Sorry if someone has pointed this out already.... a China design center will have plenty of engineering challenges for a less costly and probably smaller car than M3 or Y, but they won't be starting from a blank sheet of paper. The drivetrain would I think be at most an iteration of the last one built for M3 and Y. Sure, that underlying advanced design will be resized for Model 2 (4) but that is a more manageable engineering task than making a fully new design that is improved in a number of ways.
IMO the low cost of the new EV will be driven by a number of factors. In no particular order: Lower battery cell cost, less raw materials due to smaller size, lighter weight. Greater automation reducing labor cost. Design improvements coming for most/all future Tesla's, along the lines of the new wiring module, which saves a great deal of wire and labor. Having the new, lower cost model partly designed by a new China Design Center will have a number of benefits, but lower cost of the eventual product won't necessarily be the most important of them.
You are missing the point, I think. Numerous people have discussed platform engineering, including me. The Chinese designs will follow sound industrial practice, by designing maximum practical parts commonality, specifically including a "skateboard". There will not be "a model'. There will be a product line, with a number of models including probably a sedan, an SUV, a Crossover, a pickup a minivan and perhaps several of each. If suitable arrangements can be made there will be badge-engineered product for others too. Don't be so restrictive and the economics suddenly become compelling for modestly priced vehicles.
Why? Fixed cost absorption vastly reduces the cost, even when variable costs are a less scalable quantity. That is also why multiple brands share quite similar architecture and share every component they can share without damaging their positioning.
Perhaps the best example is the VAG design philosophy. Check it our. They do lots of things wrongly, but not this! Numerous engine parts are shared from VW Fox to Lamborghini and Bugatti. They're designed with shared dimensions and specifications as much as practical. That allows them to make tiny volume Bugatti and Bentley as well as Fox et al without totally destroying economics. Tesla does that now with motors, as I described in an earlier post and has others have done more eloquently than do I.
Please don't think there will be 'a China designed cheap model'. There will be a broad array, plus factories to build components for all, and factories worldwide to assemble and manufacture parts and vehicles.
BAIC has just done that for GM, with the results already visible in new gains in market share in a number of markets.
These have already been discussed here and elsewhere so I will not repeat them.
It is only to emphasize again that Tesla is far beyond thinking of single models. They announce single models and promote single models. The design and build multiple models using parts in various models (from Plaid Model S to Space X rocket fins) and build factories to support the range.