Recurring Payments and pricing updates

We have the auto-renewal-checkbox installed on our website and utilize Paypal Express to receive payments. Recently, pricing has been updated for our membership but I am curious if existing members that have selected to auto-renew will pay the new price or the old one?

If they are locked into paying the old price, how can I update so they pay the new price? Would their memberships need to expire in order for this to work?