Consider the intertemporal allocation of a nonrenewable resource (NRR) between two generations, 1 and 2, with...

 

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Consider the intertemporal allocation of a nonrenewable resource (NRR) between two generations, 1 and 2, with each generation being 35 years apart. The inverse demand and supply for this NRR are P₁ = 40 - Q./5 and P₁ = Q₁/5, respectively, with Q, and P, denoting quantity and price in period i = 1, 2. Therefore, demand and supply conditions are the same in generations 1 and 2, i.e., the non-discounted MNB is the same for both generations. There is a discount rate of 4% per year implying (1 +0.04)35 4. The maximum quantity of the NRR is Qmax = 100. . • Q1. Determine generation 1's marginal net benefit MNB₁. . . • Q2. Determine the static equilibrium quantity for generation 1, i.e., the quantity Q₁ when generation 1 does not consider its impacts on generation 2. • Q3. Determine generation 2's marginal net benefit expressed in present value. • Q4. Determine the dynamic equilibrium quantity for generation 1, i.e., the quantity Q₁ when generation 1 considers its impacts on generation 2. • Q5. Determine the dynamic equilibrium quantity for generation 2. . • Q6. Determine the social marginal cost curve for generation 1. Q7. Determine the unit depletion tax that should be imposed on generation 1 to ensure an efficient allocation of the NRR between the two generations. • Q8. If a higher discount rate were to be used for the analysis, the dynamic equilibrium quantity Q₁ for generation 1 would: A) Decrease; B) Remain constant; C) Increase. Consider the intertemporal allocation of a nonrenewable resource (NRR) between two generations, 1 and 2, with each generation being 35 years apart. The inverse demand and supply for this NRR are P₁ = 40 - Q./5 and P₁ = Q₁/5, respectively, with Q, and P, denoting quantity and price in period i = 1, 2. Therefore, demand and supply conditions are the same in generations 1 and 2, i.e., the non-discounted MNB is the same for both generations. There is a discount rate of 4% per year implying (1 +0.04)35 4. The maximum quantity of the NRR is Qmax = 100. . • Q1. Determine generation 1's marginal net benefit MNB₁. . . • Q2. Determine the static equilibrium quantity for generation 1, i.e., the quantity Q₁ when generation 1 does not consider its impacts on generation 2. • Q3. Determine generation 2's marginal net benefit expressed in present value. • Q4. Determine the dynamic equilibrium quantity for generation 1, i.e., the quantity Q₁ when generation 1 considers its impacts on generation 2. • Q5. Determine the dynamic equilibrium quantity for generation 2. . • Q6. Determine the social marginal cost curve for generation 1. Q7. Determine the unit depletion tax that should be imposed on generation 1 to ensure an efficient allocation of the NRR between the two generations. • Q8. If a higher discount rate were to be used for the analysis, the dynamic equilibrium quantity Q₁ for generation 1 would: A) Decrease; B) Remain constant; C) Increase.

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