Question

Efficient Allocations for Depletable Resources

n = 2 time periods.

Inverse Demand Curves:

P₁ = 10 - 0.4q₁ for period 1 and

P₂ = 10 - 0.4q₂ for period 2.

Marginal Costs for the two periods:

  MC₁ = $3.00

  MC₂ = $3.00

Discount rate = 15%

Resource Availability Constraint:

  Q = q₁ + q₂ = 25 billion units.

Q1* = 12.15

Q2* = 12.85

PV(MUC1) = 1.86

MUC2 = 2.14

4. Calculate PV Producer’s net benefit (PNB_t) t= 1 and 2, and PV consumer’s net benefits (CNB_t) for periods 1 and 2.

Graph it

For period 1, Calculate P1* =10 - 0.4q₁*. Then

TNB1 = CNB1 + PNB1= area of triangle + area of rectangle for period 1.

For period 2,

Graph it

Calculate P2* =10 - 0.4q₂*. Then

PV (TNB2) = PV(CNB2) + PV (PNB2)

5. Calculate PV stream of TNB’s for periods 1 and 2. That is, PV(TNB₁, TNB₂) = TNB₁ + PV(TNB₂).

PV (stream of TNB’s in the two periods) = TNB1 + PV(TNB2)

Answer 1