This topic has come up a couple of times in comments on previous posts. Suppose there's an increase in labour productivity. Maybe because of improved technology. How will that affect labour demand, and employment?
I'm just going to work through the absolutely standard long-run classical textbook analysis of this question, with the help of a couple of diagrams. There is nothing new here for advanced macroeconomists. This post is aimed at people who have a basic understanding of introductory economics.
The answer is that labour demand can either increase or decrease, though "normally" it will increase. And employment can either increase or decrease, though "normally" it will decrease. (I will try to explain what I mean by "normally", but it roughly corresponds to "what has normally happened historically".)
The production function slopes up. As you increase employment, you produce more output. But the slope decreases as you move up along the production function. That captures the idea of diminishing returns. As you add more and more labour to a fixed stock of capital and land, holding technology constant, the extra output from an extra hour of labour (the "marginal product of labour") decreases. The slope of the production function is the marginal product of labour.
The red curve on the second diagram shows how the marginal product of labour falls as employment increases.
If the economy is perfectly competitive, firms will maximise profits by choosing a level of output and employment where the marginal product of labour equals the real wage. The red curve is both the marginal product of labour curve, and the labour demand curve. Start on the horizontal axis, at a given level of employment, and the height of the curve tells you the marginal product of labour. Start of the vertical axis, at a given real wage, and the curve tells you the level of employment at which the marginal product of labour will equal that wage. And that's the quantity of labour the firm will demand at that wage.
Now suppose technology improves. We can get more output with any given amount of labour. The production function shifts up. We now have the new, orange production function.
What happens to the labour demand curve when the production function shifts up? That depends. It depends on precisely how the production function shifted.
Suppose the production function shifts up the way I have drawn it. Notice that the slope of the production function increases at any given level of employment. That means the marginal product of labour increases at any given level of employment. And that means the labour demand curve also shifts up, to the orange curve in the second diagram.
An improvement in productivity (in this case) causes an increased demand for labour. That's what a lot of people can't handle. It just sounds wrong. "If productivity increases, you won't need as much labour to produce any given amount of output, so the demand for labour will fall". That's the Lump of Labour Fallacy. Who says output will stay the same?
When productivity increases, we can: consume the same amount of output and work less; work the same amount and consume more; or any combination of the two. We would even consume a little bit less, and work a lot less, if we wanted. It depends on what we want. It depends on preferences.
The dark blue curve labelled I on the first diagram is an indifference curve. It shows preferences. The representative person in this economy is indifferent between any of the points on that curve. They would prefer to consume more output, and would prefer to work less, but exactly the right trade-off between extra consumption and extra work will leave them indifferent, so it slopes up. But it gets steeper as we move up along it. That's because the more hours we are currently working, the more extra consumption we would need to persuade us to work an extra hour and give up one more hour's leisure. The slope of the indifference curve is called the Marginal Rate of Substitution between leisure and consumption.
The dark blue line on the second diagram shows how the MRS (the slope of the blue indifference curve) increases as hours of employment increases.
If the economy is perfectly competitive, a person will maximise utility by choosing to work that number of hours at which the real wage equals the MRS. The extra consumption you get from an extra hour's wages will be just enough to compensate for the loss of an hour's leisure. So the dark blue curve is both the MRS curve and the labour supply curve. Start from a level of employment on the horizontal axis, and the height of the curve tells you the MRS between leisure and consumption of the typical person. Start from a level of real wages on the vertical axis and the curve tells you how many hours people will want to work.
When productivity improves, and the production function shifts to the orange curve, people are better off. They can have more consumption while working less at the same time, if they want. They can get onto a new, higher, indifference curve. That's the light blue curve in the first diagram.
What happens to labour supply when productivity improves, and people are better off? That depends on the shape of the new indifference curve. The way I have drawn it, the new curve will be steeper than the old curve at any given level of employment. That means the labour supply curve has shifted up and to the left. Labour supply falls. For any given real wage, people will want to work fewer hours now they are better off. (Remember, all output gets paid to people as income in one form or another, either as wages or as non-wage income; capitalists are people too.)
So, what happens to employment when productivity increases?
We can look at either diagram to give us the (same) answer. The second diagram tells us that equilibrium is where the supply and demand curves cross. That's where the MRS (the height of the supply curve) equals the Marginal Product of Labour (the height of the demand curve). The first diagram tells us that equilibrium is where the indifference curve kisses the production function. If two curves kiss, they must have the same slope at the point where they kiss. The slope of the indifference curve is the MRS; the slope of the production function is the MPL; so MRS=MPL where they kiss. Two ways of looking at the same equilibrium point.
The way I have drawn the production functions and indifference curves, the labour supply curve shifted left a little bit more than the labour demand curve shifted right. So employment fell a little, and output (and hence income and consumption) increased a lot. (And real wages increased a lot). Historically, over the last 200 years in advanced countries, that is exactly what has happened. It's the "normal" case. We could have chosen to work a lot less and consume only a little bit more, but we didn't. Increased real wages, due to the increased marginal product of labour, gave us sufficient incentive to work only slightly fewer hours.
But it didn't have to happen that way. And it might not always happen that way in future. I could have drawn the curves very differently from the way I drew them.
Go back to the shift in the production function.
Case 1. Suppose the new technology lets us produce 55 apples with the same amount of labour that would have produced 50 before. And 110 where we could have produced 100. And 220 where we could have produced 200. A 10% output increase across the board. That's what I drew (roughly). It means the marginal product of labour increases by 10% everywhere. And the labour demand curve shifts vertically upwards by 10% everywhere. Case 1 is roughly consistent with what has normally happened historically.
Case 2. Suppose the new technology lets us produce an extra 10 apples everywhere. So we produce 60 with the same amount of labour where before we would produce 50. And 110 where we produced 100. And 210 where we produced 200. A 10 apple increase across the board. The production function shifts up parallel. The slope stays the same at any given level of employment. So the MPL doesn't change. So the labour demand curve doesn't shift at all. Good for whoever owns capital, land, or the rights to the new technology. But of no benefit to someone who only gets wage income. Or is it? Yes, it still is. Because people with non-wage income will be richer, and chose to work less, and so labour supply will fall, and so real wages will rise.
Case 3. Someone invents and builds 10 robots, which work exactly like human workers. The production function measured against human+robot labour stays exactly the same. But measured against human labour only the production function shifts left by 10 human workers. And that means the slope of the production function, for any given number of human workers, is flatter than before. The labour demand curve shifts left. Good for whoever owns the robots, and for whoever owns land and capital, but bad for those who only get wage income. Or is it? Yes it is, because it is very unlikely, given historical experience, that the extra income from robots will cause human labour supply to fall by enough to offset the increased labour supply by robots. Real wages will fall.