Consider a two-period model of a perfectly competitive firm that owns the tights to a finite deposit of a non-renewable resource. The firm's total recoverable reserve of the resource is 3180 tons, which the firm expects to extract fully over two periods. The firm's total extraction costs are given by the function C(qt) = 0.05qt^2. The market price of the resource is expected to remain constant at $200 per ton. The market interest rate is 5 percent.

a) solve for the firm's efficient extraction quantities in each of the two periods.

b) confirm that the efficient extraction quantities are consistent with the Hotelling rule.