Yesterday there was a interesting exchange on Twitter about Capital Theory. JW Mason asked how you distinguished price from quantity for capital – a dimensionality problem.
This is an interesting response because it was the same technique – reducing fixed capital to variable capital – labour – with a single dimension – as pioneered by Torrens and Malthus, endorsed by Marx and revived by Sraffa and Von Neumann,
This approach – though seemingly very attractive – produces lots of problems:
- It can produce negative labour values (and negative surplus values) – what are the meaning of these?
- It is very difficult to account for the required total labour split between the joint products – unless you assume fixed proportions of capital intensity and fixing the labour input price in advance. It is a partial equilibrium system that cannot explain the labour market. JS MIll backed down from the LTV for joint products for this reason saying it was down to ‘supply and demand’ however this is an unsatisfactory and circular argument because it cannot explain the supply curve of labour – itself a set of prices.
- Prices equal dated labour only at zero profits – it cannot handle expanded reproduction with accumulation.
- What about depreciation? The price of the capital good must include a contribution to a depreciation fund, however unless you fix its age in advance (and there is no such thing as a purely technical age as its economic age varies with labour share and interest rate) you cannot fix its age and hence price the durable capital good.
Nick is right that the land of an orchard can be valued as the NPV of each of the apple trees. However this explain the maximum surplus as rent. The landowner can capture that rent themselves if they farm it themselves. However how does the farmer value the apple trees and price the apples – they need a depreciation fund to replace the trees when they get old, but when is that?
This explains why rent is different from capital, you need to price the capital before you can set a rent, you can never set a rent and then price the capital.
[Incidentally Nick Rowes approach is conceptually the same as Wicksell’s pupil Ackermann’s thesis of an ‘Axe Model’ of Capital – it was Wicksells mathematical analysis of this that first led him to discover Wicksell Effects – See Lutz’s book on Interest Rate theory]
An orchard can produce a physical surplus over a year (an own rate) but this is neither profit not interest unless and until you have accounted for the replacement of seeds (depreciation) which requires you to know the opportunity cost of the lost apples (this is the mistake in Samuleson’s critique of Schumpeter’s theory of interest). A dead stand of trees still has a value, but the same stand with the same number of lives trees has a higher value because the land is valued because of the joint production of apple trees and apples.
All of this rather sums up the many problems with capital theory and why it has hardly advanced a jot since the 1960s. One can simply abandon capital theory – go General Equilibrium and treat capital as a Crusonia tree mush. Itself deeply unsatisfactory. As I explain here neoclassical approaches have abandoned a theory of distribution and cannot explain profits.
This shouldn’t be a council of despair because each of these problems with joint production has a potential solution. The staring point I think is determining the optimal economic ‘strike point’ at which you cut down the apple trees and replace them. Then if you have a rate of interest you can calculate the depreciation fund and then the NPV of the apple trees. It only gets us part of the way there – interest rates are still unexplained – but it is a start. Faustmann the pioneer of forestry economics came up up the neat solution that the optimal strike point is where the flow of income from the tree is increasing at the same rate as the rate of interest. He then valued the land as the value of it with the trees cut down and the value of the trees as the total return minus the value of the land. Of course this implies correctly that the value of an Orchard with live trees is far more than bare land.
Of our 4 problems this solves only number 4. However authors have come up with solutions to problems number 2 and 3, and then problem 1 can never occur as labour coefficients can never be negative once you apply these solutions. In a future article ill apply these – including Von Staklenbergs application of vector math to the problem.