I'm trying to figure out the subtle differences between "auswirken auf" , "einwirken auf", and "wirken auf". Dictionaries tend to all point in the same direction, and that is "impact/have an impact on/etc", but I feel that there is certain emphasis that these words convey, and I'm not able to figure out the difference. Now, I think the easiest (for me) is "sich auf etwas auswirken", which means, "have an effect on". Let me then just give three examples:
Der Forscher untersucht, wie Politik auf die Wirtschaft einwirkt.
Der Forscher untersucht, wie sich Politik auf die Wirtschaft auswirkt.
Der Forscher untersucht, wie Politik auf die Wirtschaft wirkt.
Are both sentences correct, and is there a large difference between the two? My first guess is., 1. ... how politics INfluences the economy, and 2. ...how politics impacts... but I am not quite sure. Any help appreciated!