I was at a NASA workshop in Mountain View. An informational placard outside had two plots of growth, one with an unchecked exponential curve, and one with a curve that comes up to a peak and goes down. It asked which made more sense as a growth curve.

My idealized mathematical self thought, naturally, the exponential growth curve, because it expresses what happens when y-dot equals alpha y.

But I asked a passing Caltech astrophysicist, who (not surprisingly) gave a better reply. The curve that flattens out and goes down, he said, because exponential growth is impossible to sustain. Physical limits on some aspect of the system must intervene and impose a new law.

> Physical limits on some aspect of the system must intervene and impose a new law.

Just because Apple didn't become the first trillion dollar public company by marketcap (lets assume that chinese bank ipo for a brief second didn't count), doesn't mean that it would have broken a physical limit on the system.

There was a time not long ago when 100 billion companies didn't exist

and there was a time when private venture capital didn't value new businesses at 1 billion dollars

although I don't see the fundamentals to support such large companies, apple, or another company, isn't breaking anything if it does achieve the ability to grow larger

Might inflation due to quantitative easing, for example, be at least partially responsible for the higher valuations we see today?

Partially, Apple's metrics aren't that outlandish though. You could just use the age old price to earnings ratio and see it isn't wildly inflated, they make bank and speculators value it at 11 times said bank right now

The higher valuations of private companies IMO has little to do with quantitative easing. Despite any bubble talk, very little funding actually goes into these private companies. The S&P 500 returns nearly 1 trillion a year to shareholders via dividends, VCs put like 50 billion into these high growth startups.

Low interest rates from quantitative easing might contribute greatly, but I wouldn't say the inflation targets have much to do with it.

The inflation rate for the last 12 months was 0.9%, and has varied from 0.1% to 3.2% over the past 5 years. [1] So, no, inflation is not responsible for the higher valuations.

Higher valuations come partly from businesses having more cash because they are not spending money expanding, and because the low interest rates encourage companies to borrow money to buy back stock, which increases EPS and dividends, which increases share prices. Of course, there has been some legitimate growth over the past years, too.

[1] http://www.usinflationcalculator.com/inflation/current-infla...

Consumer price inflation is not responsible for the increase in equity valuations, but quantitative easing and bond buybacks certainly do. QE reduces the yield of bonds, making stocks look more attractive and hence resulting in more money flowing into stocks.

It additionally devalues the dollar, which leads to assets to be worth bigger numbers. QE has been mainly flowing to investors and the financial sector, and ts been staying there, hence not translating to consumer price inflation.

So yes QE is responsible and QE caused inflation and inflation is also responsible. This inflation is confined to investment assets.

Inflation should be considered, but for what it's worth, inflation rates, while still positive, have been decreasing (overall) for several decades now - including the most recent, which featured quantitative easing. See: http://inflationdata.com/Inflation/Inflation/AnnualInflation...

Apple is still proportionally smaller than IBM, which achieved like 15% of S&P500 in 1985.

for some reason, I really don't think that particular metric matters.

(for reference, the S&P 500 calculation was around 170 in 1985, compared to 2,098 today in 2016)

OK, let me frame the question as, "continual positive growth in revenue relative to the rest of the market", i.e. outperforming the market, and then either Apple becomes the market in goods, or the rules change.

A chart of growth rate might have a peak, but a chart of the thing that is growing is more simply modeled as a sigmoid that has an initial exponential growth portion, then a logarithmic portion which ends in a plateau.

That depends.

Time-delayed negative feedback produces a peak and a crash.

I'd really like to see this placard. Are you able to find a copy of that placard online?

I tried and failed before I posted. It was a metal sign placed outside "Building 3" (the Spanish-style place) here: http://naccenter.arc.nasa.gov

It's not readily accessible, and there seems to be no street-view coverage there. The photos listed nearby on google maps have a location that is far enough off to be useless.

My guess is most natural growth curves are exponential at early times, inflect, then reach asymptotic behavior.

That was a lot of words to use just to agree with the above. Well played?