Demand-determined productivity

A quick thought after this twitter conversation:

Important point: if your product is information, your productivity is definitionally proportional to demand https://t.co/oulNUf2oNS

— Alex Harrowell (@yorksranter) October 15, 2017

There is quite a large set of firms for which productivity is fundamentally demand-driven. This is a distinct point from Verdoorn’s law, the argument that productivity improvement is most likely to happen when firms are producing close to capacity. Consider me writing a research note about productivity, which is apparently what I do instead of writing blog posts about productivity, because society considers the first activity to have measurable productivity and therefore pays my gas bill.

Productivity is defined as outputs divided by inputs. The most common form of this metric is labour productivity, output divided by inputs, per hour worked. So the production cost of that report is just what it cost to employ me for the time I spent working on it. That’s the input. The output is going to be the price Ovum charges for it, multiplied by the number of copies we sell. Actually, most copies are part of a wider subscription to our research and some are free as part of consulting projects, but we can get around that by saying it’s the weighted average price multiplied by the volume. (If you are enough monopolist to set your prices where you want, there’s a whole other ball of wax here.)

It’s therefore obvious that the more copies of the report that go out, the higher productivity will be. Measured productivity is exactly proportional to demand. This is true whether Ovum sells more copies if demand goes up or whether it increases its prices. This seems silly, but it’s inherent in the definition of productivity. It’s also something you logically have to believe if you believe demand and supply are meaningful concepts and you are trying to be consistent. If people want this research, that probably says something good about it, and any productivity metric needs to take account of that.

This sticks out a lot for information goods, because it usually costs very little to reproduce them. Issuing one more PDF costs next to nothing. The point is stronger than that, though. Information goods are a special case of a much bigger general case. To say that it cost x hours of my time to prepare this report, and it costs basically nothing to reproduce it, is to say that the process of preparing it has high fixed costs and negligible variable costs.

This is a little counter-intuitive, because we usually think of labour as a variable cost. Obviously they could sack me, but just as obviously, if you want to sell research on telecoms companies you’ll have to employ telecoms analysts. The relevant distinction is between costs that are fixed or decreasing with respect to volume, and costs that increase with volume.

The whole project of industrialisation, after all, is about using more capital, a fixed cost, to reduce the marginal cost of production and take advantage of economies of scale. The set of firms whose cost structures are dominated by fixed costs rather than volume-variable ones is therefore large. A chemical plant that takes in cheap ingredients and produces a much more valuable compound might spend a lot of capital to set up its process, which is then a fixed cost. It will not spend dramatically more running flat out because its inputs are cheap. Therefore, its productivity is determined by demand.

The same would be true about capital-intensive manufacturing, about software, a lot of IT services, anything that sells intellectual property, and anything where output changes in variety more than it changes in volume. Also, anything whose cost schedule, aka supply curve, has a step function will show this behaviour in the short run. If you are at step x, you can increase output up to step y without spending more money, and therefore both productivity and profitability will increase with demand until you hit the step.

We can also restate this point as a distinction between processes with decreasing or constant returns to scale, and those with increasing returns to scale. If returns to scale are constant or less at the current scale, productivity is indifferent to demand. If they are increasing, productivity is demand-determined.