Their has been much hand wringing by economic thinkers about Secular stagnation and the ‘puzzle’ that if growth is due to productivity – as growth theory says it is, how we can continue to grow when many economies have such stagnant productivity. The issue I think is that we aere seeing productivity from the perspective of a single firm not from the economy as a whole..
One of the key problems with the concept of productivity is dimensional analysis. You can measure units of physical output per units of physical input – but entropy ensures you always lose. Productivity using cobb-douglas like production functions mixes physical output per unit time with value of labour input / unit time and throws in another dimensionless value – capital input – for good measure. Hence productivity, and its derivative, total factor productivity, becomes a dimensionless and meaningless modelling artifact.
We have to start by creating a dimensionally meaningful measure of productivity – the flow of profit per units time over the flow of labour value inputs per unit time.
When measured correctly and in this manner – labour savings in one branch of the economy are – over time – precisely matched by purchases of products with marginally increasing use of labour, until the labour saved in one branch is mopped up by new less productive labour hired from the profits made.
The argument step by step.
Why do we innovate? – we innovate to save costs of labour.
According to the Babbage’s classic theorem division of labour is employed because it enables high cost labour to be replace with low cost labour.
That labour saved gives the firm a competitive advantage which translates to profits. Profits which can be competed away in Schumpeterian fashion.
If spent and not hoarded those profits translate to additional labour employed in other branches of the economy.
That spending can be either investment or consumption – it does not matter for the theorem how profits are split between rent, interest and profit simply that ultimately they are spent on investment or consumption – which also does not matter for this theorem (in matters in other regards regarding growth – as this is as we shall see a Taylor series geometrical contraction).
Take as an example it being spend on production. The capitalist in receiving profits and now eventually deciding to spend spends the marginal increment of profits on a consumption good on his or her demand schedule that was previously considered less desirable than their previous purchase. If two dissimilar but otherwise identical goods are seen as equally desirable then the one with the cheapest production cost (in a completive market where this translates to sale price) will be chosen. At the margin an extra increment of spending power translates to spending on an additional good which was previously not purchased because its costs were too high because of its more labour intensive production. Consumption therefore takes place along a demand schedule with a declining marginal productivity of labour.
For sake of argument assume no fixed capital. Then is there is $100 spend from additional profits from saving $100 of labour then if spent on consumption that additional spending power will be spent and respent throughout the economy until that $100 is all spent on $100 of additional labour along the declining marginal productivity of labour curve. The economy as a whole has not saved any labour, it is bigger and more profitable but not more labour saving when seen as a global system. How quickly this process plays out – and how quickly the spending flows from labour share to capital share and back depends on the velocity of money.
Take for example spending at restaurants; a hard up entrepreneur may choose to dine at a diner with one person behind the counter, a well off one at a starred restaurant where one cook may cook five or six meals a nighty rather than 50. Wealth enables you to afford more labour intensive, less productive consumption goods.
The same process applies to investment only, with declining labour productivity on a schedule of competing investments.
Readers of the blog will note that introduction of fixed capital does not vary these assumptions, as this can be discounted back to present value of labour using a perpetuity rule. We can maintain our dimensional purity.
This is identical in form to other processes of geometrical contraction related to the velocity of money in economics – as discussed for example by Khan (the keynsisan multiplier) of Phillips (endogenous monetary expansion in banking).
Key to all of this is that the receipt of profits and the act of spending profits occurs at different times and for different reasons. The velocity of money and the distribution of the profit share here are key to total labour share. It appears from the perspective of a single firm that a labour saving innovation decreases the labour share. If spent instantly, then respent instantly – and if not subject to rent or interest then the 1-r (rate of profit) labour share remains unchanged, however the labour share is divided amongst a larger group of workers. Are these workers worse off? It depends on the real wage not just the labour share, if the industry in which the innovation takes place is competitive and produces final consumption goods then the wage measured in wage basket goods may increase even though labour share may be declining or stagnant. Growth however is dependent on an ever enlarging labour force. If this is constrained, for example of demographic change or inmigration control’s, this hinders the process by which profits return to labour share. Similarly the extraction of profits by rentier income hinders the return.
Note we don’t assume declining returns to firms with a single process. These may indeed experience increasing returns. The ‘law’ diminishing marginal returns only applies to competing products on demand and investment schedules not cumulative innovation to a single production process.
As this is a process over time towards a limit we don’t need to make the equilibrium assumptions that the limit is ever reached. Rather it is a tendency to reach that point as an attractor.
If innovation occurs in uneven bursts then there will be long tail effects over time in reducing productivity economy wide. The first thing we should ask when we see puzzlingly low productivity is where we are in the cycle of distribution of spending from the initial growth forming investments. The process or urbanization for example, especially those founded on resource wealth, is a cycle from very high productivity initial investments, sucking in labour through successive waves and less and less high productivity growth, creating a large local market but not necessarily a competitive export orientated one.
Consider a case where innovation occurs at a steady path but driven by investment – it is an endogenous variable. But then investment collapses, profits are restored rather through working longer hours, later retirement and wage cuts. The transmission mechanism back to labour share is ten boocked through rentier extraction, weak demographic growth and reduction inmigration. This seems to be a reasonable scenario for Europe and Japan.