Assume there are two periods: today (0) and tomorrow (1) and that, after tomorrow the world comes to an end. Further assume there are 10 barrels of oil in the ground. Let the total benefits in each period be given as: B(qt) = 10qt−0.5qt2 and the total cost of extracting the oil in each period be 2qt . If the discount rate is 10%. Suppose that we use up all the oil in the ground over the two periods. (a) Find the net benefits in each period. (b) If a social planner wants choose a level of output q for periods t = 0 and t = 1 so as to maximize the discounted sum of net social benefit over both time periods, what is the optimal allocation of output over the two periods? (c) Obtain the prices for the two periods, i.e.,
Assume there are two periods: today (0) and tomorrow (1) and that,
after tomorrow the world comes to an end. Further assume there are 10 barrels of oil
in the ground. Let the total benefits in each period be given as: B(qt) = 10qt−0.5qt2
and the total cost of extracting the oil in each period be 2qt
. If the discount rate is
10%. Suppose that we use up all the oil in the ground over the two periods.
(a) Find the net benefits in each period.
(b) If a social planner wants choose a level of output q for periods t = 0
and t = 1 so as to maximize the discounted sum of net social benefit over both
time periods, what is the optimal allocation of output over the two periods?
(c) Obtain the prices for the two periods, i.e., p0 and p1.
(d) Find the royalty in each period. Show that, the discounted value of the royalty
in each period is the same and it is equal to the shadow price of oil (λ).
(e) Verify the Hotelling rule (i.e., show that the growth rate of the
royalty is equal to the discount rate).
(f) Provide an intuitive account of the Hotelling rule.
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Assume there are two periods: today (0) and tomorrow (1) and that,
after tomorrow the world comes to an end. Further assume there are 10 barrels of oil
in the ground. Let the total benefits in each period be given as: B(qt) = 10qt−0.5qt2
and the total cost of extracting the oil in each period be 2qt
. If the discount rate is
10%. Suppose that we use up all the oil in the ground over the two periods.
(a) Find the net benefits in each period.
(b) If a social planner wants choose a level of output q for periods t = 0
and t = 1 so as to maximize the discounted sum of net social benefit over both
time periods, what is the optimal allocation of output over the two periods?
(c) Obtain the prices for the two periods, i.e., p0 and p1.
(d) Find the royalty in each period. Show that, the discounted value of the royalty
in each period is the same and it is equal to the shadow price of oil (λ).
(e) Verify the Hotelling rule (i.e., show that the growth rate of the
royalty is equal to the discount rate).
(f) Provide an intuitive account of the Hotelling rule.
Please I need answers to d, e, and f parts
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