Now demonstrate how those scenarios would equal out in estimated cost and estimated wattage. I like your reasoning, but I think its not realistic.

Good question...

A 7770 GPU chip is around 125mm^2 (roughly same as the cell). OEMd in large quantities in 2013, I'd say $30 for Sony.

A10-5600 street price the boxed version just under $100. plain chip, OEMd in large quantities, I'd say $40-$50 for Sony

4G ram, 1G GDDR5 ram $40.

Blu-ray $20, harddisk $40,  rest of stuff on board $40 (high, but needs more than two dual-phase voltage regulations as it is now).

board $10, power supply $30, case, assembly $10, things I forgot now $50 (like controllers, cables now that I reread it)

Grand total: around <=$300 manufacturing

so product price intially $450 possible.

XBoxNext: roughly the same (but they can spend money as they like)

Using newegg....PS4 cost based on your system

HD7770 - $120 to $160 - 2013 ~$90 Sony's mass price ~$70 (20%ish)
A10-5700 -  (5600 is A8) $120 - 2013 ~90 Sony's mass price ~$70
4GB RAM - (very fast ddr3 to match CPU) $30 - 2013 $25 Sony's mass price ~$15
 - There is no GDDR ram as it what's on the APU plus the ram on system.
Blu-ray - $50 - 2013 $40 Sony's mass price ~$20
250 HDD (2.5") - $60 to $100 - 2013 ~$60 Sony's mass market price ~$40
Controller - $25

That's a sub-total of ~$215 without a lot of other components, licensing, packaging, etc. Those things should easily double this price to around $420. Keep in mind that this is just the cost of goods. This doesn't including shipping, marketing, R&D, and other things I'm forgetting. All in all this would be closer to a $600 system in order to sell at a basic profit. (for reference, 3DS at launch was broken down to a cost of ~$120 and at $170 we know it is losing money.. probably had a break even closer to $200 and that difference in material cost and final cost is going to grow as the systems weight, size, and components grow)

So by my ballpark, Sony would need to sell this for upwards of $500 to appease its investors and still have a large loss. There is no way Sony is aiming for a base system of over $400. No way. Plus, most people are arguing for more RAM on top of that, bigger HDD or SSD, or even newer GPUs etc.

Now for X360 based on your other post. (keeping simple with some stuff from PS4)

HD7770 - $120 to $160 - 2013 ~$90 MS's mass price ~$70 (20%ish)
AMD FX8-8150 - $190 - 2013 ~$130 MS's mass price ~$100
4GB RAM - (very fast ddr3 to match CPU) $30 - 2013 $25 MS's mass price ~$15
Blu-ray - $50 - 2013 $40 Sony's mass price ~$20
250 HDD (2.5") - $60 to $100 - 2013 ~$60 Sony's mass market price ~$40
Controller - $25

Sub-total of ~$245. Same logic as above brings it to a basic price ~$620. Rest of logic is same.

There is no financially viable way you'll see tha type of system from MSony. It simply makes no sense. EVen if I'm being crazy with the full cost price and I should not be essentially doubling it from the subtotals above, its still in the $350 as a MINIMUM for either system. Then you add the shipping, marketing, R&D, etc as I did above and you're looking at a full cost of $500 as a minimum. That MAYBE would work but I think its really streaching the realm of possibility as that's the base price not including anything MSony does to compete directly with the gamepad. Nothing for a Kinect bundle or a Move bundle or if Sony does what Sony usually does a Sony bundle with its own gamepad or kinect style setup (cost more than Move).

I just don't see how that would make any sense to either company; even considering selling at a max $100 loss at launch.

Don't add marketing and R&D to a piece of hardware. Those are operating costs not associated with the unit itself. Shipping, packaging, wholesale, retail, and licensing are probably around the $100 range for a console, maybe more. Let's say the other components turn that $215 to an even $300 so adding in everything else $400. I suppose as high as $450 depending on licensing or higher costs than assumed. That is still in a reasonable range for a new system.

To continue on marketing and R&D, those cost can not be tacked on to a system. They are not divisible per unit, they are not based directly on unit sales or units available on store shelves. Those costs are already acquired (R&D) or made seperately from the system (marketing). You've been reading the nonsence people post on this site haven't you?

I would simply avoid all the talk of cost of particular components and ask "What do Microsoft or Sony gain by releasing a system that is 10 times as powerful as the current generation consoles for a cost that is greater than $600 per unit that they don't gain by releasing a system that is 4 times as powerful as the current generation consoles for a cost of under $400 per unit?"

I could be wrong but I suspect a system that was 4 times as powerful, output at 720p@30fps, and sold for $300 would be more popular and profitable than the more powerful alternative.

Why should Sony switch to x64 architecture? For uses that don't require back compatibility with x64 and x86 legacy SW, it wastes for it silicon, electric and computing power and money. OTOH Power architecture is very advanced, efficient and scalable, each generation can give the designer not only a wide range of computing power and power consumption, but also the choice to achieve the desired computing power through few powerful cores, many lightweight cores, fewer running faster, more running slower, more powerful and complex cores running slower, simpler ones running fasters and various steps and combinations between the opposite choices. x86-x64 architecture can't even dream the flexibility and scalability of Power.

Your prices are completely off base (I know what I am talking here. I have some insight, and I am certainly not shopping at newegg).

a) You cannot start with the price of a retail package in a shop. Obviously, MS/Sony do not buy graphic cards in shops and prie out the gpu chips. Again, the HD770 GPU is a 125mm^2 chip. The cell chip (same die size) currently costs around $18 for Sony (don't ask). The yields are lower for the HD7770 currently, but more GPU dies are on a waver than cell dies, so I added 60% "only" in my list to the OEM price of the cell. This could be a wild guess depending on TSMC/GF yields (which, if you believe TSMC/GF, are rapidly improving).

b1) Google prices for A10 procs and you will come across $100 offers here and there. Again, Sony does not buy retail boxes, they buy the bare chips as an OEM. Also note that a console APU/CPU does not need the PCI interfaces, so this reduces die size and power somewhat (not really a big savings but you basically pay for every mm^2 on the die and still there are a few mm' 2 here. Believe me, if engineers find a way to cut 10 resistors from a PC mainboard, the board is toast and a new version is produced without those resistors, this is a cent game).

b2) Whatever you meant by "very fast ram", standard 1600MHz (or 1866MHz) ddr3 is all you need. Higher speeds give measly improvements and are not worth the extra money. You can actually google spot market prices for ddr3 dram and find that 4GB ram would cost around $10. That is spot market price, not OEM price which is considerably lower. So my $40 estimate is actually on the high side due to giving the separate HD7770 better ram than probably needed.

c) we agree (Though with Sony Optiarc shutting down end of this fy, I wonder what happens here in the future)

d) we agree, although HD prices are on the decline.

e) Here your price is actually higher than mine.

f) ok.. packaging is about 50c. Shipping a 2TE unit to anywhere from China currently costs around $2500 max. Take the PS3 size and stuff as many PS3s into the container as you can, and shipping costs come out at around $1 (or $1.50, I'm too lazy to calculate it) per PS3.

"Those things should easily double this price to around $420" - sorry, not in a thousand years. Sony makes hardware components so many of the royalties are already covered with cross-licensing agreements. Blu-ray license is an unknown as Sony is part of it, but those licenses have come down dramatically (cheap Blu-ray drives are around $35.$40 in shops). Summing up, my $300 manufacturing estimate stands firm.

Then you are going into the "Manufacturing costs vs Production costs" enigma. Something many folks don't quite understand. If you go back to the early days you will usually find "PS3 costs $900 to manufacture" headlines - which is of course nonsense. The product value of the PS3 initially was $900.

Now my estimates give a manufacturing price of $300 and a supposed product value of $450. Notice that I use the words price and value. The price is a number Sony cannot influence, that's the money they have to fork over to make the box. The second number is the value of the product, something MS/Sony can influence (partially). This $150 difference pays for taxes, store margins and Sony margins. The first two are pretty unavoidable, and in Europe are in the $100 range as a rough number. That leaves us with $50 for MS/Sony, paying for all the rest. If they sell 12mio units per fy, they have $600mio to pay for advertisment, people, recouping R&D (incidentally R&D is very considerably lower than for the PS3 due to using off-the-shelf chips this time). Most of XBoxNext R&D expenses might be Kinnected (sorry, couldn't resist the pun).

That is not much but quite doable, considering that you have PS3/PSV/PSP software revenue/MS store revenues to cover some of those costs.

Lazy programmers want to code with Intel mmemnonics I suppose. They had the choice to keep cell (lazy programmers still hate it), go PowerPC (lazy programmers don't know much about it and it sounds like cell) or go Intel (where you find all lazy programmers).

But this should be true mainly for games originally developed for PC or XB1, all the others and their devs should prefer Power, that's been used on GC, Wii, XB360 and it's also the architecture of Cell CPUs' PPE cores. The most likely request devs could make to Sony could be to drop SPEs, that they hate, from next CPUs, or at most just keep the ones needed for PS3 BC, and ask IBM to develop for them a multicore Power CPU, just like Ninty. Anyhow, devs could also be asking for a CPU as similar as possible to the one MS will use in XB720, so if MS will switch to x64, your "lazy programmers" explanation could perfectly apply and my doubt would be solved.
Yes, I guess that if x64 on XB720 rumours are true, then your explanation for PS4 using the same architecture is the simplest, so, applying Occam's razor, the most likely.

I'm not convinced that either Sony followed MS or MS followed Sony. I can very well imagine a scenario where neither Sony nor MS knew the other guy's path. We would have to know what happened three to four years ago in upper management, when development cycles started in earnest for next gen consoles. At that time, MS was on the PPC path, Sony was on an unsure path (continue expensive cell development basically on its own, or do else..). At that very time, AMD was starting to develop and tout its new processor architecture "that will bury anything on the market now and in the future" to anyone willing or even unwilling to hear it. I can very well see that both MS and Sony switched to AMD after hearing and accepting AMD's plans independantly, without knowing of the competitor's decision for quite a while.