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Productivity can increase in many ways. Division of labour is the most fabled of these.
But combining labour can increase productivity as well.
Consider the simple example of the typing ladies (typing pool), and its disappearance as computers came in.
Not too long ago if you had to write a business letter, you'd spend Td (time) to dictate to a steno, the steno would then go and type (taking time Tt). You'd then spend Tv time to verify the typed letter (and where necessary do a second round of checks till the letter was ready to go). Then the letter was ready to go.
For simplicity sake, assume your salary was 5 units per unit of time, and the steno's 1 unit per unit of time. Then the total cost of the letter was 5 (Td+Tv) + (Td+Tt).
With computers and printers, let's say you spend time = Tc (where Tc>Td) to type the letter, and zero time to print it. The cost of the letter is now: 5 (Tc).
The efficient solution now is to type yourself so long as 5 (Tc) < [5(Td+Tv) + (Td+Tt)], or Tc < (6/5)Td+Tv+Tt/5.
Assume you took 20 minutes to dictate a letter, and 3 minutes to verify it. Assume the typist took 60 minutes to type the letter. Therefore, you should fire your typist if Tc < 39 minutes.
Alternatively, if you dictated the letter at 80 words a minute, then you should fire your typist if you type faster than 41 words per minute. In other words you can type much slower than the typist and still be better off by firing the typist.
This paradox of combination of labour, of rolling smaller tasks into the normal job of far more highly paid and qualified professionals, explains the end of the typing pool. Division of labour has become too costly.
Many other examples can readily be found.
Businesses are constantly transferring part of their production to the consumer who benefits by reduces his waiting time by typing in his own details online and getting an e-ticket, instead of waiting in line at the travel agent.
Similarly, people prefer to check out groceries themselves to save time waiting for the more personalised service of a counter clerk.
During the first industrial revolution, productivity increased through division of labour. In the second industrial (information) revolution, productivity is increasing through the combination of labour.
As a result we are getting busier and busier even as we get richer.
Twenty five years ago I was served by a host of servants and others who did my shopping, driving, cleaning, cooking, gardening, ironing, typists, carrying around files, etc. Today I have no servant, only machines, to serve me. But machines need to be tended. So I do ALL these things myself.
I do my shopping in supermarkets, store stuff in fridges and freezers which frees me to shop only once in two or three weeks, do my own driving (modern cars don't break down much so I don't need to constantly have a driver to maintain it), wash my clothes and dishes in machines, iron using powerful high quality irons which do the job in half the time of older irons, and so on.
And of course I type my own letters, and mail them myself (usually by pressing the 'send' button on email).
WITHIN ME I HAVE COMBINED THE LABOUR OF TENS OF PEOPLE.
This is the new productivity.
Indeed, as I showed earlier, division of labour in the modern world can significantly reduce productivity.
Read more at Sanjeev Sabhlok's Occasional Blog-Economics