So the mystery is, why does it matter if your currency has a floating exchange rate? Currency is just a symbol of the value of goods, so does it really matter if you say that a loaf of bread costs one Lat, two Lats, or one Euro? It is the relative value of goods and services that matters, not the value of the currency. That is, in a perfectly efficient economy it wouldn't matter. So I decided to investigate what kind of inefficiency would lead to problems with having the same currency (or a pegged currency) as everyone else around you.
After a little thought, the answer I cam up with is that the only reason a floating exchange rate is easier is that it is difficult for an economy to deal with deflation. Every national economy produces some goods for export (foreign investment in local property acts similarly to exports) and they produce some goods and services for the local economy. During a major recession there is a lot of recalculation going on about the relative value of different goods. For example, notice that in the US the price of a home in Las Vegas has gone down a lot more than the price of watermelons. Many of the products of Latvia have gone down in value as well. In particular, there used to be a lot of foreign investment in Latvian property. Now, like homes in Las Vegas, commercial real estate in Riga is impossible to sell.
When a lot of people want to invest in Latvia, it directly increases the value of exports (and foreign investments), which gives Latvians more money, which increases the demand for goods produced for local consumption, which eventually leads to higher wages and a higher standard of living for everyone. The problem is that when demand for the exports falls, it is very hard to reverse the trend. Latvians goods are too expensive because Latvians are paid according to how much people used to value their products. Now that the exporters aren't making any money there is less demand for local goods. But local producers are still paid a lot, too, so everything in Latvia is overpriced. It is hard to lower prices because the workers are locked into high paying contracts. If you lower the prices you will be selling at a loss. In other words, inflation is easy when the economy is doing well because people like to see an increase in wages, even if it is offset by an increase in the cost of goods. But deflation is hard because people won't stand for a decrease in wages even if it is offset by a decrease in prices.
The only thing for businesses to do in this situation is go under or start firing employees who aren't locked into overpriced contracts. Unemployment goes up, which further reduces demand, and the problems get worse.
So how can a floating exchange rate help? It makes deflation easier because instead of paying people a smaller amount of currency you just make the currency worth less. In the Czech Republic, if foreigners stop investing or buying exports, they don't need as much czech currency (the Koruna). But since other people aren't buying Korunas their value goes down relative to the Euro and all of the sudden it is as if all Czech workers get a massive pay cut and they don't even realize it. It doesn't even bother them as long as they buy local goods. They just have a hard time buying things from other countries. But this deflation makes exports more attractive and imports less attractive, which in turn starts to improve demand for Czech goods both at home and abroad.
So in resolving this mystery I thought to myself: why should it stop there? What if every firm had its own currency? What if prices at Target were in Target Bucks, and Target employees got paid in that currency as well? The banks could make the process of shopping relatively easy. When you pay with your credit card the bank automatically buys however Target Bucks you need to cover the transaction. Then people could watch the exchange rates, and if the value of Target Bucks goes down everyone will go there to get cheap goods. And they can stay cheap until demand goes up because Target employees are paid in kind.
The advantages to this system would be the same as the advantages of countries having their own currency. When the economy recalculates the value of what a company is producing, both the prices and wages of that company are automatically adjusted. Management doesn't have to do a thing, they just sit back and let the market exchange rates take care of everything.
The problem with this scenario is that employees probably wouldn't stand for it. Paying Target employees in Target Bucks makes them assume some of the entrepreneurial risk of the company. If they wanted entrepreneurial risk they would have become entrepreneurs, not employees. So they will probably demand payment in a more stable currency, which will undermine the whole point of having a firm specific currency in the first place. Employees of Target probably aren't as willing to survive on Target products alone as residents of the Czech republic are to rely on local products of that country.