What specifically are you explaining? Why a hard cap at all, or why specifically 21 million as the hard cap? I’ll attempt to answer both:

Why is a hard cap a good thing? The supply of any good can either be increasing, decreasing, or unchanging. Bitcoin is a good that’s defined and controlled by its holders, who each want to maintain the most value of their coins. An increasing supply means holders are getting diluted, which they don’t want. A decreasing supply means some or all holders must be confiscated from, which they also don’t want. That leaves a fixed supply, where people are neither diluted nor confiscated from.

Why specifically 21 million? Satoshi picked a10 minute block time somewhat arbitrarily, and a halving cycle of 210,000 blocks so that a halving cycle was almost exactly 4 years (off by only 0.2% if block times are exactly 10 minutes). AFAIK 4 years was another arbitrary choice. He also picked a starting block reward of 50 coins, and a halving every cycle rather than a quartering or… thirding? Is that a word? Both of those decisions are also arbitrary AFAIK. Anyway, 210,000 blocks * 50 coins per block for the first cycle, plus 210,000 blocks * 25 coins for the second cycle, and so on, adds up to exactly 21,000,000. But since Bitcoin isn’t infinitely divisible, halving the block reward will eventually lead to decimal places being rounded off, meaning that the 21 million figure isn’t actually true, and the final number will actually be 20,999,999.9769 coins.

Were those concise? I’m not really sure šŸ˜‚

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