I wrote this partly for Sandwichman, and mostly I wrote it because this same question crops up time and time again. It's a very old question, but it always looks like a new question if the technology is new enough. People in caves were probably arguing about whether 3-D printing robots flints would cause mass unemployment. And my answer is an old one too. There's nothing new in this post.
Take a very simple example. Labour is the only input, there's a constant returns technology, and labour produces one apple per hour.
Start at full employment, where everyone works 40 hours per week, and nobody wants to work any more than 40 hours.
Suppose technology changes, so that productivity doubles. Labour now produces 2 apples per hour. What happens? Will employment stay the same, so output doubles? Will output stay the same, so employment halves? Or something in between?
Is mass unemployment a possibility?
We need to ask two questions:
1. What are preferences? Do people want to work the same hours and consume twice as many apples? Or consume the same number of apples and work half as long? Or something in between? The sensible answer is probably "something in between". But I am going to assume they want to work the same number of hours as before and eat twice as many apples, because I want to consider the worst-case scenario for coordination failures where market economies fail to do what people want them to do (plus it's simple).
2. Is this a monetary economy?
2.A Autarky. If we take my assumption about apples and labour literally, it's hard to see why money would exist. It's even hard to see why exchange would exist. Each person consumes his own production. And if he wants to work the same number of hours, and produce and consume twice as many apples, he will do so. There can't be coordination failures because there's nothing to coordinate.
2.B Barter. Suppose they don't like eating their own apples. Just because. So they swap their apples for someone else's apples. And if productivity doubles, and each person wants to work the same number of hours, and produce and consume twice as many apples, he will supply twice as many apples and demand twice as many apples in exchange. It is not true that the doubled supply of apples creates a doubled demand for apples. A doubled supply of apples is a doubled demand for apples.
2.C Monetary Exchange. Here's where it finally gets interesting. Suppose they don't like eating their own apples; and suppose they don't like eating the apples produced by someone who is eating their own apples. Just because. So they sell their apples to a second person for money, and buy apples from some third person for money.
Now we might have a problem. The supply of apples doubles (i.e. people want to sell twice as many apples for money), but does the demand for apples double (do people want to buy twice as many apples for money)? Those are not the same thing. Those are two different actions.
It is easy to imagine circumstances where the supply of apples doubles but the demand for apples stays exactly the same, so the quantity of apples bought-and-sold stays exactly the same, and people only work half as many hours as they want to work. The doubling of productivity causes 50% unemployment due to deficient Aggregate Demand. For a simple example, suppose that the stock of money stays the same, and the velocity of circulation of that money stays the same. If MV stays the same, then PY stays the same.
Does the Aggregate Demand curve slope down? If we put the price of apples in terms of money P on the vertical axis, and the quantity of apples per week Y on the horizontal axis, so the (vertical) AS curve shifts right from 40 apples to 80 apples, will a fall in P cause a movement down along the AD curve until 80 apples are bought-and-sold?
That depends. If a fall in P causes an equivalent fall in M, so that the real value of the stock of money in terms of apples, M/P, stays the same, there is no reason why the AD curve should slope down.
At a minimum, the central bank needs to ensure that M does not fall, so that a fall in P causes M/P to rise, until M/P rises high enough that people have so much money in real terms that they spend enough of it to buy the 80 apples per week. But even this may not work, if falling P leads people to expect that P will fall even further in future, so they want to hold even more money and not spend it on apples.
But there's a simpler solution. The central bank prints money and throws enough money at people and increases M until M/P is big enough and people are holding so much money they want to buy 80 apples per week with it at the existing P so that the AD curve shifts far enough right to match the rightward shift in the AS curve.
The only thing left to argue about is the precise details of how the central bank should best "throw" money at people. Helicopter money (money-financed transfer payments)? Should the government buy apples with newly-printed money? Or should the central bank lend people extra money?
And should the central bank print money in response to changes in P so as to make the resulting AD curve horizontal and shifting North at 2% per year (inflation targeting)? Or should it print money in response to changes in PY to make the resulting AD curve a rectangular hyperbola shifting North-East at 5% per year (NGDP targeting)?
But that's not what this post is about.
The debate has moved on. But we sometimes need to remind ourselves that money is what is at the root of questions like these.
It is a fallacy to assume that a doubling of productivity will automatically cause a 50% decline in employment. It depends.
It is a fallacy to assume that a doubling of productivity will automatically cause a doubling of the demand for goods. It depends.
It depends on preferences, and it depends on money.
[Update: as Brad deLong said somewhere, the central bank's job is to make Say's Law true in practice even though it isn't true (it's a fallacy) in theory. And I would add that it is also the central bank's job to make it obvious that the Lump of Labour fallacy really is a fallacy.]
(If it currently takes both land and labour to grow apples, and if the new technology means it only takes land to grow apples, and labour can't help at all to produce more apples, then yes, the demand for labour will drop to zero. Which is very bad news, if you only own labour and don't own any land. But great news if you own land. That's what workers should really be worried about, because monetary policy won't help with that one.)