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Any time an item becomes easily accessible to the general population and the demand remains the same then its price will decrease proportionate to the increase in availability.
I am thoroughly disappointed with the Guild Wars 2 economic staff if they have no plan to offset the devastating effect that free dyes will have on the game. Supposedly you are going to be able to pick up a crown every day and ten as a reward for some monthly achievement.
Great, so 5 of these crowns (price subject to change as stated by Arenanet already) will reward you with 10 unidentified dyes (also subject to change).
Now, I get around 2 unidentified dyes per hour of straight farming. That's an easy 10 silver as long as I don't identify them. For newer players, it is a great way for them to get access to an item even max level characters will buy. In other words, it is excellent starter income and a bonus for people at max level.
So what will the price be after this change? I'm thinking that if I used to get 2 per hour, and now I will get an additional 10 every two days, that I'll end up with something like 18 dyes every two days. Compare that to only 8 dyes normally and you have a 225% decrease in price. So what will Dyes be worth a week after this change? Probably somewhere around 200%-300% price decrease.
Only good thing about all this is that most people don't stockpile unidentified dyes for speculation purposes and instead either sell or identify upon finding them.
I will take back all my criticism if ArenaNet is also planning on increasing the number of dyes available in the game. It's going to take a lot of them to make up for the new number of unidentified ones, but I shouldn't judge too quickly.
They could also tweak the numbers to make the drop in price less dramatic, as in the number of crowns per day, the cost for 10 dyes, and even the number of dyes rewarded for the turn in.