Ann: Galaxy Confirms Lithium Concentrate Pricing for CY2017, page-122

Deutsche Bank I believe are the only ones to have actually gone to China and spoken at length with processor factories to gauge costs and report on them.
It's a difficult industry to pin down and - I'm going on memory here because I read it so long ago - but the range of figures I believe they gave was between $2.5-6k.
The reason for this is that some are completely manual plants (wheelbarrows etc) and some are more automated (Jiangsu). Some are also geared to process the very low grade local lepidolite and have much higher processing costs because of the sheer tonnage they have to process.
I believe they gave a figure of approx $3.5k USD as an industry estimate.

Honestly, to be more precise I'll have to track it down again. I saved it on another machine.

But this is a reasonable figure to work from to estimate the costs to produce 1k of carbonate.
I believe there may be some newer processors geared to producing hydroxide immediately from hard rock but by far the most common production method is for this to be a secondary process, which also explains why hydroxide goes for an approx 25% premium over carbonate.

AT also gave shipping at approx $50/t in his first SMI presentation.
This cost is obviously borne by our clients. My guess, given the funny number we got ($905), was that they've managed to get it down to $45 so that the input cost for a ton of spodumene for them is $950USD.

Putting all this together - our clients would have the approximate costs of $11kUSD per ton of carbonate.
This has been selling for approx $15kUSD/t in China.
I am not sure if this is inclusive of 17% VAT - but I believe it would be.

It looks like AT has pulled off a more than impressive negotiation.
Rather than stick to fitting our price within current levels we have added our own upwards pressure on carbonate price as the processor now has to add their own profit margin.
I would not be surprised to see carbonate price tick up by 10-25% very soon.