Ask HN: Does open source and free product cannibalize your paid product?

I'm in a bit of a dilemma. I have developed a product that I think would be great if it was free because not many open source, free versions of it exists but I also don't want it to cannibalize my paid products and subscriptions.

Is my assumption correct in that people who would've paid for my product would now be satisfied with the open source, free version that I released and never end up paying for the full version? Even worse, someone customizing it using their own inhouse development resources, productizing it with their own brand and selling it and becoming my competitor.

I am concerned about working all those hours into the product, open sourcing it (thereby making it available at competitors hands) and not getting paid for it.

I am also assuming that I could get some free marketing when I release the free version...but I'm not sure if this offsets the cannibalization of sales.