There are only 28 units of Metal Z on a small island. The demand and supply of Metal Z are characterized, respectively by Pd=10-0.5Q and Ps=5+0.5Q. The goal of this problem is to find the economically efficient allocation of Metal Z between consumers today and consumers of this metal 8 years from now.

(A) Assuming that the demand and supply of Metal Z 8 years from now will be the same as today, what are the formulae that would characterize the marginal net benefits of Metal Z in the present period (MNB1) and the undercounted marginal benefit 8 years from now (MNB2). Show all calculations clearly.

(B) Assuming a discount rate of 10% (r=10%) show the formula (and all associated calculations) that would characterize the present vale of metal Z in the period 8 years from now.

(C) Calculate the optimal consumption level of Metal Z in the present period and in the period of 8 years from now.

(D) Calculate the optimal consumption level of Metal Z in the present period and in the period 8 years from now, if the discount rate rose to 20%.

Requirements: ANSWER ALL PARTS PLEASE

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