If it's coming from your cable company, it can be significantly extra, if it's even available. If it's a smaller, local ISP, it may be nothing. Assigning a static IP costs the ISP nothing.
That said, I believe DSL typically uses 24 hour DHCP reservations, so leaving your modem unplugged until it renews is actually counterproductive. I haven't done enough testing on my cable modem to see how long it has to be off, or if the customer premises equipment even has any affect.