Does an increase in productivity cause labour demand to increase or decrease?

The answer to that question, and how we go about answering it, depends on whether we are talking about one small sector of the economy (partial equilibrium), or the economy as a whole (general equilibrium). (I was doing general equilibrium in my previous post).

If you start with the answer for one small sector, and just add it up across all sectors, you get into a total mess. That's the Fallacy of Composition. What's true for each of the parts isn't necessarily true for the whole.

Let's simplify massively. Ignore land and capital. Labour is the only factor of production. And let's assume all labour is identical. And let's assume constant returns to scale, so if you double labour employed you double output produced. That lets us focus all our attention on the difference between partial and general equilibrium, and ignore everything else that might complicate the story.

Suppose apples are a very small part of the economy. Suppose a new invention doubles the productivity of apple producers. What happens to employment of apple producers?

When the cost of producing an apple halves, the price of an apple will also halve. That's true under perfect competition. (It's also true under monopoly, and monopolistic competition, if we assume the elasticity of demand for apples is constant.) If the price of an apple halves, the quantity of apples demanded will increase.

If the elasticity of demand for apples is greater than one, the quantity of apples demanded will more than double when the price halves. So the demand for labour to produce apples will increase when productivity doubles.

If the elasticity of demand for apples is less than one, the quantity of apples demanded will less than double when the price halves. So the demand for labour to produce apples will decrease when productivity doubles.

That's the answer to the partial equilibrium question. It's simple. But did you notice all the implicit assumptions I slipped in there?

I assumed wages stayed the same, when I asserted the cost of producing apples would halve. But if the price of apples halves, workers' cost of living falls slightly, so they should be willing to supply the same amount of labour at a slightly lower wage.

I assumed the prices of other goods stayed the same, when I talked about the effect of a fall in the price of apples on the quantity of apples demanded. But if wages fall, because all workers can now buy cheaper apples, the price of other goods might change too.

I also assumed incomes stayed the same, when I talked about the effect of a fall in the price of apples on the quantity of apples demanded. But if wages and prices are all changing, because apple productivity has doubled, and if employment might be changing too, it is very unlikely that real income would stay the same.

All my implicit assumptions are likely to be false. The things I assumed constant will probably all be changed by a doubling of apple productivity. But if apples are only a very small part of the total economy, the effects of a doubling in apple productivity on economy-wide wages, prices, and incomes will be very small. It's OK to ignore them.

But you obviously can't ignore those things if you are talking about a doubling of productivity across the whole economy.

In the partial equilibrium experiment, what was driving the results was a decrease in the price of apples relative to other goods, which caused an increase in the quantity of apples demanded relative to other goods. That won't happen at all if the productivity of producing everything doubles. Because the price of everything will halve relative to wages. So all the analysis in the partial equilibrium experiment is totally useless in the general equilibrium experiment.

And it's all the things I ignored, in the partial equilibrium experiment, that become the only things that matter in the general equilibrium experiment.

Throw away the partial equilibrium analysis. It's not just wrong; it's totally useless for the general equilibrium experiment. Start from scratch.

The productivity of labour doubles for everything. Relative to (hourly) wages, the cost of producing everything halves. And so the price of everything halves relative to wages. Or wages double relative to prices. Same thing. Real wages, which represent the amount of goods you can buy with an hour's labour, must double. (Remember, I assumed labour is the only factor of production, so there's no capital or labour income to worry about. And if that bugs you too much, just read "labour" as shorthand for "labour, capital and land", and "wages" as shorthand for "wages, capital rentals, and land rentals".)

Output per unit of employment has doubled. Will output double, and employment stay the same? Will employment halve, and output stay the same? Will it be a bit of both? That depends.

"Maybe people can't afford to buy twice as much stuff?" That argument is totally wrong. We get our incomes from producing and selling goods. If the value of goods bought doubles, the value of goods sold doubles, and income from goods sold doubles too.

"But can we all co-ordinate on the new equilibrium where we all buy twice as much stuff and all have twice as much income?" That argument has a point. It's not totally wrong. For example, if each of us wants to save part of any increased income by hoarding money, rather than spending it, we will not co-ordinate on the new equilibrium. Output will stay the same, and there will be a 50% unemployment rate. The policy solution is to (approximately) double the money supply, so people hold twice as much money in their pockets, and will be willing to spend all their income, rather than hoard money, when income doubles. (Or, if all prices halve, the value of the existing stock of money could double that way instead).

"But maybe people just don't want twice as much consumption?" OK, that's entirely possible. Let's take the extreme case, and assume that people just don't want any more stuff at all, even if it were free. So firms, in aggregate, are simply unable to sell any more stuff. "Oh my God! Doesn't that mean there will be 50% unemployment? Doesn't that mean we have to launch a big advertising campaign to dupe people into wanting to consume more stuff? Or else have mandatory work-sharing, where the government forces everyone to work half-time?"

No. If people don't want to consume any more stuff, why would they want to keep working the same amount and earn double the income than they want to spend? If they enjoy leisure, they wouldn't.

In the "nightmare scenario", where people just don't want to consume any more stuff, labour supply will halve, at the same time as the demand for labour halves. There is a 50% reduction in employment. But that's not the same as 50% unemployment. People simply choose to work only half as much as they did before. Each individual prefers to "spend" his extra riches on lesure, rather than on extra consumption. No worries.

But there is one scenario that does worry me a bit. Suppose people enjoy working. Not for the extra consumption that the extra income can buy, but simply because they enjoy doing something they think is useful. And they hoard their money income, simply because they can't think of anything they want to buy with it, but don't want to stop working. And money is no longer merely a convenient medium of exchange, but a signal of how useful and productive a member of society the holder is. A bit science-fictiony perhaps. But I can't rule it out on theoretical grounds. The demand for money might be unbounded.