Analysis on Market Cap based on Metcalfe's Law

I thought it worth sharing some analysis.

red = f(x) = supply
blue = g(x) = growth effect
green = h(x) = market cap

Chart can be found here:

The narrative here is that we base market cap as a function of the product of supply and growth effect where growth effect is defined as the square of network participants (growth / adoption). We observe that given linear network adoption, we have linear market cap growth. We say growth is a square of participants based on Metcalfe’s law. Furthermore, market cap is asymptotic to network participants. This means given any rate of adoption we shall see the same rate of growth in market cap.

Thesis: Market cap growth is asymptotic to participant growth due to Metcalfe’s Law.

Based on this thesis, we can see that price is also determined to equal growth effect because price is market cap over supply:

p = h(x) / f(x)
  = (f(x) * g(x)) / f(x)
  = g(x)

Therefore, given linear growth, we should observe quadratic growth in price.

But, we must observe constant linear growth or an average growth that is linear over time. I would not make the case that growth is linear indefinitely unless population growth is linear by nature.

It’d be interesting to calculate the case where price is stable at a fixed rate; what growth adoption curve would be needed for such a case?