The ISP gets a set of IP addresses to use from an internet governing body who controls all IP addresses in an area (ARIN, RIPE, etc..) or from their ISP. Yes alot of ISPs have their own ISP that they link up to. They do this so that they can recycle the IP addresses if an ISP goes out of business or whatever.Why does an ISP lease IP addresses?
They lease it to you for your convenience and theirs. They use whats called a DHCP server (dynamic host configuration protocol) this allows them to send an IP address among other things to your computer/router so you don’t have to manually put it in the TCP/IP settings which could really be an issue for less computer savvy people. For the ISP they setup the server with a range of addresses and forget about it, the server hands them out and tracks it automagicly.
What are some advantages to having a long lease opposed to a short ones?
Its more of an advantage to the ISP to have a short lease sent to the client so they can reuse the IP sooner like when they loose a customer or if you change your network card or add a new PC since the DHCP server binds the leased IP address to the MAC address for the duration of the lease. Its more advantageous for the client to have a long lease as their IP address will not change as often. The lease is set in the server that says this MAC address gets this IP address for this amount of time whether its on or not. When the lease is about to expire the client will check in with the server and say its still there so when the lease does expire it will still retain its IP (sometimes).
Why does an ISP lease a IP address to me instead of a static?
Mostly because of what I wrote above but also static addressing means administrative overhead also as they would have to keep track of all the addresses they handed out in real time darn near, the DHCP server does it automagicly.