"So if the other person passes, did you want $50 or $60?"
"If the other person passes, it means they were not willing to go beyond $50 and you were, so you clearly need to pay the price beyond $50. That was your commitment to securing the purchase of the book. You need to pay the $60. Otherwise you're telling me that you were not really willing to go beyond $50."
If the other person stopped replying, there's a chance they abandoned the idea of buying it (or maybe you're being too impatient and they didn't have time to reply yet?), and if that's the case then now you only have one buyer, who wants to pay the original $50. You wanting $60 can be considered being greedy, and by requesting them to pay it you might be risking losing your buyer. However, strictly speaking, they did agree to paying $60 specifically with the purpose of being the best offer, and if they go back to $50 they are no longer being the best offer (ignoring the fact that there are no other offers).
What you should do? It all depends on how much you want to sell the book now or not. If you're willing to hold it for some more time and sell it again later, you should enforce the $60 and run the risk of losing your remaining buyer, ending up not having any buyers now. If the $10 are not that important to you and you just want to get rid of the book, take the $50 which was the value you wanted from the beginning anyway. ;-) Good luck!
A deleted comment mentioned there was "another possibility": to stop communicating with the seller (as a buyer), since the enforcement of the price at $60 was seen as unethical by them. And that comment had a good amount of upvotes, so I'd like to address that.
First, OP is the seller, not the buyer. Discussing the possible feelings, reactions and thought process you would have as a buyer are not the focus.
Second, discussing the possible feelings, reactions and thought process of the buyer who made the $60 offer, even though not being the focus, can help give an insight on how to tell them that they should pay $60 instead of $50 in a polite way. Discussing the feelings and reactions of the other person who apparently already gave up on the book, on the other hand, contributes nothing to the matter at hand. You might still want to give your opinion on OP ethics and morality, but you're definitely not giving an answer that can help OP, as is SE's purpose.
Third (now addressing the some other answers), OP is not asking for help on deciding the price they should sell it for (which by the way could be closed as out of scope for this SE from the little I observed around). They have already decided the course of action and the selling price. The question is on how to explain the decision in the most polite way. Questioning OP's ethics might be valid as a support point that you might be using to answer OP's question. But simply passing judgement without addressing the question itself is probably out of scope.
Fourth, OP has the right to renegotiate, change the price, lower it or increase it, or abandon the deal as they see fit, at any time. Just as much as any potential buyer has the right to renegotiate, ask for a lower or higher (!!) price, or abandon the deal and stop communicating at any time. OP is not Amazon, you know. ;-) Some people might consider the renegotiation as not nice. Some people might consider it normal. Some people might consider they're fools if they don't take the opportunity. OP is not doing anything illegal, so it's not up to us internet randos to judge them, we have to respect their choices. According to the help, questions that "ask us to adjudicate 'right' and 'wrong'" are off-topic. OP did not ask us to adjudicate. Yet, several answers did adjudicate "right" and "wrong". I'd suggest we all review the help and discuss more in meta. ;) This is an awesome SE that I'd love see it going past beta. Let's contribute to rounding up the corners before we go to production though. ^_^