A town is endowed with an oil reserve. The total stock of oil from the reserve is of size S. The town must sell all S barrels within two time periods. The price per barrel that the town can sell the oil for is pt = a. bqt in each period. There is a no cost of extraction, so the resource rent earned by each barrel in each period is 71': = pt. The interest rate is 7'. Let's say that the citizens of the town, concerned with the pollution that the oil will eventually generate, decide to tax the sale of oil from their reserve in period 2, at a rate of 13 dollars per barrel. There is no tax in period 1. Given all of this information, the eicient quantity to extract in period 1 is... _ m+bS+t (11 (2+r)b The town is deciding between a high tax and a low tax, which tax will lead to more extraction in period 1? Let's say that S 2 410,0. 2 240,7' 2 0.05,b = 40/41. If the town cannot tolerate the damages generated by more than 250 barrels being extracted in period 1, what is the highest tax it can set in period 2