixes up a) & b) above. 2) that it becomes unusable as soon as the rate of interest alters i.e. you cannot deal with the classical case (employment given) by your method, while mine is equally serviceable for either.
Wash out my map.  I thought at an earliest stage that you meant by a neutral invention one which required no change in (physical) capital per man to give equilibrium to the rate of interest i.e. if prices fall in proportion to rise in productivity money capital per man would fall, & money income of capital fall, in proportion to increase of productivity, so that absolute real income of capital (per unit of employment) was unchanged, & relative share in real national income fallen. I am only telling you this to try to explain my earlier letters. It was an attempt to rescue you from the charge of overlooking b) on the ground that you had chosen a special case where proportions of factors were constant--& was well meant tho' erroneous.
To sum up the whole argument--I give in detail the conditions where relative share of capital is constant in terms of my a) and b) factors. You say, "I don't understand all this stuff. I define a neutral invention as one which leaves relative shares constant (with constant rate of interest)".
But you don't really take us any further.
P.S. 1) What is the answer to my question What do you mean by the period of production?
2) Of course you can start a whole fresh group of objections about the Index N[umber] problem involved in measuring a stock of capital which is changing in physical composition.  But this difficulty is inherent in the problem, & I suspect that the same trouble must crop up somewhere whichever way you tackle it.
I shall be away a few days, so shall not be able to keep up our usual rate of returns if you answer this at once.
P.S. 3) [fig. 1]
a = rise in rate of interest required to keep capital per man constant
b = increase in capital per man required by constant rate of interest
[fig. 2] Effect of invention erroneously classified as neutral (Harrod) in my map.
2. h stands for the elasticity of substitution between capital and labour.
3. Letter 672 , [jump to page] .
4. Letter 671 , [jump to page] .
5. See letter 668 , [jump to page] .
- a. ALI, eight pages (some of which numbered) on four leaves, in HP IV-1089-1107. Reproduced by kind permission of the Provost and Scholars, King's College, Cambridge.
b. Ms: «equally a whole».
c. Commas have been added in this sentence, because the words between commas have been added as an afterthought without correspondingly updating punctuation.
1. you propounded an objection to this earlier, but it wasn't an objection because you showed that on my def. total stock of capital is constant just when I wanted it to be constant. I did not answer the point at the time as it came just before the armistice [J. Robinson's note at the top of the page].
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