Let us assume that stocking DVDs is a proper function of public libraries.
(I strongly disagree with that since supplying popular movies has nothing to do with literacy, education, citizenship, etc., and there are multiple low cost rental possibilities available to anyone. But, for the sake of argument let's assume that it is proper.)
A subscription to Netflix is available for six dollars a month (two disks per month for unlimited time).
There are 20,000 residential units in Palo Alto. If the city were to buy a Netflix subscription for all of them the cost would be 1.44 million dollars per year.
But since Netflix would pick up 20,000 subscribers with zero marketing expense, would not have any deadbeat problems and would have the opportunity to upgrade all of those subscribers to higher level plans, it is likely that a discount of 50 percent would be in order.
I don't know how much it costs the city to buy, shelve, track, check in, check out, DVDs. Consider also the very large space required. It wouldn't surprise me that the city could save money and provide better service by outsourcing DVDs