Chile controls over half of world lithium reserves (8 Million tons). Its department of natural resources is trying to figure out how to best allocate production between two periods, the present and the future. In the present, Chile faces residual demand curve: P1 = 110 10Q1 In the future, due to the rise of electric vehicles, that demand is expected to increase to: P2 = 160 15Q2 The marginal extraction cost in both periods is M EC1 = M EC2 = 10, and Chile's discount rate between the two periods is r = 0.5. [UNITS: P and M EC are in $/M tons and Q given in M tons]

Draw a graph which imposes these two constraints, and demonstrates the socially optimal consumption path. Clearly label any functions you draw and their Y-axis intercepts where possible. Label the optimal first period quantity Q1.