Hello Gaelle

Thank you for your purchase.

I am sorry to disappoint you, but unfortunately something like this is not possible with the plugin's built-in features.

If you're using Services, you can include a discount coupon which you can provide to your friends, but if you're using Events, you'll need to create a separate event with a lower price for them. That means that you should include some tags like "regular" and "friends", and then use those tags on different booking pages.

Make the page for the public to be available from your website, and the page for your friends so it can't be navigated to from the website. Then you can add different shortcodes on those pages:

[ameliaevents tag='regular']

and 

[ameliaevents tag='friends']