What happens if no one wants to buy a property at auction in Monopoly?
Philip Orbanes is the renowned master of all things Monopoly.
He is the author of 3 books on Monopoly : 


The Monopoly Companion: The Players' Guide
The World’s Most Famous Game--and How It Got That Way
Monopoly, Money and You: How to Profit from the Game's Secrets of Success.


Kevin Tostado is Director of the movie
Under the Boardwalk: The MONOPOLY Story,
a documentary about the Monopoly national and world championships that are held around the world every four years; the movie won 4 Emmy Awards, including that for Outstanding Achievement in Documentary.
Reference : http://www.monopolydocumentary.com/

Kevin Tostado answered the following question : 

How do you properly hold an auction in Monopoly?

Reference : https://www.quora.com/How-do-you-properly-hold-an-auction-in-Monopoly

"The answer can differ depending on how you interpret the rules, since it's not clearly defined within the rules that Charles Darrow wrote when he first published MONOPOLY. But I'll describe how chief judge Phil Orbanes ran auctions at the 2009 US &amp; World Championships.

When a player lands on an unowned property and decides that he or she does not want to purchase it at face value (either because they can't afford it, don't want it, or think they might be able to get it at a lower price), then that property immediately goes up for auction.

The banker conducts the auction and puts the property up for bid starting at $1, regardless of the original face value of the property. Any player, including the one who landed on it and declined to purchase it originally, can bid on the property. Any player can name a price, and there is no sequential order to how bids are offered. The auction continues until the banker concludes the auction with the highest bidder."

So, the chief judge, Philip Orbanes, at the Monopoly US &amp; World Championship says bidding starts at $1.