What does the blue pill in The Matrix actually do?

During the first meeting between Neo and Morpheus in The Matrix, Morpheus states that if Neo takes the blue pill, "The story ends; you wake up in your bed and believe whatever you want to believe." Does this mean that the blue pill acts as a selective amnesiac? A program to make Neo feel as though he dreamed the meeting, similar to his experience of having a bug implanted by the Agents? Would it include something that makes him no longer of interest to the Agents? Since, technically, all that Neo has to do, if he refuses Morpheus' offer, is get up and leave the room, why have a blue pill at all?

Answer

I seem to be in the minority here but I don't think the blue pill itself does anything remarkable. It's a placebo, or possibly an ordinary in-Matrix sedative.

I base this on two things.

First, there is an elegance to it. Why would it be necessary for the blue pill to do anything at all? And if it is just a placebo, it's a perfect symbol for accepting the irreality of the world inside the Matrix. By accepting the blue pill, Neo would be accepting the illusion both of the Matrix and the pill itself. And really, if the pill is going to wipe his memory why doesn't Morpheus say something like "You'll forget all about this"? But that's not what he says.

The second thing that leads me to believe this is Morpheus's statement:

The story ends; you wake up in your bed and believe whatever you want to believe.

Breaking it down, "the story ends" simply because the rebels stop pursuing Neo. The "wake up in your bed" phrase can be interpreted literally (they're going to sedate him and deposit him in his bed) or merely a continuation of the dream metaphor Morpheus is using (the strange things that have been happening will stop).

But the really important thing is "believe whatever you want to believe." As he points out in the next line, Morpheus is offering Neo the truth. More than that, he is giving him a choice between seeing the world as it really is and rejecting the evidence. If Neo takes the blue pill Morpheus will leave him to make his own conclusions about his recent experiences and the world he lives in. Someone who takes the blue pill would probably want to conclude that Morpheus is lying, maybe the whole experience was a trick of memory caused by the blue pill, whatever. They can believe whatever they want to believe. But if their memory is wiped, they don't have the choice to draw their own conclusions, and this is not what Morpheus is offering.