China controls 80% of the world's lithium refining, a material needed for the production of lithium batteries in electric vehicles.

The demand for lithium batteries is P = $20,000 - 2.5 Q, where Q is in tons and P is in $/ton. The long run marginal and average cost of production is constant at $2,000/ton.

a) Assuming the monopoly model applies, determine price, quantity, and profit for China.

b) Now assume new firms (including Piedmont Lithium) enter the lithium market, resulting in (perfect) competition. Determine the price, quantity, and profits, when the industry is in (long run) equilibrium.

c) Finally, compare social welfare for the two cases, and determine deadweight loss.