Section 3/6/2009. VSL Static vs. Dynamic Efficiency (Example: optimal extraction of a non-renewable resource) Defining/ measuring scarcity Definitions of sustainability These concepts are all important for the part of the course we are now covering: natural resource economics. VSL.
(Example: optimal extraction of a non-renewable resource)
Demand = 8 – 0.4(Q)
MC = 2
What is the quantity consumed that satisfies static efficiency?
Net MB = 6 – 0.4 (Q)
All these graphs point to the same thing:
Static efficiency would be achieved by consuming 15 units of the resource.
Understanding the tradeoff:
In standard consumption framework, we are trading off the consumption of two goods.
We maximize utility (as a function of both goods) subject to budget constraint.
Now: trading off the consumption in different time periods, subject to budget constraint (total stock of resource)
Period 2 consumption
Period 1 consumption
Future Valuet = Present Value · (1 + r)t
Present Value = Future Valuet / (1 + r)t
PERIOD TWO (now in present value terms) non-renewable resource
Net MB = 6 – 0.4 (Q)
Net MB = 5.45 – 0.36 (Q)
Graphically. . . non-renewable resource
PERIOD ONE non-renewable resource
PERIOD TWO (now in present value terms)
Net MB = 6 – 0.4 (Q1)
Net MB = 5.45 – 0.36 (Q2)
Algebraically: set present values of net MB equal to each other
1) 6 – 0.4(Q1) = 5.45 - .36(Q2)
2) Q1 + Q2 = 20 (Budget constraint)
Two equations, two unknowns: solve for Q1, Q2: Q1=10.238; Q2=9.762
Use Q to find prices in each period.
Marginal User Cost = the additional marginal value of a resource above marginal cost due to its scarcity.
MUC = P - MC
If we had 30 units of the non-renewable resource, we know we would just have used 15 in each period.
Price = MC.
Marginal user cost = 0
The resource would not be economically scarce.
The opportunity cost of using the resource today would have been zero, because it wouldn’t affect our use of the resource tomorrow.
BUT: SCARCITY? resource above marginal cost due to its scarcity.
If we only have 20 units.
Marginal User Cost = the additional marginal value of a resource due to its scarcity.
MUC = P- MC
Now, the resource is economically scarce: the efficient price will be higher than the marginal cost of extraction
Our decisions about use today affects our use of the resource tomorrow.
Efficient pricing takes into account the opportunity cost: today’s price is higher than it would be if the resource were unlimited.