Raise product prices and offer free shipping/delivery?

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So I've been searching everywhere for the answer to this question and can't find a definitive study, hopefully you fine people can help me out, and maybe start a discussion about this. I'm sure some of you have been in this boat before.

I'm building a local delivery app and I'm trying to decide between offering regular-priced products with a delivery fee ($8), or raise product prices slightly (average order quantity/8 = same total cost overall) so I can advertise "free delivery"

Honestly, I'm torn. One on hand, free delivery sounds great and might drive traffic, but on the other hand, the expensive cost might deter some visitors. But does it still work out better despite this?

Keeping in mind that this is a product they can just as easily go out and buy themselves. What I'm offering is specifically a delivery service. So maybe being able to say "just pay the $8 and you don't have to go out and get it yourself" is a better way to advertise the service?

Would love to hear your thoughts and stories on how you dealt with this!

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