The title suggests that this map is actually a representation of the distribution area of two newspapers; The Berliner Morgen Zeitung and The Berliner Tagesblatt. Therefore, the date must be pre - January 1939 as the Tagesblatt was closed by the Nazis on 31 Jan 39 (the Morgen Zeitung was amalgamated with the Berliner Morgenpost in mid Feb '39).
As for value I have no idea but what I do know is that with maps condition is everything (and this one is poor) unless the map is very rare which I doubt this is as it looks to me like a "give away" item. At a complete guess I would not anticipate it being worth more than a couple of Euros but it would be wise to find expert opinion.
I hope this helps
PS I believe The Berliner Morgenpost is still in circulation.
"War is an ugly thing, but not the ugliest of things. A man who has nothing for which he is willing to fight, nothing he cares more about than his own personal safety, is a miserable creature with no chance of being free unless made and kept so by the exertions of better men than himself."