That is why the size of the chip matters a lot. If it is anywhere close to the size of the 4070 then it will cost roughly the same to produce. 4070 has already dropped to around $540.
Right now the A770 cost a lot to make and was sold at probably barely a profit if not a loss.
For the 4070 that is roughly a 300mm squared. A 300mm TSMC wafer would pump out 942 chips at 100% yields. TSMC made recent claims to aim for 80% yields. Samsung is noted as saying they currently do about 60% yield on their best node. TSMC is said to be charging around $20,000 for a wafer (up to as much as $25,000). So about $36 a chip with 75%.
Nvidia is known for about a 60% profit margin overall so we can assume they sell the GPUs at roughly $60-100, 16GB GDDR6 memory is about $55. Then we need a PCB and Heatsink, assembly, packaging, marketing and shipping, plus the retailed profit margin. So call it maybe $300 minimum to get one to a store. Which accords somewhat well with the A770 sold at zero profit or a small loss being a bigger chip on a slightly older node.
So that $400 price point is possible, but then you have to ask what is in it for Intel, since they aren't a huge part of this profit chain, only the mark up they have to pass along to their board partners. Basically, they have to start turning a profit at some point. Maybe they can afford to battle at the low end another generation, but low prices only work with wide adoption.