Question

1. Assume the following two equations and the discount rate for the extraction of a natural resource: A) P= 18 -0.75 Q for Marginal Willingness to Pay B) P= 3 for a constant Marginal Cost C) Discount Rate = 6% Solve for the following in a two time period setting: 1) Find and label the equilibrium when there is no limit on Q. 2) State the assumptions needed to solve the optimal extraction rate of the resource in our setting. 3) Assume that there are only 25 units of the natural resource to be extracted, find the optimal extraction rates over the two periods. 4) Find the Total Marginal Net Benefits under the optimal extraction rates. 5) Find the Marginal User Cost for each time period of the resource.

Answer 1

Solin Given that ) J-06 9,+99=25 - p=18-0.150 Marginal cost MC = 3 Discount gate - 67. when no upper limit on extractions P = MC 18-0.750 = 3 0-150 = 15 Q = 20 %, -20 692= 20 if total Q = 40 efficient allocation irrespective of with Q =25 Max Pv of profit of extractions 2 st period net marginal benefit = 18-0-750,-3- a na period net marginal benefit = (18-0.159 where t= marginal user cost ji) opportunities of extraction of resource at margin at margin of optimal extraction net profit 18-0.159, -3=1 15-0.159 = and 18-0-1592-3= 1.064 15-0.7578 = 1.064 from 0 99=25-22 15-0.15625-92) = 1 15-18.45 + 0.7542 = 1 0.759, -3.75= 1 - 0 -0.759, +15 = (1-06) — ☺ from solving 04 11.25=(2.06) 11125 -5.46 0.7592 = 5.46 + 3.75 22.06 92-12-28, 9, -12.71 marginal User cost = 9.46 Total marginal net benefits: 2,-12-28 92 = 12.1

is St yeay more than half of total extractable amount is extracted Net benefit yo+01 - 18 -0.45 013-70) -3+/18 - 0.75 (12.48) -3) e (15- 9.5325 106 : 5.47 +5.76 =10.932