chapter 6sbkunwar.weebly.com/uploads/1/0/9/8/109848430/chapter_6.pdf · Chapter 6 Depletable Resource Allocation: The Role of Longer Time Horizons, Substitutes, and Extraction Cost

Chapter 6

Depletable Resource Allocation: The Role of Longer

Time Horizons, Substitutes, and Extraction Cost

© 2012 Pearson Education, Inc. All rights reserved. 6-2

Chapter 6: Depletable Resource Allocation: The Role of Longer Time Horizons, Substitutes, and Extraction Cost

• Introduction• A Resource Taxonomy• Renewable, Recyclable and Depletable

resources• Efficient Intertemporal Allocations• Market Allocations of Depletable Resource


Introduction

How do societies react when finite stocks of depletableresources become scarce? Is it reasonable to expect that self-limiting feedbacks would facilitate the transition to a sustainable steady state?

Or is it more reasonable to expect that self-reinforcing feedback mechanisms would cause the system to overshoot the resource base, possibly even precipitating a societal collapse?


Introduction

• This chapter presents the topic of resource scarcity within the general taxonomy of resources.

• This chapter studies the implications of both efficient and profit-maximizing decision-making.


A Resource Taxonomy (Classification System)

• A resource taxonomy is a classification system used to distinguish various categories of resource availability.– Current reserves are known resources that

can be extracted profitably at current prices.

– Potential reserves resources potentially available. They depend on people’s willingness to pay and technology.

• At higher prices, potential reserves are larger since more expensive extraction techniques will be economically feasible.



– Resource endowment represents the natural occurrence of resources in the earth.• This is a geological concept since the

endowment is not a function of price.• Reserves represent an economic concept.



• Example of oil;

–Current reserves of oil:• Millions of barrels of oil that are currently

being extracted at a current price of ~$50/barrel.

–Even though current reserve is usually given as a number, it usually fluctuates with prices.



– Potential reserves:• The exploration interest. Oil trapped in rock pores.

– Not profitable to mine at the current price.» The higher the price, the higher the potential reserves

because extraction techniques will be economically feasible.



– Resource endowment:• Every single drop of oil that is available in the

earth. – The upper bound of the available resource.



• The US Geological Survey (USGS) has developed a classification of resources illustrated in figure 1, which has two dimensions – economic and geological.


FIGURE 6.1 A Categorization of Resources (1 of 2)



• A movement from top to bottom represents movement from cheaply extractable resources to those extracted at substantially higher prices.

• A movement from left to right represents increasing geological uncertainty about the size of the resource base.



FIGURE 6.1 A Categorization of Resources (Additional classifications)


A Categorization of Resources (Additional classifications)

1. Identified resources are of known quantity and quality based on geologic evidence.

2. Measured resources are those for which quantity and quality are estimated with a margin of error less than 20%.

3. Indicated resources have been estimated from sample analyses and geologic projections.

4. Inferred resources are materials in unexplored extensions of demonstrated resources (identified and measured) based on geologic projections.


A Categorization of Resources (Additional classifications)

5. Undiscovered resources are surmised to exist on the basis of geological knowledge and theory.

6. Hypothetical resources are expected to exist.

7. Speculative resources are undiscovered materials that may occur in known deposits in favorable geologic settings.


• The seven categories listed above will fall into an additional category depending on the economic feasibility of extraction. – Reserves will be those resources that are

measured, indicated or inferred and economic.

• Since infinite prices are not likely, the entire resource endowment cannot be made available.

A Resource Taxonomy(Environmental Economics Classifications)


1. A depletable resource is not naturally replenished or is replenished at such a low rate that it can be exhausted. (Fossil Fuels)– The depletion rate is affected by demand, and thus by

the price elasticity of demand, durability and reusability.

• Examples:– Energy Resources: Oil, natural gas, uranium, coal etc.– Other Minerals: Copper, nickel and zinc



2. A recyclable resource has some mass that can be recovered after use. – Glass, paper, plastics etc.– Copper is an example of a depletable, recyclable

resource.• Each year in the U.S.A., nearly as much copper is recovered from

recycled material as is derived from newly mined ore (copper.org)

• Known worldwide copper resources are estimated at nearly 5.8 trillion pounds of which only about 0.7 trillion pounds (12%) have been mined throughout history... and nearly all of that is still in circulation, because copper's recycling rate is higher than that of any other engineering metal. (copper.org)

– Current reserves of a depletable, recyclable resource can be exhausted, but can also be augmented by economic replenishment and recycling.



3. A renewable resource is one that is naturally replenished. – You could potentially maintain the flow of these

resources perpetually.– Some renewable resources are storable and others are

not.– Examples are surface water, grass, fish, soil, forests

and solar energy.



• The management problem for depletableresources is how to allocate dwindling stocks among generations while transitioning to a renewable alternative.

• The management problem for renewable resources is in maintaining an efficient and sustainable flow.

A Resource Taxonomy


• Most minerals (e.g., fossil fuels) follows a depletion curve in its extraction rate.– It rises quickly and then slows down to a peak

and they fall rapidly either faster or slower than it rose.

– Follows this equation (Not needed!)

A Resource Taxonomy


US Crude Oil ExtractionPeaked in 1970.

Source: http://www.roperld.com/science/minerals/FossilFuelsDepletion.htm


US Coal Extraction



US Natural-Gas Extraction



Efficient Intertemporal Allocations

• The Two-Period Model Revisited

–Dynamic efficiency is the primary criterion when allocating resources over time.

• Dynamic efficiency assumes that society’s objective is to maximize the present value of net benefits from the resource.



• Recall the two-period model from Chapter 5.

Two period model:

1) Rising MUC2) Falling Quantity


Efficient Intertemporal Allocations(Two period model)

• Recall the two-period model from Chapter 5. – We assumed resources were extracted at a

constant marginal cost.– Marginal user cost rises over time.

• Marginal user cost increases because of increasing opportunity costs. (We have taken resources that could have been available to the future generation!)

• Additionally, it rises at the rate of discount (r) in an efficient allocation to preserve the balance between present and future consumption.



• Recall the two-period model from Chapter 5. – This model can be generalized to longer time

periods.– An n-period model presented uses the same

numerical example from Chapter 5, but extends the time horizon and increases the recoverable supply from 20 to 40.

R = 10%Q = 40Time is unlimited


FIGURE 6.2: Constant Marginal Extraction Cost with No Substitute Resource: (a) Quantity Profile (b) Marginal Cost Profile

Assumptions: 1) constant marginal extraction cost, 2) increasingMarginal user cost, 3) falling quantities consumed.


FIGURE 6.2: Constant Marginal Extraction Cost with No Substitute Resource: (a) Quantity Profile (b) Marginal Cost Profile

Assumptions: 1) constant marginal extraction cost, 2) increasingMarginal user cost, 3) falling quantities consumed.


• The N-Period Constant-Cost Case

– The graph shows total marginal cost and marginal extraction cost.

– With constant marginal extraction cost, total marginal cost (or the sum of marginal extraction costs and marginal user cost) will rise over time.

Efficient Intertemporal Allocations: Finite Resource


• The N-Period Constant-Cost Case (Notice the following)

1. The vertical distance between the two equals the marginal user cost. The horizontal axis measure time.

2. As in the two-period case, the efficient marginal user cost rises in spite of the marginal cost of extraction being constant.• Rising marginal user cost reflects increasing scarcity

and the intertemporal opportunity cost of current consumption on future consumption.



3. As costs rise, quantity extracted falls over time.

4. Quantity extracted falls to zero (period 9) at the point where total marginal cost reaches the maximum willingness to pay (or choke price = $8) for the resource such that demand and supply simultaneously equal zero.



• What is the efficient allocation if the depletable resource has a renewable substitue?– What is the efficient allocation of a oil or

natural gas when there is solar or wind substitute?

• In this case the resource exhaustion will not be too problematic since we can switch to renewable resource at an appropriate time.



• Transition to a Renewable Substitute– An efficient allocation implies a smooth

transition to exhaustion and/or to a renewable substitute.

– The transition point to the renewable substitute is called the switch point.

– At the switch point the total marginal cost of the depletable resource equals the marginal cost of the substitute.• After the switch point, the MC of renewable is cheaper

than depletable resource.

Efficient Intertemporal Allocations:Renewable Substitute+ constant MC


• Suppose for our previous example: – There is a perfect renewable substitute that is

infinitely available at a constant cost of $6.

• The total marginal cost (TMC) for the depletableresource in the presence of a $6 substitute would never exceed $6, because society could always use the renewable resource instead, once it is becomes cheaper.

Efficient Intertemporal Allocations:Renewable Substitute+ constant MC


FIGURE 6.3: Constant Marginal Extraction Cost with Substitute Resource (Efficient Paths): (a) Quantity Profile (b) Marginal Cost Profile

• The transition to renewable from depletable resource would occur at the TMC of $6


FIGURE 6.3: Constant Marginal Extraction Cost with Substitute Resource: (a) Quantity Profile (b) Marginal Cost Profile

• The transition point is called the switch point, where consumption of renewable resource would begin.

• Prior to the switch point, only depletable resource is consumed. At the switch point, the MC of depletable resource rises to meet the MC of renewable resource and transition occurs.

• After the switch point, only the renewable resource is consumed.• The consumption of depletable resource is much higher (fast exhaustion) than the previous

example, because there is a renewable substitute.


• Constant Marginal Cost Case (No Substitute)

– What if R increases to 15%?

• Constant Marginal Cost Case (Renewable Substitute)

• What if MC_renewable is $9 instead of $6?

Excel Examples:


P = 8 – 0.4qMC = $2


P = 8 – 0.4qMC = $2MC_renewable = $6


• A more realistic assumption is to consider marginal extraction cost as an increasing factor.– Example, when you mine, the costs increases as you go

deeper to extract more.

• The big difference now is in the behavior of the marginal user cost. – Until now, we assumed that marginal user cost increased

at the rate of r.– When extraction costs increases, marginal user

cost declines over time.• MUC reaches zero at the transition point.

Efficient Intertemporal Allocations:Increasing Marginal Extraction Costs


• Why does MUC decline?

– Marginal user cost is an opportunity cost reflecting the forgone future marginal net benefits.• In the case of increasing marginal extraction costs,

every unit extracted now raises the cost of future extraction (marginal cost increases).

• This means that the sacrifices made by the future generations diminishes.

• By the last unit, the marginal extraction cost is so high that earlier consumption of one more unit imposes no sacrifice at all.



• Increasing Marginal Extraction Cost

– For this case, the marginal user cost declines over time and reaches zero at the transition point.

– The resource reserve is not exhausted like the constant marginal extraction cost case.• This is because it becomes more expensive to use

than the substitute after some point.

• Going back to our example, it means the MC ≠ 2.– MC = 2 + 0.1Q. (now)



FIGURE 6.5: Increasing Marginal Extraction Cost with Substitute Resource: (a) Quantity Profile. (b) Marginal Cost Profile

• From TMC chart: As the marginal extraction cost increases, the gap between MEC and TMC declines.

– This is because the marginal user cost becomes smaller. At year 7, the total marginal cost equals the TMC of the renewable resource at which point the switching occurs.

• Switching point occurs at year 7


• The search for new resources is expensive. – As easily discovered resources are exhausted, searches

are initiated in less rewarding environments, such as the bottom of the ocean or locations deep within the earth.

• This suggests the marginal cost of exploration, which is the marginal cost of finding additional units of the resource, should be expected to rise over time, just as the marginal cost of extraction does.

Efficient Intertemporal AllocationsExploration and Technological Progress


• The higher the expected rise in the marginal cost of extraction, the larger the potential net benefits from exploration.– You find new sources that were previously unprofitable if

MC of extraction keeps on rising.

• Technological progress would reduce the cost of extraction.

• Total marginal cost could actually fall with large advances in technology.

• Lowering the future marginal cost of extraction would move the transition time further into the future.



•Exploration expands the size of current reserves

•Technological progress keeps marginal extraction cost from rising as fast as it otherwise would

–Both delay the transition to renewable resources.



Market Allocations of Depletable Resources

• We have so far examined how efficient allocation of substitutable, depletable, and renewable resources over time would be defined in a variety of circumstances.

• But,– Can the private market, involving millions of

consumers and producers each reacting to their own preferences, ever result in a dynamically efficient allocation?



• Appropriate Property Right Structures–Markets will behave well as long as the

property-rights structures governing the resources are exclusive, transferableand enforceable. • Under these conditions, it is in the best

interest of the producers to think long term to maximize profits (mainly because of marginal user cost).


• A resource governed by a well-defined property rights structure has two potential source of value:• A use value when sold• An asset value when it remains in the ground

• A use value is the value acquired when the resource is sold, e.g., timber sales.

• An asset value is the value to the owner while the resource is still in the ground. – If the price of the resource is rising, the resource in the ground

is becoming more valuable as long as it is saved.



– As long as prices increase, a producer who sells resources in the earlier periods loses the chance to take advantage of higher prices in the future.• Thus, business cannot be myopic.

– Presented with well-defined property rights and reliable information about future prices:• Producers will choose an allocation that provides the

maximum present value of net benefits for society, or a dynamically efficient allocation provided that social and private discount rates are equal.

– Figure 6.2 – 6.5 are dynamic efficient allocation + profit maximizing allocations.



• Environmental Costs– The environmental costs that are not

internalized by producers is one of the biggest failings of the property rights structures.

– If environmental damage is not part of the extraction decision, two problems arise:1. The price of the depletable resource is too low.2. The extraction of the depletable resource is too

high.

– In this case, the allocation will not be efficient. Need to take externality into account.



• The inclusion of environmental costs would result in higher prices

• Which will dampen demand;– From this point of view, the resource should last longer

since smaller amount would be extracted.• However, the supply side effect causes the

transition point to be sooner;– It gets expensive to extract all the cumulative

resources. • Which effect dominates depends on the shape

of the marginal extraction cost curve.



• Let’s look at the case of the increasing marginal cost case.

• What happens if the environmental damage impose a cost (tax) of $1?– MC = $3 + 0.1Q



P = 8 – 0.4qMC = $2 + 0.1Q


FIGURE 6.6: Increasing Marginal Extraction Cost with Substitute Resource in the Presence of Environmental Costs:(a) Quantity Profile (b) Price Profile (Solid Line—without Environmental Costs; Dashed Line—with Environmental Costs)


• On the demand side,– The inclusion of environmental cost results in higher

price => demand will be lower• This lowers the rate of consumption, making the

resource last longer.

• On the supply side,– Higher marginal cost means smaller cumulative amount

of depletable resource would be extracted in an efficient allocation.

– The cumulative amount extracted would be 30 instead of 40.

– This would hasten the switch when the switch to renewable resource is made.



• What if the environmental cost were associated with the renewable resources instead?– The transition for the efficient allocation would

be later than the market allocation.



Summary

• Efficient allocation of depletable and renewable resources – Constant marginal cost– Increasing marginal-cost– Technological progress

• Market allocations – Property rights– Environmental costs

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chapter 6sbkunwar.weebly.com/uploads/1/0/9/8/109848430/chapter_6.pdf · Chapter 6 Depletable Resource Allocation: The Role of Longer Time Horizons, Substitutes, and Extraction Cost