Logic apps has a consumption plan where you only pay for what you use rather than a flat hourly rate. This can save money. I think it's a reasonably priced service. All Azure customers can open a free billing support ticket via the Azure portal to get a pricing quote. Technically only the billing support team are authorized to provide exact pricing quotes or estimates. Please do let us know if you don't have a support plan to open a service request.
Pricing - Logic Apps | Microsoft Azure
I hope that helps a little bit and gives you a little bit of a place to start.
Regards,
Oury