Economics is a strange profession where much of what is proposed is apparently social or at least contextual construct (such as profit or utility maximisation), some is a rule of thumb with a lot of exceptions and question marks (such as market efficiency) and some is a kind of science that seems universally true but is left unexamined in formal terms.

One of these latter features is economy of scale. Economy of scale is understood in as the principle that, as economic production of a good grows, the marginal cost of production (that is, the cost of one additional unit on top of what has already been produced) goes down.

For example, if you are picking fruit, you might use workers with ladders up to a certain scale, and then as the production grows, switch to an orange picking machine operated by workers. Or, in factory, you might switch from a few smaller machines each producing 10 items per day to a single larger machine producing 50 items per day.

There are multiple phenomena taking place under the name of economy of scale. In the first example above, there's the substitution of labour for machinery, which in many cases has an efficiency effect. In the second, more classic example, the machinery just gets bigger. Why does this reduce marginal costs?

The key insight explaining economy of scale is the emergence of non-linear scaling between production inputs and production outputs. This has one particular basis in geometry called the square-cube law, something that Galileo brought to attention in his magnus opus Two New Sciences, but extends to a variety of non-linear scaling properties that extend across space, time and complexity in economic production. So let's explore.

The best way to understand this is to consider the difference between, say, a block of some pigment and the same volume of pigment in powder form. What is the relationship between the two? The relationship is that while the volume of the two sets of pigment is the same, the surface area of the two is vastly different.

And to get from the block to the pigment, you would cut the block into increasingly smaller pieces, each time increasing the  surface area - but never increasing the volume. This accounts for how a block of pigment is less soluble than powder pigment: because the greater surface area of the powder allows for more rapid absorption of water.

This curious principle, of the non-linear scaling of surface area in relation to volume, has lots of implications for economics.

Imagine that one is shipping a block of stone from a mine to a workshop, and that that stone has to be wrapped before being sent. On the same basis as powder having more surface area than a block, if you cut the stone up into smaller pieces before sending it, you will increase the amount of packaging each time you cut it - even if the amount of marble being shipped is the same.

This first example is the seed, focussed directly on non-linear scaling of surface area vs volume, of the whole world of economies of scale.

A related example which opens up this example would be chopping the stone into small chunks but then bundling that back up into a shape resembling a block. What happens here is that the irregular surfaces of the pieces cause the bundle to trap air, and there for still require more wrapping than the original block of stone. And, of course, the chopping of the original stone, and rearrangement into a bundle, adds extra work.

From this we learn that whether directly or indirectly, smaller items in a production context require more handling for the same effect. We may call this amount of handling required by the size of the product the 'transaction surface' of the item, which accurately links the both geometric, spatial root of economy of scale to the actual economic costs - so called transaction costs - of the increased handling as unit size decreases.

This idea of transaction surface is required when studying economies of scale in practice, since it may hard to see precisely or at least quickly, where the economies are being made.

If we imagine a large factory producing cars, it can be hard to see exactly where the economies of scale are being captured - even if our intuition, whether natural or trained, may make it seem obvious that a few large machines making many cars are more efficient than a lot of smaller machines making smaller cars. Why, precisely, is this in fact so? Let's find the transaction surfaces.

We can explore with a hypothetical comparison: comparing a large production facility with a series of smaller facilities, aiming in each case to produce the same number of cars.

If we start with the sheer spatial surface area required, we will see, for example that a group of smaller production facilities will likely require more land area for storage of parts, since the parts may not be stacked as high as they might be in a large facility: with every division of parts, you need to start another stack. This is a direct result of the separation of a raw volumes into smaller volumes, with the attendant increase in surface area becoming an economic transaction cost.

Most of the scaling implication of larger production facilities are not however so obvious as this - and are in fact much more interesting and powerful in production design.

Another example of transaction surface, that is in fact directly related to the non-linear scaling of surface to volume, but is much more implicit is … pipe design.

If we imagine a pipe network of all the smaller production facilities, compared to that of the pipes for the larger facility, in our example, the volume of fluid, say paint to spray the cars, might be equivalent in each case, since we are aiming to paint the same number of cars, after all.

The difference between the two is that, since in the smaller facilities the pipe diameter will be narrower, because of a smaller flow of paint, the ratio between the surface area of the pipe and the volume of the paint transmitted is higher. That's just a fact of the spatial relation between volume and surface area - just a more hidden example from the block and powder case!

More surface area per unit volume means … more friction, and thus higher powered pumps required for the same output rate, and indeed higher likely hood of blockage needing maintenance.

This is an example that shows how all-pervading, and frankly invisible, and fascinating, and thus complicated!, economies of scale endd up being.

Some more examples from the comparison of car plants of difference sizes. A classic case would be, for example, the use of lifting machinery. We can imagine a crane that has a lift capacity of 10 tons, and per use of the lift arm requires a fixed amount of energy. These cranes come in a standard size and are used to hoist car body parts in bulk into the factory.

In the case of the smaller production units, we can imagine the crane carrying only 5 tons of parts per lift, because the volumes per factor are smaller, compared with the larger factory that is carrying 10 tons of parts per lift. This leads to a clear efficiency gain in energy used at the larger plant. This is the classic economy of scale.

And we can understand the general transaction surface of the smaller volume production is higher because more 'transactions' - ie economic activity of an intermediate sort - are required to generate an outcome. In this case, the higher transaction surface of the smaller factories is expressed as more lifting required, and thus more energy (and more cranes!) for the same amount of parts moved.

A more subtle example of economy of scale is actually only revealed by comparing two cases of production inside a single factory - again revealing how complex economy of scale is in practice, even while based on a single concept of a transaction surface.

If we consider the case of a large factory producing one or two cars in a day to a case in which the same factory is producing many cars in a day, the economy of scale is not in the scale of the equipment itself, but in the volume of production.

Across these two cases, the transaction surface of the production machinery is the same - for example the amount of energy to start and keep running the production equipment - but the amount of output is different. So, the proportional transaction surface of the individual output cars is different: larger per car in the case of the smaller production run, because of the additional amount of resources required to produce it, even if the machinery is itself the same size.

Economies of scale, based on the concept of transaction surface,  has many inherent factors. This is a not full theoretical investigation of those, but here's a sample of their diversity:

  • spatial/geometric factors: pure spatial or geometric considerations, such as surface areas of packaging or piping vs volume.
  • spatial offset: the addition of spatial increments based on the pure geometric scaling factors, such as spare space in packaging box, when products are packed separately into standard packaging; or the airgaps in a bundle of items packaged together, but unable to join up efficiently, such as steel packed as ball bearings (which cannot be packed without gaps) rather than a single solid; or the user space required around a piece of equipment which is the same, whether the equipment is large or small.
  • mechanical factors: engineering properties, such as the standardised lift strength and energy burn of a crane's hoisting action, no matter what it is used to lift.
  • process factors: time-based properties, such as the amount of time it takes to spin up and close down a power plant, and thus a limit on production of short-run amounts of energy.
  • labour efficiency: the deployment of labour for different purposes, or replaced by machines/technology, to produce some element at larger scale.

There are more factors to economies of scale, and many of these are second order effects. But all of them are based on the non-linearity of some relationship under different scale conditions, in space or time.

Second order factors would include statistical efficiency and financial efficiency.

Statistical efficiency arises where, for example, there is more redundancy which leads to less down time. For example, if you rationalized a group of smaller car plants into a larger car plant, and were thus able to use the cranes previously available to the smaller car plants more efficiently,  you would have surplus cranes, which could be used as backups in the case of failure of the primary tools. This in turn would reduce waste in overall factory production, since other processes would not have to be shut down, as they would have been in the smaller plant if  crane failed.

Financial efficiency is the ability of a producer to offer prices at a far lower price if they get a large order, knowing, as they do, they have the capacity to still make a profit on the lower price, even while they may undercut the price of competitors.

And this financial efficiency second order factor is the dominant effect of economies of scale in the live economy: enabling and driving more, and cheaper goods, and the rise of large producers who legitimately override smaller producers through their production, and thus pricing, efficiency at scale.

None of this explanation of economies of scale, around the principle of transaction surface, is a justification of economic choices. It's just a description of facts.

There's lots of reasons why you might choose to design production in a very different way: efficiency in one variable may be irrelevant to broader economic welfare (although that is not likely in all cases).

For example, if by taking workers away from machines you achieve a scaling efficiency in the cost of products, you might also reduce the quality of the goods, where finishing and detailing by humans is what makes them particularly attractive. Or you might just decide that people want to work more closely with machines, or even directly as hand-made crafters.

Actually there are other arguments against fixed focus on economies of scale, beyond anything relating to the role of labour in scale efficiencies. These include the flexibility that comes into play when, if you have smaller production facilities, rather than just one large one, you can adjust output according to varying demand, with less waste.

And, conventionally, there is a 'diminishing return' to scale where, at some point, costs particular to large scale production start to outweight the efficiency benefits. For example, if a car factory is very large, and it uses equipment that is itself only made in a single factory, because so large, if that equipment breaks it cannot be replaced until that single factory can produce more. This is less likely to happen with smaller production, that may use more universal and high volume tools.

What you cannot argue with is that economy of scale has an effect that is different from the economic choices themselves, and if it is the case that consumers want cheaper goods, which are cheap because their production exploits the fact of differential transaction surfaces at different scales, this is not a result of 'capitalism' or anything other aspect of the political economy.

The efficiency gain is just as viable in a command economy, or any other sociopolitical arrangement of production. And economies of scale are part of that. Economies of scale are so universal, in fact, to human processes and engineering, at any level of sophistication - because based on such universal geometric and spatial underpinnings - that, I believe, it makes no sense to see economies of scale as specific to a particular economic approach, or even economics itself. They are all around, and always will be.

The image above, from Galileo Galilei's Two New Sciences from 1638, shows the practical implications of non-linear properties, specifically the square-cube law, governing the scaling of a marble column. What the images demonstrates is that the volume of a marble column expands more rapidly than the surface area, if you scale it proportionally - and thus also the weight! - leading to unexpected, or intuitively unpredictable, mechanical effects.