Consider a private property model with two periods. Two firms each own a resource (e.g., a forest, a fishing lake) of size 25. Hence each firm i can extract q1 i 25 in period 1 and q2 i 25 q1 i in period 2 to sell in a market. The market has inverse demand p(qt) = 100 qt in each period t, in which qt = qt 1 + qt 2 is the total amount extracted in period t. Production costs are zero, and firms seek to maximize total profit across the two periods. (a) Find the Nash equilibrium extraction levels in periods 1 and 2 and the equilibrium market prices. (b) How would your answer change if the two firms extracted from a common resource pool? That is, assume there is a total pool of 50, the firms extract q1 1 and q1 2 in period 1, and they spilt what is left in period 2each firm i gets to sell up to q2 i = 1 2 (50 q1 1 q1 2 ) in period 2