Question

Consider the following supply and demand equations for a depletable energy resource, with subscripts representing the time period. D0=100-2Q0 S0=50 : D1=100-Q1 S1= 30

A) If the discount rate is 2%, and the total stock of the resource at the beginning of time period 0 (Q-bar) is 90 units, determine the allocation of Q in each period that maximizes the net present value of total benefits (NPVTB) across both periods. This is known as the optimal allocation or dynamically efficient allocation.

B) Calculate the scarcity rent associated with your answer in part a.