a classification system used to distinguish various categories of resource availability
3 categories of resource taxonomy?
1. current reserves 2. potential reserves 3. resource endowment
are resources that can be extracted profitably at current prices
resources are potentially available. They depend on people's willingness to pay and technology
represents the natural occurrence of resources in the earth
is not naturally replenished or is replenished at such a low rate that it can be exhausted. The depletion rate is affected by demand, and thus by the price elasticity of demand, durability and reusability
has some mass that can be recovered after use. Copper is an example of a depletable, recyclable resource
is a resource that is naturally replenished. Examples: water, fish, forests, solar energy
The management problem for depletable resources?
management problem is how to allocate dwindling stocks among generations while transitioning to a renewable alternative (i.e., ENERGY)
The management problem for renewable resources?
management problem is in maintaining an efficient and sustainable flow (FORESTS AND FISH)
efficient intertemporal allocations..
use the 2-period model
what is the primary criterion when allocating resources over time?
Hotelling's Rule of Nonrenewable Resource Extraction
states that the present value of the marginal net benefits is constant over time.
a producer is indifferent between selling the last unit of oil this year or next year. What would the present value have to be?
PV of a barrel of oil would have to be the same in both periods. P0 = P1/(1+r) --> (1+r)P0 = P1 --> (P1-P0)/P0=r Hotelling's Rule
Suppose the price of oil next year (year 1) is $110 per barrel. According to Hotelling's Rule, what must be the price today (year 0) if the discount rate is 10%
Hotelling's rule: (P1-P0)/P0=r --> (110-P0)/P0=0.1 --> solve for P0 to get 100. ANS: The price today must be 100 if the discount rate is 10%
oil price assumptions?
1. the price of oil increases at a rate equal to the discount rate. 2. oil prices will rise over time
intuition about trend of oil price
if the price of oil today is greater than price of oil tomorrow [P0(1+r)>P1] extract all the oil in the current year. If the price of oil today is less than the price of oil tomorrow [P0(1+r)<P1] leave all of the oil in the ground.
What about the case where the costs of extraction are increasing as the resource stock declines?
if we introduce costs, then the marginal profit becomes M(pi) = p - MC, where MC is the marginal cost of extraction.
Marginal cost of extraction:
Modifying this (Hotelling's) rule to allow for marginal extraction costs:
[M(pi)1 - M(pi)0]/M(pi)0 = r --> Marginal profit (marginal net benefit to the firm) increases over time at a rate equal to the discount rate
Suppose there are 100 tons of Madisonite, a newly discovered non-renewable mineral. Assume the following: 1. 2-period model 2. discount rate = 10% 3. Marginal cost of producing Madisonite is $10 4. Inverse demand curve for Madisonite: p = 80 - q 5. initially, 50 tons produced in the first period and 50 tons produced in the second period **is this equal division of Madisonite a market equilibrium? Does it maximize social net benefits?
No, market equilibrium is 50.95 for period 0 and 49.05 for period 1. This allocation is efficient (by Welfare Theorem) because it maximized the present value of social net benefits.
Observation of Hotelling's Rule of Resource Extraction?
1. notice that the efficient solution does not require maximizing current social net benefits. Why??
Why does the efficient solution not require maximizing current social net benefits?
because there is an opportunity cost of consuming resources today, namely the value of consuming those resources in the future. This is called the MARGINAL USER COST
second observation of Hotelling's rule?
2. notice that efficient allocation requires consuming more in the first period than in the second. Why???
Why does efficient allocation require consuming more in the first period than in the second?
This reflects the opportunity cost of holding Madisonite in the ground. Opportunity cost of FOREGONE INVESTMENT.
What happens to the 2-period model with higher discount rates?
Higher discount rates imply faster extraction, so we will consume even more today. Higher discount rate is associated with greater impatience.
What are two costs to extracting a non-renewable resource (such as oil) today?
1. Marginal extraction cost (MEC) 2. User cost
the cost at the margin of actually extracting the resource. Extraction takes place only if Price is greater than or equal to marginal extraction cost
the opportunity cost of not having the resource in the future. As a result, the price of the resource is USUALLY greater than the MEC.
In a 1 period world, what is the equation for Marginal Net Benefit (MNB)?
MNB = P - MEC
In a 2 period world, what is the marginal net benefit?
MNB = P - MEC
Optimality at point where P = MEC?
It is NOT socially optimal to go to the point where P=MEC because there is an opportunity cost that must be considered
Marginal user cost in a 3-period world?
Marginal net benefit in the current period equals the present value of the MNB next period and it also equals present value of MNB two periods---hence; PV MNB is the SAME across all periods
What can be inferred about price when looking at Hotelling's Rule?
P(t) = MUC(t) + MEC(t)
Market equilibrium result:
the result that everyone in the market is happy with the allocation over time--maximized the present value of social net benefit over time
Hotelling's Rule market equilibrium??
P(t) - MEC(t) = [P(t+1) -MEC(t+1)] / (1+r)
todays price minus todays MEC is equal to tomorrows price minus tomorrows MEC divided by 1+r
Constant marginal extraction cost in N-Period? (The N-Period Constant-Cost Case)
with constant marginal extraction cost, total marginal cost (or the sum of marginal extraction costs and marginal user cost) will rise over time
A graph shows total marginal cost and marginal extraction cost. What do the vertical and horizontal distance between them equal?
the vertical distance between the two equals the marginal user cost. The horizontal axis measures time.
Why does marginal user cost rise over time?
rising marginal user cost reflects increasing scarcity and the intertemporal opportunity cost of current consumption on future consumption.
Empirical test of Hotelling's Rule: tracking prices for 9 non-renewable resources from 1967 to 1994
There was no upward trend in prices. Why?? We assume perfect information, constant costs. In the real world, technology advancements lower price of extraction (ex: horizontal fracking)
The cartel problem of oil?
The member countries of the international cartel called the Organization of Petroleum Exporting Countries (OPEC) collude in order to gain monopoly power
what is collusion?
withholding oil in the market in hopes to keep prices higher than they would be in a free market. This is bad for efficiency.
Members of OPEC?
Algeria, Indonesia, Iran, Iraq, Kuwait, Libya, Nigeria, Qatar, Saudi Arabia, United Arab Emirates, and Venezuela
Compatibility of Member Interest
Individual cartel members have incentives to cheat on production agreements. If everyone else keeps oil off the market, then the individual who chooses to increase production gains a LOT. Enforcing the collusion agreement is essential for the success of the cartel.
Price elasticity of demand
measures the sensitivity of demand to price changes.
What if demand is not sensitive to price changes?
then there are big potential gains from cartelization.
In the long run, what does price elasticity of demand depend on?
depends in part on the availability of substitutes. Thus in the long run, price elasticity of demand is usually larger.
substitutes for oil...
are expensive and transition times are long. Ex: solar energy sets are a long-run upper limit on the ability of OPEC to raise prices
What if marginal extraction costs increase over time?
As costs rise, quantity extracted falls over time.
When does quantity extracted fall to zero?
falls to zero at the point where total marginal cost reaches the maximum willingness to pay (CHOKE PRICE) for the resource such that demand and supply simultaneously equal zero.
transition to a renewable substitute?
an efficient allocation implies a smooth transition to exhaustion and/or to a renewable substitute.
What is the transition point to the renewable substitute called?
At the switch point, the total marginal cost of the depletable resource equals what?
the total marginal cost of the depletable resource equals the marginal cost of the substitute
Transition to a renewable substitue: does total marginal cost increase?
the rate of increase of total marginal cost slows down after the time of transition because the marginal user cost represents a smaller portion of total marginal cost for the second, higher cost resource.
how does technological progress affect cost of extraction and transition time?
technological progress would reduce the cost of extraction, lowering the future marginal cost of extraction thus moving the transition time further into the future.
total marginal cost and technological progress?
total marginal cost would actually fall with large advances in technology. New discoveries mean more resource to exploit more cheaply--also pushes back transition time.
So far we have assumed well-defined ownership of the resource. What happens if the resource is non-excludable??
incentives change with common pool resources. There is no incentive to delay harvest as someone else will harvest if you don't. So discount rate is effectively infinite.