Tietenberg 8e Ppt07 Final

8/10/2019 Tietenberg 8e Ppt07 Final

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Copyright 2009 Pearson Addison-Wesley. All rights reserved.

Chapter 7

The Allocation

of Depletable

and RenewableResources:

An Overview


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Copyright 2009 Pearson Addison-Wesley. All rights reserved. 7-2

Introduction

This chapter presents the topic of resourcescarcity within the general taxonomy of

resources.

This chapter studies the implications of bothefficient and profit-maximizing decision-

making.


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Objectives

Introduce natural resource economics.

Present a resource taxonomy.

Present the basic vocabulary such as

depletable resource and recyclable resource.

Illustrate the difficulties associated with

scarcity measures.

Illustrate economic feasibility of resourceextraction.


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Extend the 2-period model to an N-periodmodel.

Present the efficient allocation of resourcesover time with constant marginal extractioncosts and with a transition to a renewablesubstitute.

Present the efficient allocation of resourcesover time with rising marginal extractioncosts.

Discuss the effects of environmental costs onthis model.


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A Resource Taxonomy

A resource taxonomyis a classificationsystem used to distinguish various categories

of resource availability.

Current reserves are resources that can beextracted profitably at current prices.

Potential reserves resources potentially available.

They depend on peoples willingness to pay and

technology.

Resource endowment represents the natural

occurrence of resources in the earth.


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FIGURE 7.1

A Categorization of Resources (1 of 2)


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FIGURE 7.1

A Categorization of Resources (2 of 2)


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FIGURE 7.1

A

Categorizationof Resources


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A depletable resource is not naturally replenishedor is replenished at such a low rate that it can beexhausted.

The depletion rate is affected by demand, and thus by the

price elasticity of demand, durability and reusability. A recyclable resource has some mass that can be

recovered after use.

Copper is an example of a depletable, recyclableresource.

A renewable resource is one that is naturallyreplenished.

Examples are water, fish, forests and solar energy.


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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.


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Efficient Intertemporal Allocations

The Two-Period Model Revisited Dynamic efficiency is the primary criterion when

allocating resources over time.

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.


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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.

The graph shows total marginal cost and marginal

extraction cost.

The vertical distance between the two equals the marginal user

cost. The horizontal axis measure time.

Rising marginal user cost reflects increasing scarcity

and the intertemporal opportunity cost of currentconsumption on future consumption.


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FIGURE 7.2 (a) Constant Marginal Extraction

Cost with No Substitute Resource: Quantity

Profile. (b) Constant Marginal Extraction Cost

with No Substitute Resource: Marginal CostProfile


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As costs rise, quantity extracted falls over time.

Quantity extracted falls to zero at the point

where total marginal cost reaches themaximum willingness to pay (or choke price)

for the resource such that demand and supply

simultaneously equal zero.


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Transition to a Renewable Substitute

An efficient allocation thus 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 ofthe depletable resource equals the marginal

cost of the substitute.

FIGURE 7 3 ( ) C t t M i l E t ti


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FIGURE 7.3 (a) Constant Marginal Extraction

Cost with Substitute Resource: Quantity

Profile. (b) Constant Marginal Extraction Cost

with Substitute Resource: Marginal CostProfile


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Transition to a Renewable Substitute

The transition can for two depletables with

different marginal costs will also be a smooth

one. 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 thesecond, higher cost resource.


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FIGURE 7.4 The Transition from One Constant-Cost

Depletable Resource to Another


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Increasing Marginal Extraction Cost For this case, the marginal user cost declines

over time and reaches zero at the transitionpoint.

The resource reserve is not exhausted.

The marginal cost of exploration can beexpected to rise over time as well.

Successful exploration would cause asmaller and slower decline in consumptionwhile dampening the rise in total marginalcost.

FIGURE 7 5 ( ) I i M i l


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FIGURE 7.5 (a) Increasing Marginal

Extraction Cost with Substitute Resource:

Quantity Profile. (b) Increasing Marginal

Extraction Cost with Substitute Resource:Marginal Cost Profile


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Exploration and Technological Progress

Technological progress would also reduce

the cost of extraction.

Lowering the future marginal cost of extractionwould move the transition time further into the

future.

Total marginal cost could actually fall with large

advances in technology.


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Market Allocations

Appropriate Property Right Structures

Markets will behave well as long as the

property-rights structures governing theresources are exclusive, universal,

transferableand enforceable.

A resource governed by a well-definedproperty rights structure will then have both a

use value and an asset value to its owner.


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Environmental Costs

The inclusion of environmental costs wouldresult in higher prices

which will dampen demand;

from supply side effect, which causes the transitionpoint to be sooner;

Which effect dominates depends on the shape of

the marginal extraction cost curve.

The concept of external environmental coststies together the fields of environmental and

natural resource economics.

FIGURE 7 6 (a) Increasing Marginal Extraction Cost


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FIGURE 7.6 (a) Increasing Marginal Extraction Cost

with Substitute Resource in the Presence of

Environmental Costs: Quantity Profile. (b) Increasing

Marginal Extraction Cost with Substitute Resource in

the Presence of Environmental Costs: Price Profile(Solid Linewithout Environmental Costs; Dashed

Linewith Environmental Costs)


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Summary

Efficient allocation of depletable andrenewable resources

Constant marginal cost

Increasing marginal-cost Technological progress

Market allocations

Property rights

Environmental costs

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Tietenberg 8e Ppt07 Final