Ricardo was sceptical
‘Well we will see’ said Mr Ricardo, the quantity will change, but the prices will remain the same – just you see
‘if my theory labour embodied in the proper measure’ is correct then shifts in demand caused by equalisation of factor returns will see a shift in demand but not a shift in price’
Maybe so’ said Torrens ‘But we have a situation where the capital good trades at the price of the labour it commands not embodies, whilst the consumption goods trade at labour embodied’
‘Aha’ said Adam Smith ‘So in our state of pure competition if the labour commanded is greater than the labour embodied then the it will be rational to stay in that line of production, unless more productive lines come along, whilst others will be attracted to labour in that line, with the same provisio, whilst if the converse is the case it is rational to withdraw ones labour from that line of production into lines with a higher rate of surplus.’ ‘So it does not matter if for a time labour embodies and labour commanded are different, over time they will come together to the same rate – in the long run – at least in the frictionless profit free economy we have theorised’.
Babbage was puzzled by his next print out.
‘There is no stable solution, with different value rates of surplus labour shifts to the higher surplus lines of production, but this changes the prices which causes labour to reallocate’ ‘As labour shifts the labour commanded value of arrows shifts back to 2.5, interesting the original labour embodied value, but now both deer and beavers have rates of surplus less than 1 so none hunts deer or beavers and so noone buys arrows’.
‘Hmm’ chipped in James Mill ‘I think you have another hidden assumption, there is a gap in between the labour embodied and labour commanded prices of the variable capital good – so if Mr Ricardo is right and labour embodied alone determines value then we must be missing some aspect of labour embodied. And I think I know what it is – the labour accumulated in the fixed capital of the machines Adam Smith uses to make the arrows. If this is corrected then their will be equal rates of surplus.’
‘Very interesting’ said Adam Smith ‘But first I would like to hear from Mr Ricardo his justification for thinking that only labour embodied determines value’
‘Thank you’ said Ricard ‘For many less rigorous neo-classical economist have found my passages on the subject ‘notoriously difficult’ so let me give you a simple explanation’
‘Labour commanded is the value of labour that an amount of produced goods can purchase’
‘But this is not an invariant measure of value, in some years the labour commanded value may rise but the real wage, the amount of consumer goods such as corn that can be bought with the labour commanded, can fall, So it is not an invariant value. Labour may sometimes purchase greater, and sometimes a smaller quantity of goods, so it is the value of the goods which varies, not that of the labour the wages from which purchase the goods, which has not varied’
‘Yes’ said James Mill ‘Your argument is often stated as one of needing to have an invariant measure of value before you can tackle the issue, but people often miss the importance of TIME in your argument.’
‘The external factors such as bard harvest, war, restrictions on imports, these are what change the price of corn’.
‘Ok’ said Torrens, but in our model we have a completely frictionless economy, without war or storms or anything, so what it is that causes the discrepancy between labour embodied and labour commanded?’
‘There is no discrepancy’ said James Mill ‘We have miscalculated labour embodied’ ‘We have missed the value, the accumulated labour, that the fixed capital of the arrow making machine passes on to the arrows and then on to the value of the deer and beavers’ ‘The labour embodied value of the arrows was 2.5 dubloons, the labour commanded value 10 dubloons, I submit that the machinery Smith owns adds 7.5 hours of ‘accumulated labour’ per day.’
‘Aha’ interjected Marx ‘But because of depreciation dead labour – what you term ‘accumulated labour’ cannot add to value, only living labour. That labour applied at the point of production alongside variable capital can do so’
‘But you are wrong’ Said Adam Smith ‘Having now got an eternity to study depreciation we can apply the correct mathematics for depreciation and see if Mill was right, if you were right Marx no-one would ever accumulate capital for form fixed capital goods they would have no advantage in doing so’
‘You see depreciation is an expense – a cost – a price – which must be determined at the same time as all other prices – simultaneously – isn’t that right Hotelling’
‘Accountants Mr Smith use the matching principle to match that cost over the economic life of the capital good, note the economic life not the physical life which might be less’
‘This is because the cost of expenses for the fixed capital may be less than its output, however if the capital still has a physical life left may still have a positive scrappage value. Whilst if you have completed your depreciation fund to buy a new machine you don’t need to depreciate it again – it is sunk capital, so it may become economic to keep it in use or sell it.
Such sunk cost capital however is a different commodity to a newly produced capital good, in our simple economy we are only considering produced goods, not found or seized commodities that were not paid for and provide their services for free. Those goods attract rent, not profit or wages’
‘So we should only consider the depreciation and use of the arrow machine during its economic life?’ Asked Smith
‘Correct’ replied Hotelling ‘
‘But we can only calculate that if we know the rate of return on the machine or else we won’t know how long a period to depreciate over, and if we don’t know the cost of depreciation how can we calculate that?’ Asked Ricardo puzzled for once.
‘Not a problem’ replied Hotelling, using my formula you can calculate the returns for each age of the machine, the term which produces the maximum surplus of outputs over inputs is the economic period of depreciation, you then use the matching principle over that period to calculate the value of the per-period depreciation fund’
‘not as simple as that’ Sraffa had arrived.
‘You are rightly treated fixed capital of different ages as separate products – quite rightly – this is an example of joint production – each period production create two products not one, the fixed capital and the consumer good’
‘why does that make a difference’ Asked Torrens, pleased that his method was being applied.
‘Because, and this is a tough one, the assumption behind labour embodied calculations for a product is that the product is the same over the period in which you calculate labour – its called the ‘reduction to dated labour’
‘With joint products you have you have one product, the fixed capital product, which is brand new, so you have to calculate the imputed labour which would have been necessary to produce a machine of that age’
‘Like say purchasing an old machine and repairing it to the same standard as a new one>’ Asked Ricardo
‘Correct’ said Sraffa ‘now with joint products you get two or more prices, so to isolate the component of fixed capital to get its embodied labour you can get negative labour inputs – I know of no reasonable interpretation of this.
‘Hang on’ said James Mill
‘I posited that if we calculated the accumulated labour inputs to the fixed capital good we would bridge the gap between labour commanded and labour embodied, Sraffa seems to be implying that of we did that our calculation would be too high because of negative labour inputs – so instead of understating the embodied labour we would be overstating it.
However, and here’s a thought, what of we then knocked off this negative value from the total embodied labour – what if we ‘discounted’ it, if we come up with a correct method to calculate this discount rate for each product would we not have proven the labour embodied theory of value?’
‘In this approach the value of embodied labour would always be positive if the rate of surplus of the process using labour is sufficient to cover economic depreciation, by using the matching principle negative labour values have an economic interpretation, they are gross input values not net output values. New output values must be positive in a viable process’.
‘Indeed labour embodied and labour commanded values would be the same’ replied Adam Smith ‘All the fuss over the difference’
‘But how do we calculate the discount rates for each product?’ asked Marx
‘And would such rates be consistent with equilibrium prices? Added Hotelling
Continued in part 3