Saturday, 27 January 2018

Automation and Real Wages



Economists generally work on the basis that improvements in technology lead to higher real wages.  Conventional production functions (when combined with other assumptions) invariably produce this result.  Looking at the Cobb-Douglas production function, as the most common example, an increase in total factor productivity raises labour's marginal product.  With the normal assumptions about competition, this leads to higher real wages.

Although I have no problem with using such things at times, I am wary of simple aggregate production functions.  It seems clear to me that technological developments can lead to reduced real wage levels, even without considering how such developments might impact on monopoly power.

Although I'm sure others have produced models that illustrate this, I'm not aware of any and, in any event, I like to experiment with things myself, so I have constructed a little model of production in which technological innovation leads to a fall in real wages.

There is a single good produced by a combination of labour and capital.  There are two possible production techniques, each of which requires a fixed quantity of labour and a fixed quantity of capital to produce a fixed quantity of the good.  These quantities are set out in the table below:


Output
Labour Input
Capital Input
Technique A
12
1
1
Technique B
24
1
4


Total labour and total capital are fixed.  There is perfect competition and no demand deficiency.  This has two implications:

1. The use of each techniques will normally be such that will ensure full employment of both labour and capital.  However, if the ratio of available labour to available capital is too extreme, then all production will use a single technique (whichever maximises use of the abundant factor) and some of that abundant factor will be unutilised.  This possibility is ignored here - it is assumed that available labour and capital always lead to some combination of possible techniques.

2. The real wage will be at a level that ensures the return on capital is the same for each technique.  If it were not, suppliers of capital would switch technique which would lead to shortages or surpluses in the labour market.  With the numbers here, the real wage works out as 8 units of output per unit of labour.

Marginal productivity is not well defined for each individual technique.  However, given the above conclusion about how the techniques are combined, there is a marginal productivity of labour at an aggregate level.  It is relatively easy to show that this is equal to the real wage.

If we take factor supplies of 12 units of labour and 24 units of capital, we get the following output matrix:


Labour Used
Capital Used
Production
Technique A
8
8
96
Technique B
4
16
96
Total
12
24
192


We now want to consider the innovation of a new technique involving a more intensive ratio of capital to labour.  For this to be beneficial overall, it must yield a higher return on capital given the prevailing real wage.  The details of this new technique are:


Output
Labour Input
Capital Input
Technique C
30
1
5


Technique C dominates technique B at all levels of the real wage, so the latter is completely abandoned.  Since the relative factor input ratios have changed, there is also a change in the amount of resources devoted to technique A.  The new levels of production are shown below:


Labour Used
Capital Used
Production
Technique A
9
9
108
Technique C
3
15
90
Total
12
24
198

The change in techniques also impacts on the real wage, which must settle at a new level to continue to equate return on capital across techniques.  In fact this involves a fall in the real wage to 7.5.   

The interesting thing here is that although labour productivity (labour's average product) has increased, its marginal product has decreased.  Real wages have therefore fallen, even though output per head has risen.  The corresponding change is that the return on capital has increased.

My belief is that, on the whole, technological progress results in higher overall real wages.  However, I do not think we can assume that all new innovations will do this.