1. Dynamic allocation of depletable resources. (1) The NPeriod, ConstantCost, NoSubstitute Case: The inverse demand curve in year t can be written as: pt = 8 _ 2th _ 3%2 The marginal cost of extracting that resource is constant c=2. Total amount of resource Q=40, r=0.01. a. Write down the maximization problem for the dynamic allocation of the resource over 11 years. b. Write down_the equations describing the allocation that maximizes the present value of net benets. (You do not need to solve it) (2) The NPeriod, Constant-Cost, with an Abundant Renewable Substitute case: The inverse demand curve in year t can be written as: pt 2 8 2th 3Qt2 Let qt be the amount of a constantmarginalcost depletable resource extracted in year t and (Is: be the amount used of another constant-marginal-cost resource. The marginal cost of extracting the depletable resource is constant c=2. The marginal cost of the substitute is assumed to be d=3. Total amount of depletable resource Q=40, r=0.01. 0. Write down the maximization problem for the dynamic allocation of the resource over 11 years. d. Write down_the equations describing the allocation that maximizes the present value of net benets. (You do not need to solve it)