Econ 342: Environmental Economics Chapter 5 In-Class Assignment

1. The inverse demand function for the depletable resource is P = 11 – q and the marginal cost of extracting it is $1 per unit. The total supply of this resource is 10 units.

a. What is the definition of a dynamically efficient allocation of a resource? I am not asking for the formula. [2 points]

A dynamically efficient allocation of resources is one that maximizes the present value of the net benefits of the possible uses of a resource over time.

b. Assuming a discount rate of 50% what is the dynamically efficient allocation of the resource over time? Give an answer accurate to two decimal points. [Remember you only need to discount the second period] [10 points]

PV[MNB1] = PV[MNB2] The net benefits in each period are: Marginal Net Benefits 1 = MB1 – MC1 Marginal Net Benefits 2 = MB2 – MC2 To get the present value, we discount:

𝑀𝑁𝐵$(1 + 0.5),

= 𝑀𝑁𝐵/

(1 + 0.5)$

11 – q1 - 1 = (11 - q2 - 1)/1.5

We also know, q1+q2 = 10

Solving;

10-q1 = (10-q2)/1.5

10 - q1 = [6.67 - (10-q1)/1.5] 10 - q1 = [6.67 – 6.67 + 0.67q1)]

q1 =5.99 q2= 4.01

c. Present the efficient allocation in a graph [Remember the graph for dynamic allocation we did in the class] [10 points]

d. What is the marginal user cost in each period? Give an answer accurate to two decimal points. [8 points]

MUC = P – MC We need to first find out the price for the dynamically efficient allocation We know,

P1 = 11 – q1 => 11 – 5.99 P1 = $5.01 P2 = 11-q2 => 11 - 4.01 P2 = $6.99 MUC1 = 5.01 – 1 = $4.01 MUC2 = 6.99 – 1 =$5.99