What if a process has more than one input: say one person and a envelope-licking machine? Then more sealed envelopes will be produced per hour because of the help of the machine. The person has become more productive by virtue of the availability of a machine. We call the introduction of the machine labour-saving technical change if less labour is required per unit of output assuming that the wage relative to the rental rate of machines has not changed.
What if, further, that after having worked with the envelope-licking machine for a month, the person finds that they can produce even more sealed envelopes than they could when the machine was first introduced. Now we have an example of capital-saving technical change. Presumably the worker has become more familiar with the workings of the machine. In the jargon of economists, they have accumulated human capital, in this case specific to a certain type of machine. This may be termed learning-by-doing. Now the introduction of the machine was a necessary, but not a sufficient condition for human capital acquisition.
Often the realization of economies of scale requires an investment in machinery, capital, and possibly a larger workforce as well. The classic example of economies of scale is due to geometry. If one stores a liquid, say oil, in a cubed shaped vessel exactly 1m3, then to build such a vessel one would require six sides each of 1m2 (1m by 1m). If the material is $1 per m2, then the vessel would cost $6 per m3 of oil stored. Now to store more oil, one builds a vessel out of sides that are 4m2 (2m by 2m). This would cost $4 per side for each of 6 sides for a cost of $24, four times as expensive as the smaller vessel. One could now store 8m3 of oil at a cost of $24 for the vessel resulting in a cost of $3 per m3 of oil stored, compared to $6 per m3 for the smaller vessel. The unit storage cost has fallen. Of course in the real world, the sides of the larger vessel would have to be stronger as they support more weight associated with the larger volume. The economies of scale realized will therefore be less than in the example, and at some large enough size, the increase in cost of the stronger sides will be greater than the gain in volume. At that point economies of scale will be exhausted.
Historically, the identification of the sources of growth is inexact. Usually changes that occur in firms’ production processes display all three types of changes simultaneously, and dividing them up is part method and part assumption. We also observe that productivity improvement, whatever its source, may be generated by an entrepreneurs desire to improve the production process, but also by the perception of a large market. Going back to Adam Smith's observations that the division of labour is limited by the extent of the market, what may motivate the introduction of a new process is an entrepreneurs view that they can sell more output if only they could produce more. Usually this coincides with an invention of a new process, although it is not often that the inventor is also the successful marketer.
In summary, we usually observe improvement due to the introduction and improvement of machinery, often termed labour-saving technical change; through the acquisition of human capital, or by the realization of economies of scale. Often the introduction of new machines allows for economies of scale and we observe more output, more machines, but not necessarily more workers.
What probably happens is that over the long run, employment in other sectors expands to absorb all labour released from the sector undergoing rapid labour-saving technical change. This tends to occur with wages continuing to rise. For example it has been recently noted that employment in the service sector in Canada has been steadily increasing while employment in the capital-intensive manufacturing sectors has been steadily declining. Some claim that this is bad because productivity growth in the service sector is more limited than in manufacturing and therefore as the service sector grows, intensive growth in Canada will accumulate more slowly. This view is not universally accepted, however.
Another theory is that growth in services represents capital-saving technical change. In this story, the management component of a firm grows because it acts to coordinate more efficiently the activities of the manufacturing component. We observe growth in the managerial class relative to the working class. While we measure greater productivity gains in manufacturing, we neglect to attribute some of those gains to the service sector.