Question

Full solutions for all of the 7 Questions:

Suppose we are analyzing the intertemporal allocation of oil. Assume a generation is 35 years, and we are concerned with only two generations. The demand and supply functions for oil in the present generation are given by

Demand: Pd = 200 - 0.6 * R1

Supply: Ps = 5 + 0.7 * R1

where R1 is the quantity of oil extracted and consumed in the first generation. The demand and supply functions for oil in the second generation are assumed to be the same (simply substitute R2 for R1 in the two equations).

The total stock of oil is assumed to be known and given by S = 291.

Annual interest rate is r = 4%, which for 35 years works out to be approximately equal to 4 (1.0435 ≈ 4).

Thus the generational discount factor that should be applied to the second generation's net benefits is DF2 = 1/4. You should work either with the approximate generational interest rate (4) or the approximate generational discount factor (1/4) -- do not use the precise values.

Question 1) Solve for the static equilibrium price and quantity in the first generation, that is, the P1 and the R1 that results when no consideration is given to future generations. Calculate :

R1 =   ?

P1 =   ?

Question 2) Given the static equilibrium, the second generation will consume the oil that is leftover. What is the present value of the total net benefits derived from oil consumption in both generations?

TNB =   ?

Question 3) Solve for the intertemporally efficient price and quantity in the first generation.

R1_e =   ?

P1_e =   ?

Question 4) What is the present value of the total net benefits derived from the intertemporally efficient oil consumption in both generations?

TNB_e =  

Question 5) What is the optimal resource depletion tax in the first generation?

t =  

Question 6) Now suppose the annual interest rate r is zero. Solve for the intertemporally efficient extraction quantity in the first generation.

R1_0 =   ?

Question 7) Now suppose the annual interest rate r is infinite. Solve for the intertemporally efficient extraction quantity in the first generation.

R1_inf =   ?

Answer 1

Pd=200-0.6R1

Ps=5+0.7R1

1) Pd=Ps

200-0.6R1=5+0.7R1

200-5=0.7+0.6

195=1.3R1

R1=195/1.3

=150

Pd=200-0.6*150

=200-90

=110

Ps=5+0.7*150

=5+105

=110