Part 3 of a multipart series on fiat and bitcoin's intrinsic (and extrinsic) value
Part 2 here

The Satoshi's Maximum Value

Now, if copper and zinc are the essential natural resources to sustain a "penny based" currency system, electricity is the natural resource used to sustain a "bitcoin-based" currency system. Therefore, a transaction fee should, in theory, stabilize at the price of the electricity used to mine it. Any more, and miners would keep popping up until their utility companies raised their rates. Any less and it wouldn't be worth mining bitcoin anymore, and everyone would just use some other coin (seriously, who's going back to the dollar?).

Now we've pinned the value of bitcoin to a relationship between bitcoin transaction fees and electricity rates. What exactly does it cost to mine a bitcoin block? Let's fast forward to around 2100 when all new bitcoins have been mined, and the only reason to mine transactions is because of transaction fees. So according to the Bitcoin spec, there's 1MB of data per block, and the type of transaction with the smallest digital footprint is ~250 bytes (the bitcoin protocol does offer complex transactions than "Alice pays Bob", but those require more space on the block). So you're going to get at most about 1MB/250bytes=~4000 transactions per block. Now, how much energy does it take to mine that block? Well, there's a nifty website that has most of the work done, and seems up to date. Looking at the footer at the bottom, we can do a bit of multiplication.

12.5 BTC/block x 1 day / 0.0006350 BTC x $3.72 / day x 1 block / 4000 transactions = $18.31 / transaction
These calculations are subject to change after the time of writing, but the sources should stay up to date

So we're getting at least $18.31 / transaction since you could in principle just have one (or zero) transactions per block. But when Bitcoins cease to mint around 2100, transaction fees will be the only reason to mine bitcoin. Reality check: my girlfriend invested her first $20 in bitcoin at a bitcoin ATM and was told her deposit was on the order of her transaction fee and the network took like 3 days to process it. This also matches up pretty well with current data. So this estimate seems to check out with the market. If that's the cost of the energy necessary to process a transaction, what's the highest price a bitcoin could be? Well, you need to be able to divide your transaction into a part for the spender and a part to incentivize the miners. So the satoshi shouldn't, in principle, sustain a price higher the cost of energy to mine it. Which in turn caps the bitcoin at ~$20 / satoshi x 100,000,000 satoshi / BTC = $2,000,000,000 / BTC. So there you have it, 1 BTC can't be more than $2 billion. That cap will follow the price of electricity required to mine the block. Note that as hardware becomes more efficient, it mining blocks will become more difficult, and therefore draw more power.

Long Term Death of Bitcoin

I'm going to wrap this post up with a glimpse into the far future--the inevitable heat death of bitcoin.

It's no secret that block rewards will eventually end. At this point, there will be no new bitcoins in circulation, and as people die, lose keys, or conduct faulty transactions, the amount of bitcoin in circulation will decrease indefinitely as the coins end up in wallets to whom nobody can unlock. Granted, I think people would just jump ship to competing currencies or some fork long before the bitcoin network becomes a group of three people exchanging and mining two satoshis.

Little johnny will get his satoshi as soon as grampa starts up the mining rig