[1]: http://cepr.net/publications/reports/latvias-internal-devalu...
When I read economics textbooks, I see a marked contrast to physics textbooks. e.g. in physics, they might explain about a pendulum using equations etc, but then they show you real experimental data, to show that your equations about period vs pendulum length are correct. I have not found economics textbooks that do that.
The more basic thing that economics gives me is akin to this: when iron ships were first proposed, sceptics might say 'iron sinks, so iron ships are impossible, you are crazy'. You can answer this by putting an iron saucepan in the kitchen sink, and showing that it floats.
So (macro) economics can tell me some basic things about 'which way is up'. But putting even half-accurate numbers on things is difficult. imo economics is often done best when you view it using historical case studies + theory to know which way each effect acts.
This is not to say that what you ask is impossible, but when that is done (by experts, not me), it is not convincing enough to convince others that it is right.
Then why don't they lower their prices? Why do they need to rely on a devaluating currency (which might come automatically from the market, or from the central bank actively buying foreign currency at high price)?
Internal devaluation can be done, it is just a slow and painful process (usually including higher unemployment).
With a free-floating currency, prices for foreign buyers can change overnight. This can allow quick responses to shocks. In contrast, internal devaluation (deflation) is a very slow process (how do you coordinate everyone in a country to reduce their prices).
e.g. for the UK circa 2008 the economy had problems (more reliant on finance sector than most other countries) and the currency dropped, making UK exporters more competitive. Italy or Greece a few years later would have also seen their currencies fall, had they not been locked into the same currency as Germany. Instead, their exporters have problems with competitiveness which take many years to equilibrate (they must have lower inflation or deflation relative to Germany).
There is a subject called 'Optimum Currency Areas'. As always, there are tradeoffs, more homogeneous economic areas face this particular problem less and so are more likely to benefit from a single currency.