Rationing for libraries

When a library finds that more than one person wants to borrow a particular book, they have to have some way of rationing access to the book — deciding who gets to borrow it first, and for how long. At my local library, they achieve this by lending books for three weeks at a time, and preventing you from renewing the loan if someone else has requested the book. If lots of other people have requested the book, I think they get to borrow the book for up to three weeks each in the order they placed their requests.

But what if the first person to borrow the book reads a few pages, gets bored, and doesn’t look at it again till it’s due back? Perhaps they intend to read the rest of the book, but never get around to it. Everyone else waiting to borrow the book might place a greater value on having earlier access to it than the first borrower places on keeping it for the full three weeks. Could the library arrange for less wasteful rationing of access to their books?

I’ve mentioned before an interesting talk I once heard Moshe Haviv give about efficient queueing systems. When he started the talk, my initial idea of a queue was standing in line at a New Zealand Post shop. But he started talking about queueing systems where people might bid for earlier service, and even queueing systems where the entrance of a higher bidder would interrupt the service already being given to a customer.

The cost of administering a bidding system in a New Zealand Post shop might outweigh any benefits from serving people in an economically efficient order, and certainly so if people at the counter being served could be made to stop everything, wait for someone else to be served, and then try to carry on from where they left off. But there are all sorts of queues with different characteristics, and the request queues for particular books at a library might be better suited to such a system that allows interruption of service.

Here’s how it might work: If the library has a book you want to borrow, and it’s just sitting on the shelf, you can borrow it free of charge, just as at present. You can, if you like, put in a bid for how much your access to the book is worth — maybe 20 cents per day —, but even if you do, you still pay nothing to borrow it, as long as no-one else wants to borrow it; this helps ensure that you have no incentive to pretend that access to the book is less valuable to you than it really is, and you don’t need to try to guess how much other people value it, and base your bid on that.

Then someone else discovers the book in the library’s catalogue and also wants to borrow it. Not knowing what your bid is (or even if it’s non-zero), they put in a bid of 10 c/day. Now, because your retaining the book is depriving someone else of access to it, you have to pay the 10 c/day they bid. This helps ensure that you have no incentive to pretend that access to the book is more valuable to you than it really is, and encourages you to finish with the book more quickly, now that someone else wants it.

If a third person wants to borrow the book, and puts in a bid of 50 c/day, then the library asks you to return it within a certain time limit — say, a week —, and requires you to pay the full 20 c/day you bid until then. If you take more than a week to return it, then you have to pay the full 50 c/day that the third person bid.

Suppose you do return it on time, and you still want to borrow it again after the third person has finished with it. Then you leave your 20 c/day bid active, forcing the third person to pay that much while they’re borrowing it. When they’re finished with it, they return it to the library, and the library lets you know you can pick it up, and starts charging you 10 c/day for it again, assuming the 10 c/day person hasn’t given up waiting and cancelled their bid.

So you can see that this system rations access to books by allocating it to the people who value it the most (relative to how much they value money), and encourages people to finish with books quickly when other people are waiting for them. The library could even do away with the requirement to renew the loan every three weeks; as long as the library has some way of informing you when someone else is willing to pay more to borrow the book, you can keep it as long as you like (or as long as you can afford to, if someone else has put in a lower bid than you). The library might still want you to show up with the book every nine weeks, to prove that you haven’t lost it, though.

One possible objection is that this system may diminish the public-good aspect of a public library. If part of the purpose of the library is to provide access to books to both rich and poor alike, then allocating access based on willingness to pay might seem to be counter-productive.

This is an important consideration, and needs to be weighed up. On the other hand, even when scarce resources are allocated by queueing, rather than price, there are often subtle ways in which richer people end up with better access than poorer people.

When borrowing books from libraries, or making reservations, rich people might be more likely to have cars, fewer or more flexible working hours, or more frequent opportunities to reserve a book online, effectively giving them preferential access to the library’s most popular books.

So if rich people are going to have better access to the books anyway, then why not make them pay for the better access in a way that encourages them to finish with books sooner when other people want to borrow them? At least then the library could use the extra revenue to buy more books for everyone to borrow.