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Comment by typest | Hacker News Reader

Are the market caps of Apple and other tech giants growing as exponents, or sigmoids? This, to me, is the big question. Can multi-trillion dollar market caps continue to grow at this rate, or will they taper off?

Naively, one expects to get returns as a percentage of investment. In this multiplicative sense, Jeff Bezos at a 188B net worth is much closer to being a trillionaire than a one-billionaire (a factor of 5 vs a factor of 188). But can Amazon's market cap continue to grow in such a fashion? What bounds it (and that of other tech companies)?

One might assume that they have to be bound by world GDP (80T). But if they're truly creating value, can't they expand world GDP along with themselves?

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GDP is value created per year. Market cap is (a proxy for) value created over the whole future existence of the corporation, at some discount rate. The obvious cap on market cap of a company is total world wealth, which is on the order of few hundred trillion.

Thanks, yeah, I felt a little uneasy with the comparison. I figure this means market cap should be a bounded function of GDP, yeah?

You're basically asking how to convert assets (market cap) to income (GDP). But there isn't a fixed conversion: it depends on your discount rate (how valuable is future money compared to current money) which itself you can loosely think of as related to interest rates, which themselves change over time. Alternatively, think of the P/E ratio, which also changes over time. There's no bound. If you think humanity will exist forever, and you're willing to wait forever, and you think Apple will continue selling iPhones at a large profit forever, its value is effectively infinite.

This statement seems to assume wealth is a fixed constant, which it isn’t. Theoretically if it was believed a company will create a thousand trillion in wealth it could be valued against that.

http://www.paulgraham.com/wealth.html

To be a bit pedantic, GDP is not "value created per year". GDP is a measure of economic activity. That's it.

GDP = private consumption + gov expenditures + total investments + net imports/exports. IOW, it's a measure of the $ value of things bought/sold. IOW, economic activity.

That said, over short time horizons, GDP can be used as a rough proxy for many other economic metrics. But only because the structure of an economy doesn't change drastically in just a few years. As you increase time horizons, the structure of an economy changes and GDP becomes a poorer proxy for other economic metrics. If this is so, why do so many people use GDP? Because it's easy to measure fairly accurately.

In the long term exponential growth is physically impossible because it would imply infinite GDP. Even if apple's value is currently growing exponentially it will eventually stop.

Yes, in the long term, the universe will succumb to heat death and all value will go to zero. But on any time scale we might like to talk about (our lives, the life of the Earth), it seems plausible that exponential growth could continue (or at least, the long term argument doesn't apply).

This is a good moment for black swan thinking. Any time you get somebody arguing earnestly 'exponential growth will of course continue because it will continue, barring heat death of the universe' it's probably a crash indicator :)

Heh, don't jinx it.

If, as it has done so far, exponential GDP growth means exponential energy growth, then in a century or a bit less we will generate more heat as a byproduct of energy consumption as the earth is able to dissipate at livable temperatures.

In this framework growth has to end, on earth at least, much sooner than later.

They will all clearly taper off at some point, and one day go to zero / be subsumed by another company.

Seems like they are RELUs lately :/

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