Inequality and Technical Stagnation

8/02/2013 09:04:00 AM
Technological stagnation in late antiquity.
The idea that technological innovation has stagnated in recent decades has become a popular topic in the econosphere (also, see herehere, here and here; for a historical take, see here). In the past, I have criticized this idea for ignoring the most important aspects of technological advance--even though we haven't come out with any newly invented household appliances that are nearly as life-changing as the inventions in the first half of the twentieth century--like the refrigerator--we have continued to improve the production methods for all types of appliances, and that is possibly the most important kind of technological progress.

However, supposing that the thesis is correct, it still seems to me that in fact we have come up with lots of potentially life-altering inventions that simply never made it to mass production for the middle class. Why would this be?

One simple answer is that these inventions didn't make it to the mass market due to proprietary gridlock. There are two prongs to this: first, a new invention is likely to require use of several already patented works not owned by the new inventor. In principle, who ever owns those patents should be willing to license them; however, since the new invention differs from the primary uses of those patents, the new inventor could easily see himself priced out of the market. Second, the new inventor himself will seek patent protection for his invention, which comes with some perverse incentives. In perfect competition, the incentive is to release the best possible product to the market as soon as possible at the lowest possible price. With patent protection, however, you have a monopoly on the product, and so the incentive is to restrict supply to charge as high a price as possible. To do that, you need to fight the Coase Conjecture, which basically means you adopt a "planned obsolescence" strategy: start by selling a stripped down version of the product, and then in each period there after add back just enough features to render the older version obsolete and undesirable--such a strategy prevents the resale market from competing against each new version of your product, undermining the result in the Coase Conjecture. The archetypal example of this is the Apple iPhone, which released six different versions, each better than the last, despite the fact that none of the relevant technology has changed significantly over that period (ok, readers might disagree with that point. I have in mind things like the iPhone processor: yes, processors on iPhones improved, but all of the versions of iPhones have had pretty crappy processors compared to just about any computer--keep that in mind).

A second, more interesting possibility is that the rising wealth inequality is responsible for the deceleration of technological innovation. Here's how: suppose that the population consists of two classes: most people are middle class, but there is a small extraordinarily wealthy upper-class. Suppose you come out with a new invention--say, a 3D printer--which really could revolutionize how we live, but unfortunately, it is very expensive to produce. For the rich upper-crust, that's no problem at all--they can afford anything. But for the middle class, that's a deal breaker--they gotta save their money to put food on the table. The result is that all of the extremely wealthy buy the 3D printer, but none of the middle class do. But here's the caveat: at this scale of production, the production function is characterized by increasing returns to scale. Now, the capital and labor to produce the 3D printer must be diverted from production of things middle class people buy, so prices of things for the middle class rise (see: Baumol's Cost Disease), the middle class gets poorer and buys less, which partially offsets the already small increase in GDP from sales of the new 3D printer.

Now suppose the government redistributes the wealth. The middle class now owns significant shares of the capital stock, which was previously owned exclusively by the rich. Now, all of the sudden, the middle class actually can afford the 3D printer, so production booms. But remember that the production function was increasing returns to scale? That means that the price of the 3D printer actually plummets--households are now buying two or three instead of one! Its a technology revolution! The massive increase in sales of 3D printers raises GDP, but since the production function is increasing returns to scale, relatively few resources need to be diverted away from producing everything else, so those prices do not rise much, and  hence the offsetting effects are quite small. Hence, GDP rises by a lot. The result is that we would observe a much larger increase in measured total-factor productivity under this second scenario than in the previous scenario with more inequality.

In general, I believe that production functions always have roughly the same shape: at very low quantities, there is increasing returns to scale, while at very large quantities there is diminishing returns to scale. In the case of industrial products, at least, we will never find ourselves on the diminishing returns to scale portion of the production function, because in this case it should be possible to reduce costs by downsizing factories--that is, instead of one giant factory with diminishing returns, we could build two smaller factories each with lower average costs (if the production function is twice continuously differentiable, then at least one point is characterized by constant returns to scale, and this is in a sense the ideal firm size).  However, it is possible to find ourselves on the increasing returns to scale portion of the production function if demand is insufficiently large to warrant a bigger factory. By restricting demand for expensive new inventions to a very small group of individuals, it is in this sense that rising income inequality can cause technological stagnation.
Theo Clifford 8/04/2013 05:44:00 PM
While it's clear that some planned obsolescence is going on at Apple, you're underestimating both the tech advances in smartphones in the last six years and also the degree of competitiveness in the smartphone market.

I would also caution against drawing major conclusions from mental models assuming increasing returns to scale for one good and not others.

Also implicit in your model is that rich people will not want to own more than one 3D printer.

The costs of redistributing the capital stock may also be high.

Are modern markets small enough for increasing returns to scale to matter?

Thought-provoking, though.
Matthew Martin 8/05/2013 01:51:00 PM
Good points. I'm definitely making some assumptions about the nature of the utility functions by assuming that the rich won't simply buy lots of 3D printers. At the very least, we could get this result with a "bliss point" in the utility, where people only value a certain number of printers, but no more. I believe Mankiw has a more general version of that kind of model, in which high levels of inequality and bounded utility functions result in periodic financial panics and contractions in GDP. In the context of that kind of model, all I'm doing here is pointing out that the result in Mankiw's model could potentially be mistaken as technological stagnation.
Metatone 8/05/2013 09:11:00 AM
As an engineer I can pinpoint precisely what's wrong with using processors for your example - phone processors are chosen as a compromise between processing power and electrical power consumption. The clue is that phone processors aren't just old desktop procs (e.g. pentiums) but new designs.

That aside, I'm sympathetic to your argument, Yglesias's example of cars in Nambia also gives clues that "technology" is not the only force at work.
Matthew Martin 8/05/2013 01:58:00 PM
I figured that would be a controversial point. I realize that issues of battery life and overheating prevent us from using the same processor arrangement as in PCs, but is it really true that Apple was unable to produce better processors than what they did? The new Microsoft Surface seems to me to offer a counter-point: the Surface Pro has, as I understand it, considerably more processing power than an iPad, even though their processing units are basically the same. But I'll admit I'm not an engineer.