Earlier this week I posted about production functions which must have felt very dry but I promise there is a payoff (terms defined in the previous post are linked). Let’s consider a production function with three factors: computers, skilled labor and unskilled labor. What we are interested in thinking about is what happens as the price of computers drops (since that’s what we have obviously observed dramatically over the last decades).

Much of the literature seems to suggest that skilled labor is a technological complement to computers. You may recall this means that as you add more computers you have to add more skilled labor in order to get more output (in a Leontief-style production function). That is intuitively appealing. Just plopping down a computer without hiring someone to program it won’t do much.

But it is also potentially misleading. To understand why we need to dig a bit deeper into the notion of complements and substitutes. Let’s hold the output of a firm fixed for a moment. Then the firm will choose the lowest cost combination of factors to achieve that output. In our case the firm gets to choose a mix of computers, skilled labor and unskilled labor.

Now consider a production function in which it is possible to technologically substitute computers for both unskilled labor and skilled labor but where the presence of computers also increases the marginal rate of technical substitution between skilled labor and unskilled labor. In plain English: adding computers makes it possible to let one skilled worker replace many more unskilled workers than without the computer.

So now as the price of computers drops there are two countervailing effects on skilled labor. On the one hand the firm could substitute the computer for skilled labor. On the other hand the presence of computers makes the substitution of skilled labor for unskilled labor more appealing for the firm. The net effect on skilled labor then depends on which of these two forces is stronger!

Put differently, it is entirely possible that over some range of price decline in computers, computers and skilled labor behave as if they were complements because firms will buy more computers and hire more skilled labor, even though at a purely technological level the two are substitutes for each other.

I suspect that this is what has been going on which has an important implication. As the price of computers drops further and as firms have done a lot of substitution of skilled labor for unskilled labor, the substitution of computers for skilled labor will start to dominate. That is the period we are entering now and it will start to put wage and employment pressure on skilled labor which until now experienced a lift from computers.

A sufficiently detailed firm level data set that includes IT spending and breaks down employment by skill level might already show this effect today. One place where it shows up anecdotally is in the much smaller relative firm sizes of high tech startups such as Instagram, Whatsapp and Tumblr exited north of a billion dollars with relatively few employees.