So the price will not go up or down in purchasing power unless something will happen in the economy as without this change there won't be any reason for the change price.
I'm not saying that the purchasing power of 1 BTC would change; I'm just trying to understand how would the economy look like. Would productivity rise or fall over the long term?
There won't be any clear way to determine this since we don't know what will happen to a lot of other stuff.
Let's assume the population grows, there will definitely be an increase in productivity since there is a constantly growing need for products, even if there is a lower incentive for people to spend their coins there will be an unstoppable need for a lot of basic stuff from food to education to housing, things you can't really postpone, more goods needed, increase in productivity but still deflation.
If on the other hand there will be no population increase, no increase in production, we will have deflation as well as economical decline.
This is a basic scenario, throw in another twenty variables, a change into lifestyle and consumption and needs and you will need a crystal ball for it.
Oh, and the purchasing power of
BTC if left alone with no other currency will definitely swing one way or the other, we're talking about a fixed supply, it's not quite the same as gold which was though the entire history continuously mined with more and more in circulation alongside silver.
Low inflation is helpful for economy because it makes your goods more competitive on the global market (for example: due to lower tier countries are accepted to eurozone EUR is getting cheaper and it gives boost for economy). But if you accept only BTC then your products are rapidly getting more expensive.
The scenario is with no other currency present, so your goods will cost the same as long as the manufacturing process is the same, bitcoin will no longer grow in price as there is no longer such thing as
BTC price.