# Changes in relative value

It’s interesting how the relative values of things change over time. Agatha Christie, looking back on her early life, remarked that she “couldn’t imagine being too poor to afford servants, nor so rich as to be able to afford a car.” I assume that by the time she died she drove but had no servants, like most of the rest of us.

One of the biggest drivers of changes in relative values has been the exponential improvement in semiconductor technology due to Moore’s law. Even those of us in the business underestimate it. People just aren’t very good about thinking about exponential change. I can remember running the numbers and working out (a long time ago) that we should have workstations that ran at 10MIPS, with a megabyte of memory and 100 megabytes of disk. What didn’t even occur to me was that these would not be refrigerator-sized boxes, they would be notebook computers; or even Palm Pilots. And a high-end 1 BIPS “supercomputer” with 16 gigabytes memory and a 2 terabyte disk would have seemed totally unbelievable to me, even as I read the numbers off the graphs. But that’s what I’m typing this blog entry on.

If you are not in a business where exponential change is the norm, people find it really had to think about. For example, in How laypeople and experts misperceive the effect of economic growth people were asked what would be the overall increase in national income in 25 years if it grew at 5% per year. Over 90% underestimated and only 10% of them were even within 50%. Surprisingly, the experts weren’t much better than the laypeople. Quick, what is the percentage increase? See the end of the entry for the answer.

If the timescales are extended more then the numbers become even more dramatic. Alex Tabarrok in his TED talk shows that if the world GDP continues to increase at 3.3% per year for the rest of this century (below what it has been running at) then the average per capita income in the world will be \$200,000. That’s the world average, not the US which should be in the millions. Our great-grandchildren will be much richer than us (if we manage to avoid catastrophes like blowing up the world).

However, there is also a problem with our thinking when going the other way. Those of us in electronics and semiconductor tend to think other industries are basically like ours, with R&D driving an underlying exponential growth and thus the accompanying fast upgrading of old equipment. Battery technology, for example, doesn’t increase exponentially in line with Moore’s law. It would be great if an AA battery could contain 1000 times as much power as it could back in 1990, let alone a million times as much as it held in 1970. You’d only need one for your Tesla roadster.

Our cell-phones don’t last too long, not because they break but because the new ones are so much more powerful. So we junk them after a couple of years, along with our computers. But that’s not true for cars. No matter what great new change in cars happens (better MPG, lower emissions, super airbags, whatever) then it takes 20 years for most cars to get it. Many of the cars that will be on the road in ten years are already on the road today. Power stations, bridges, railroads, aircraft are all on even longer timescales. For example, I just looked and over 60% of all Boeing 747s ever built are still active, including some that first flew in 1969 (complete list is here).

When part of life improves exponentially and part doesn’t is when we get the type of dissonance that Agatha Christie experienced from unexpected changes in relative costs. Amazingly, and luckily, disk drive capacity has improved even faster than Moore’s law even though it depends (mostly) on different technology breakthroughs. But things involving large amounts of physical stuff, like metal, just can’t change very fast. Henry Ford would be amazed at various features of our cars, but he’d still recognize them. Early computer pioneers wouldn’t have a clue about a microprocessor.

The answer to what would be the overall increase in national income if it grows at 5% per year for 25 years is about 250%. A good rule of thumb everyone should know is that if something increases exponentially (compound interest) by x% then it takes 70/x years to double. So in this case it will double in 14 years and almost double again in 28 years (so about 3.5x in 25 years, which is a 250% increase).

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