What is proper ratio of money spent on amp/preamp/integrated vs speakers? 1:1?

To go back to the original question about whether there is a model ratio for component costs, I would suggest that the speakers should determine the amplifier chosen. Rather than cost, the key issue is the power required to properly reproduce the kind of music you like at the volume you like, in the room in which you listen.  Simplistically, highly efficient speakers require less power than less efficient speakers. Large listening rooms generally require more power than smaller ones.  More power is a safer bet than not enough. 

And let’s not forget the impedance of the speakers. Speakers rated at 4 ohms need amps that can deliver the required power at that impedance, not at 8 ohms. Furthermore, some speakers function at an impedance as low as 2 ohms at some frequencies. Inexpensive amps may well noticeably distort at such a low impedance.  So try to match the speakers you like (and can afford) with an amp that can drive them and bring out the best in those speakers. 

With respect to those suggesting that $500 is all you need to spend for an amp or that an iPhone will suffice as a source, perhaps they would benefit from auditioning somewhat better equipment. Or maybe they listen primarily to rock at high volumes and can’t differentiate between the distortion of the electronic instruments used in the recording vs. that generated by their audio equipment. Listen to an acoustic guitar through an iPhone vs. a modestly priced DAC like a Dragonfly and I am reasonably confident they will hear more lifelike and otherwise improved sound. 

audiotroy, you are absolutely right about many people changing speakers without first making real effort to make them sound right. Yes, not only electronics but even a single pair of cables can make or break the sound. I could easily demonstrate it to almost anyone with my system. And I am not talking junk cables.
Well, when you got $250k JM Focal Grand Utopia, perhaps you don't need another $250k to make them sing their best, but I don't really know. I just know that some use top of the line Allnic or VAC electronics with them with apparently great results.

I understand the desire for big amps - we British used to make do with 50 watt amps and laughed at the folks across the pond with their 200 watt abominations. We were still laughing when the Krell landed here UK side - then the laughing stopped.

Gradually a cultural change ensued and nowadays a 100 wpc amp is seen as a good thing - some would say 200 wpc are even better - but I think that depends upon choice of speakers. Still more power never hurts.

However it should be asked that apart from the power output of an amplifier, what other measurable differences are there? Have you seen how low the distortion stats are even in the most budget of budget amps? Magazines barley waste time printing them. And they have been that way for decades.

So what else is there? Sure there's all kinds of fancy topology out there, but  none that makes any kind of sonic difference above the threshold of hearing.

Basically you have a choice, get yourself a sufficiently powered transistor (sand) amp or delve into the esoteric world of tube/valve amplification. That's all folks!

If I give you free speakers ratio becomes infinite.