Has any European country ever formalized its economy by recognizing two currencies?

Yes. This was quite common in the 19th century. It was... not always a good idea.

I was wondering if any country formally allowed payment in alternate currencies.

It is very difficult to prohibit tradesmen from voluntarily accepting hard currency in lieu of domestic currency. And even if it were possible, it would be stupid.

Most countries have rules stating that tradesmen are permitted (or sometimes even required) to provide change in the local currency, and nearly all countries demand that their tradesmen quote prices in the local currency.

What is pernicious is issuing credit or collecting taxes in hard currency, or promising to exchange hard currency for domestic currency on demand and at a fixed rate.

Limiting lending to and collecting taxes in domestic currency encourages residents to exchange the hard currency they earn from export businesses into soft currency, to meet tax obligations and settle debts.

The benefits to my mind: Tourism seems largely unaffected by currency valuations in tourist-heavy countries. Greece for instance has had huge increases in prices since adopting the euro but tourism has risen concomitantly. It's also much easier for a visitor to use their own currency locally.

Allowing the tourist industry to use foreign currency should not be a problem. You would probably want to encourage the tourist businesses to exchange the hard currency for domestic currency after it has passed through one or two local businesses, to avoid developing a parallel economy. There is no particular economic reason to do that (as long as taxes and credit is all in domestic currency you should be good), but there are political reasons to be wary of parallel economies.

Second, a quick conversion of payment for today's labor into a stable currency encourages investment and savings.

It would actually tend to reduce investments, by increasing the required return to equity. However, it would level the playing field between the little guy, who cannot easily arbitrage between foreign and domestic equity markets, and the big guy, who can. Which is probably worth the (small) decrease in aggregate investments.

However, hard-currency deposits would have to be very heavily regulated. If you allow your banks to accumulate hard-currency liabilities without keeping hard currency at hand to meet them, you're setting yourself up for a run on your currency. So while I would not personally prohibit hard currency deposits, I would require the central bank to purchase enough hard currency in the open market to match the total hard currency liabilities of the domestic economy, so it may act as lender of last resort in hard currency during a run on the currency.

- Jake

Friends come and go. Enemies accumulate.