Why would a digital Yuan (or some other national currency turned into a CBDC) "help fast-track international settlements" in that currency?

How China Influences the U.S. Dollar

https://www.thebalance.com/how-does-china-influence-the-u-s-dollar-3970466

For export transactions to United States companies/consumers, Chinese firms typically receive dollars as payment for their exports. These firms then deposit the dollars into local banks, in exchange for yuan, which can be used to pay their domestic workers and vendors. The local banks then send the dollars to China's central bank, the People's Bank of China (PBOC). The PBOC holds the dollars in its foreign exchange reserves and regularly adjusts these reserves by buying or selling dollars via foreign currency markets in exchange for yuan. By stockpiling dollars, the PBOC reduces the supply of dollars available for trade, putting upward pressure on the dollar and downward pressure on the yuan. By selling dollars, the PBOC effects the opposite result.

It is important to note that the PBOC does not sit on cash reserves. It uses the dollars it accumulates to buy U.S. Treasuries, which are safe-haven assets that provide some incremental return over cash.

The Same Problems Plaguing the Yuan Will Plague China's Digital Currency

https://qz.com/1899402/why-chinas-digital-yuan-wont-internationalize-the-renminbi/

Because the digital currency is little different from the yuan itself, it will on its own “not be a game changer that elevates the renminbi’s role in international finance,” wrote Eswar Prasad, a professor of trade policy at Cornell University, using the currency’s official name. “After all, the Chinese government still restricts capital inflows and outflows, and the People’s Bank of China still manages the renminbi’s exchange rate. Neither policy is likely to change significantly anytime soon.”

What investors are looking for in a reserve currency isn’t the technology—it’s a currency that’s stable, underpinned by a strong economy, freely convertible, and able to be used widely.

But it still raises the issue: how does e.g. a US consumer get their hands on digital Yuans with which to pay something that they buy directly from China (e.g. via Alibaba)? Any exchange that would sell those digital Yuans that would have to take dollars in, no?

Not necessarily dollars... you could sell anything to China in exchange for some Yuans. If you're Apple, you could sell them the plans to build the next iPhone - or more likely, contract out the manufacturing but sell the phones in China for Yuans for more than the manufacturing cost. (To bootstrap the process, they'd have to get a loan in Yuans, or pay for the first batch with USD)

Think for a moment about how the US dollar works. How do you get US dollars to pay for things with? You sell stuff to the USA and they pay you in dollars. (You could sell things to a different country, but that country had to previously sell something to the USA to get the dollars)

If you do you trade in a certain currency, the country that issues that currency basically gets a bunch of goods for free. You have to give them something, to get the currency, to trade with! It only costs a few cents for the USA government to print a $100 bill, but any other country has to pay $100 worth of goods to get one¹. Some theorize that this is actually the true reason for the USA's economic success so far. It's easy to be wealthy if everyone is giving you free stuff all the time.

Yes, dollars count as something you can sell to China and get yuans for.

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What about the digitization side? Well, as I understand it, the current settlement process for international transfers is horrendously inefficient.

Let's get something straight to begin with: All US dollars are either physical cash, or held at the Federal Reserve. There are no digital dollars outside of the Federal Reserve. (There are the fake dollars in your fractional reserve bank account, but those aren't real dollars anyway)

So how do you transfer dollars - let's say from France to Brazil?

First, let's say your bank in France is the one that converts your euros to dollars. Let's randomly say it's BNP Paribas. It has to look up the current euros-to-dollars exchange rate and check that it has enough dollars. If so, it just moves the euros out of your account, and moves the dollars in. The bank does not access currency markets for this, except to check the price. Why not? Because trading is expensive, man, they can't do it every time someone wants to send money. (First sign of horrendous inefficiency)

But really, it doesn't have dollars. It has a claim on dollars, but it doesn't actually have the dollars. What BNP Paribas has, is a bank deposit at a different bank, denominated in dollars. It could be an American bank, it could be a really big European bank (probably in London or Frankfurt), if BNP Paribas is big enough it might even have its own Federal Reserve account (not likely though). Let's randomly assume that BNP Paribas has a dollar account at HSBC France, and HSBC USA has a Federal Reserve account.

(BNP Paribas also has a bunch of dollar cash, in case someone wants to exchange physical money, but that's not what you're doing here)

So. Anyway. That's the French side of the story. The Brazilian story should be similar. Let's say your recipient uses Banco do Brasil and they have an account at Wells Fargo (USA)².

So you send $100 from your bank account (in Euro) to your Brazilian friend's bank account (in USD because I'm not going to figure out what happens if both ends need to exchange currency). What happens?

Approximately something like this:

1. BNP Paribas looks up the exchange rate of USD/Euros and applies their spread (say 100.00 USD = 81.00 EUR)
2. BNP Paribas checks the amount of USD they have in their account at HSBC France (they have millions of USD, it's all good)
3. BNP Paribas subtracts 81 EUR from your account and records that they made 81 EUR profit (simplifying the accounting here)
4. BNP Paribas records that they made 100 USD loss
5. BNP Paribas calls up HSBC France and requests to send 100 USD from BNP Paribas's account to your friend's Brazilian account
6. HSBC France subtracts 100 USD from BNP Paribas's account
7. HSBC France calls up HSBC USA and requests to send 100 USD to your friend's Brazilian account
8. HSBC America calls up the Federal Reserve and requests to send 100 USD from HSBC America's account to Wells Fargo's account
9. HSBC America calls up Wells Fargo and requests to send 100 USD that it just received in its Federal Reserve account to your friend's Brazilian account
10. Wells Fargo adds 100 USD to Banco do Brasil's account
11. Wells Fargo calls up Banco do Brasil and says: "You have received 100 USD, it's a transfer from this guy's account to this guy's friend's account"
12. Banco do Brasil adds 100 USD to your friend's account

GOOD. LORD. Who the f**k designed this system? Well nobody designed it, it's just what happens when there's no leadership and everyone is trying to do the best they can.

Oh, and did I mention the part where the Federal Reserve won't let you have an account if you have connections to Iran, or you do business with any business that has connections to Iran, or you do business with any business that does business with any business that has connections to Iran? Yeah. Everyone is at the mercy of the US government's rules and there's f**k-all they can do about it, because if they don't comply, they lose access to non-physical dollars. Even if they find a bank that supports Iran and make an account, that bank will lose access to dollars.

Now imagine you want to send your friend a bitcoin. It goes like this:

1. You write a transaction that says you're sending 1 bitcoin to your friend's account
2. You put the transaction on the network
3. You wait a while and see whether it got accepted

MUCH. EASIER. And the government can't censor your transaction. (The USA's government used to be utterly horrified by the prospect of losing control over who gets to send money, but when bitcoin turned out to be a flop and a gambling game instead of a serious currency, they got a lot less worried)

Now, the reason everyone doesn't use bitcoin is that its price is so volatile, nobody has control over the money supply (which is why the price is so volatile), transaction costs are high, and a couple of other technical flaws. China wants to make a cross between bitcoin and dollars with the advantages of both - easy transactions and monetary policy. If they do it well, it's possible that everyone will start using it just to get away from the horrible nightmare that is the current system I just described.

And then everyone will start sending free goods to China to get their money, instead of the USA. Imagine what this will do to the value of the yuan and the dollar, not to mention their countries' wealth. All those dollars that are floating around and being used for trade, well, people don't need them for trade any more, so they're going to buy stuff from the USA (cancelling out all the free stuff the USA got) and sell it for yuan instead.

That's also why you occasionally hear about plans to give everyone a Federal Reserve account. That would make transactions just as easy (you just tell the Federal Reserve to do the transaction), it would still let the USA censor and spy on transactions like they want, and it would prevent everyone cashing in all their dollars at once since they'd still be using dollars for trade. If digitization is going to happen then the USA at least wants it to happen to them.

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¹ I cannot find the attribution or the exact quote; it may have been Ben Bernanke.

² I don't even know if Wells Fargo do this kind of thing, but let's pretend.