# Shoot that Beaver – Clearing Up Confusions About the Labour Theory of Value

Few concepts have caused more confusion in economics than the Labour Theory of Value. Many of the arguments both for and against it have hidden assumptions. This post is an attempt to get to the bottom of the principal issues.

Robinson Crusoe had long departed the Island but instead a party of Economists and Philosophers had been shipwrecked on the way to an ill judged conference in the New World . They quickly saw it as an opportunity to test their ideas.

‘Ok’ said Locke, ‘why don’t I hunt beaver and you Hume hunt deer and we will see how we do’. Neither could imagine Adam Smith hunting beaver.

They decided to use as means of exchange some old dubloons dividing them up equally. Adam Smith advised that so long as the value of the coins was less than the costs of mining and minting new ones it would hold its value.

‘Right’ said Hume, today with 10 hours labour I’ve managed 3 deer, how many beavers Locke’ – ‘two for 10 hours also’.

‘So in terms of equal effort the exchange of deer to beavers is 3:2, 3 1/3 hours labour for beavers and 5 for deer. So if we set 1 dubloon equal to 1 hour then deer cost 3 1/3 dubloons and beavers 5. We are not seeking to hypothesise about the origins of money here simply to use it as a means of exchange in our calculation’.

‘Right’ replied Locke, why do we know that this is a correct price, what if for example I had only worked two hours or been really inefficient and others could be more efficient?’

‘Competition’ chipped in Adam Smith. If someone charges too high a price for the effort involved then you might as well do it yourself, if they charge too low they will be working more hours than others for the same return. That’s why I say the price of goods is equal to the labour commanded by them, which is equal to the amount of labour undertaken in their production.’

‘Ok’ said Hume, it’s what old Weiser calls ‘opportunity cost’ the ‘disutility’ of labour, but who is making a profit here?

‘No one’ ‘each party is covering the cost of their labour and reproducing themselves as a worker. They are realising a small physical surplus which they and their families consume. If the return was less than the ability of each to reproduce their labour they would withdraw it and enter another occupation. I think many of my readers have got confused on this issue confusing a physical surplus per-se with profit, and returns to one factor or another, such as capital, with profit.’

‘Right’ said Locke ‘ We are getting to the bottom of things’ ‘Your later commentators, such as Engels I think, said this simple labour theory of value only operated under barter, I think we have shown with our monetary system that this is not correct’

‘Yes’ said Smith ‘let’s be clear what I did say’

‘In that early and rude state of society which precedes both the accumulation of stock and the appropriation of land …’ (p 65; Oxford/Liberty Fund edition)

‘So I was saying that it didn’t apply when there is rent’ ‘The phrase ‘accumulation of stock’ is often misinterpreted, stock cannot accumulate unless there is a separate entity a firm, which is profitable, the capitalisation of which is the value of the stock. In our simple system there is no profits rather each is self-employed, so each simply earns a factor income, wages for sale of consumer goods for Hume and Locke and wages for sale of capital goods for myselfurn on the capital goods is not profit, I could rent them out for example and under the free completion assumption we have adopted the returns are driven down to just that necessary to retain it in production’.

‘I note Ricardo is arguing with some other Economist at the other end of the beach, I think they may join in with our discussions later.’

‘But isn’t there a set of hidden assumptions’ replied Hume ‘firstly in this simple exchange there is no capital goods and no land only one factor labour’

‘correct’

‘Also you assume as you stated that there is what our successors called ‘perfect competition’ that anyone can enter cost free another goods market and produce goods in it’

‘That is right’ said Smith ‘I made quite clear in the Wealth of Nations that under such ‘perfect competition’ there is no ‘profit’ above the return of factors – and m friends Ricardo and Marx would like to discuss that later, about whether the theory holds in cases when there is profit,

‘but first lets see if the theory holds if we introduce capital goods’.

‘Great’ said Hume ‘what do you have in mind?

‘Well said Smith I’ve been saving some food and that has enabled me to spend a day whipping up some bows and flint arrows. Smith had managed to make 20 arrows. ‘The bows are a gift just pay me for the arrows’. ‘Oh and lets ignore that Voletrra chap for a moment and imagine an infinite number of deer. Note this means that initially we will only be dealing with ‘variable’ capital, capital consumed alongside labour, rather than ‘durable’ or ‘fixed’ capital which I would hope we look at later.’

So off Hume and Locke went and spent a day hunting. Hume this time managed 7 Deer, Locke only 3 beavers as the arrows were less effective given Beavers Tendency to duck underwater.

They met at the end of the day.

‘Ok’ said Smith ‘ How many Deers and Beavers are you going to give me for my arrows’

Locke noted that they had each used up 10 arrows in the day ‘I think our successors called this depreciation’

‘Yes terrible of me to omit this in my writings’ said Smith

‘So you will each need to set aside a fund, a depreciation fund, each day to buy new arrows. The fact that they only last a day makes that easy to calculate’

‘My productivity has been increased by 50%’ said Hume, ‘so rather than 2 hours labour for a deer its 1′

‘So has mine’ said Locke, but less so ‘rather than 5 hours to catch one beaver its now 3 1/3′.

‘So now do deer and beavers exchange at the ratio of 5:3 1/3?’

‘Hang on’ said Smith, so how much are you going to pay me for 10 arrows?

‘ Well’ said Hume ‘if the labour theory is correct then you spend 1/2 hour on each arrow so that’s what I should pay you ½ hours worth of Deer in dubloons’

‘But you will be paying me ½ your daily output for a capital goods which doubles your output’ replied Smith ‘you would be no better off’.

‘Its even worse for Locke, he would be paying me half his daily output for a decrease in the production he takes home, from 2 Beavers to 1 1/2 , he would be worse off and so rationally would not use arrows.’

‘But I’d already worked that out so I’ve developed a more efficient method, I’ve cast the arrows in metal, now I can make 40 in a day. What difference does that now make?’

‘Ok’ said Hume now I can shoot 20 Deer a day, each ½ an hours labour, ½ a dubloon, the arrows are now ¼ of an hours labour so if I give you 2 ½ hours labours worth, 2 ½ dubloons worth or 5 Deer, then I will make 7 ½ dubloons a day when before I made 7.’

‘And for me’ said Locke, ‘its now 1 1/6 hours per beaver, 6 beavers a day so if I pay you Smith 2 ½ dubloons worth of Beaver which is 1 1/6 x 2 ½ = 2.0167 beavers I will have 6-2.0167 beavers left at the end of the day 3.983333 beaver which is worth 4.64 dubloons.

‘And I’, said Smith, ‘will make 3,983333+7.5 dubloons a day = 11.4833 dubloons a day I’m quids in! – though to be fair we haven’t calculated my outlay costs’.

Hang on, said Torrens overhearing, there’s a problem. If Smith makes over 11 dubloons a day (perhaps less when we consider cost of metal) and Locke only makes just under 4 why should not Locke make only arrows, indeed why should even Hume not make only arrows?’

‘Because if we only made arrows we would have no-one to sell arrows to, nothing to eat and no hats to wear’ Said Hume, rather pleased with himself.

Precisely, said Torrens ‘Imagine I was investing in one or another of your three processes’ ‘I would invest in the one which makes the most profit’, ‘But equal capitals must produce equal value, as I have said many times, which means competition again, as Smith and Ricardo have emphasised is the levelling factor, a price will exist that equals out that rate of return.’

‘But the rate of surplus (in price terms) here must be equal across all three goods’ says Adam Smith ‘otherwise someone would transfer their labour to another good’s production, although in this simplified case the rate of surplus is measured in wage units, so we don’t need to calculate them separately’.

‘But would then will we still have a zero rate of profit?’ said Locke.

‘Let’s work it out’, sad Torrens, ‘and lets be careful not to mistake a surplus from a profit if is simple a higher wage return on labour, lets instead look at the ratio between monetary value of the inputs to production and outputs from production’.

‘Remember our constraints, we need a set of prices which ensure the rate of return on all three goods in monetary terms is equal, otherwise capital in advance will switch to other lines of production, and the monetary return per unit of labour is the same otherwise labour will switch ‘.

‘Please also note how simplified our system is, no profit, no stocks, no lending, no interest, a constant period of turnover of 1 day and only variable capital not fixed capital’ Said Torrens

‘There is savings however to advance towards the variable capital produced, what Mc Culloch in a phrase I adopted called ‘accumulated labour’.

‘These are precisely the qualifiers which I and Malthus stated meant that when they didn’t apply the ‘simple’ labour theory of value would not hold.’ ‘Also returns are constant, so the average value of labour is the same as the marginal contribution’.

‘Babbage over here has programmed Mathcad Victorian Edition into his difference Engine’ ‘Babbage what’s the results?’

After much wirring and cranking the results were punched out

‘The first run is without any reallocation of labour’

‘Assuming a numeraire of a hours labour equal 1 dubloon the price of beavers is 5 dubloons, the price of deer is 16.667 dubloons and the price of arrows is 10 dubloons’

‘So lets work out the rate of surplus again for each line of production’, said Hume ‘because it seems these are radically different and so labour would be reallocated’

Babbage scribbled some notes

‘As the input hours are the same we can ignore them as they make no difference to the calculation Hume advances funding for 10 arrows worth 100 dubloons, the output is 20 beavers worth 333.3 dubloons, so the rate of surplus is 3 1/3′

‘For Locke he also advances 100 dubloons, his output is 6 beavers worth 30 dubloons so his rate of surplus is -0.66

‘For Adam Smith we haven’t calculated his input, but for simplicity assume his input is metal which costs 100 dubloons a day, his output is 40 arrows worth 400 a day so Smiths rate of surplus is 4′

‘So we have the same problem again’ said Torrens ‘Shooting beavers is not a viable technique, so labour and capital will be reallocated to the other two lines and unless the rate of surplus is even for both ‘in equilibrium’ then capital ‘accumulated labour, and ‘live labour’ as Marx calls it will continue to be reallocated.

‘So lets do the calculations again with these assumptions’ said Babbage, and perhaps we should ask Ricardo’s opinions as he stresses this process of reallocating capital and labour.

‘This is interesting, without production of beavers then the prices of everything else remains the same’

‘Indeed they must’ its was Ricardo ‘as the labour embodies in each product is the same’ ‘If we divide the budget, 100 dubloons, by the labour ratios of your first calculation you come up with the same price, 16.66 dubloons for Deer and so on – so a simultaneous equation was unnecessary, the system was ‘overdetermined’

‘I was wondering when you were going to ask for our opinions’ Said Ricardo arriving with his friends. ‘I would very much like to explore the impact of the variables Torrens set out on the Theory, as well as any impact of differences between ‘labour embodied’ in production and ‘labour commanded’ by the value of what is produced.’

‘Things are going to get a lot less empirical’ signed Adam Smith

‘Not necessarily’ said Ricardo, with Babbage’s Engine we can quickly test and simulate our theories so lets do it.

‘Lets try this again’ said Babbage ‘Hume will reallocate some of his labour to making arrows until the rate of surplus in both arrows and deers is the same. ‘ ‘The total ‘given demand’ to use malthus’s phrase, or ‘effective demand’ to use Keynes’s is set at 200 dubloons for the turnover period, we assume no hoarding, no savings’

The story picks up in part 2.

International Urban Planner

Posted on September 19, 2013, in political economy. Bookmark the permalink. 4 Comments.

1. J.St.Clair

i love reading all of your articles…..you are one of the best writers….thinker…and study ‘er….

2. Derek R

Good stuff, Andrew. However it only reinforces my view that this type of Theory of Value is really a Theory of Cost. At the end of it I know what the cost of an item is in hours, doubloons or whatever but I all I know of the value of an item is that it is greater than that cost.

Anyway, I am eager to see Part 2.

• Just wait for part two today – there are a few surproses

• Thanks, I nearly added Von Kaltenbergs vector approach to reducing the dimensionalities of joint production, with that you dont even have to make the debrau type assumptions you do.