As mentioned by Prasad, there is a lot of free tools over the internet that you can just copy and paste and it's done. So I would say it's pretty easy for us developers to do that...
Where it could raise the price is if you want some king of interface where you can add or delete videos yourself on your website. That's the more complicated part because the developer have to deal with file upload, security, maybe some PHP related configs, etc... But if you are just asking him to put that video there and this other one there and nothing else, I don't think he deserves a big amount of money for that !
For a more precise advice, I would suggest you to give us more infos about how he's making your website. If he is making it from scratch it would justify the price, but if he's using an existing CMS (content management system) the price could probably be lower.
Also maybe you could tell us the price he is asking (or an approximate) ? I haven't personally set a price on such things but maybe if someone else here have already done something similar he could tell you if the price is acceptable, or not ! :)