Good question Ken? After many decades of them barely breaking $100, they suddenly jumped up over $200, and just as quickly over $300. Now we might see $400 in the near future!
I gave $500 for a #4 takedown engraved, which I thought was a little nuts, and justified it because of the engraving and the neat canvas takedown case. Now I'm feeling pretty smart to be ahead of this sudden craziness.
My personal opinion is the little #2 that is a far better gun has gotten way overpriced, with prices approaching a decent #1 Sporter. So guys saw the Rem. #4 as an affordable option and began buying them. Then bidding wars got the diminutive #4 to stupid prices, and once a few sold to high it became the new average price.

I have a couple of them, I paid under $150 each many years ago. The majority of #4s out there are takedown and are often loose. Id be willing to pay a little more for a solid frame. But really, the #2 is a better rifle all the way around.

I think although they are at the low end of the Remington scale, they are close if not at the top of the single shot "Boy's rifle" scale. Solid frames are a stronger design than any boys rifle made by Stevens and better in quality of material and finish than H&A's 922's. And it looks like they reflect that in prices. 
Just my $.02

My kid's guns.

I have 4 Granddaughters and when each was born, I bought a Rem No. 4.  I completely restored them and now each girl has one with her initials on it.  Since this picture was made, I have added one of Ken Womacks No. 4 tang sight to each rifle.  I don't know how much they will ever shoot them, but they will always know Grandpa made it for 'em.
Phil

Started buying them about 17-18 years ago and I gave $100 for the first one.  I had to pay over $200 6 years later for the last one.  I was relieved when my sons retired from the baby business and I didn't need to buy any more
Phil

thanks.  American Black Walnut.