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The Allocation of Depletable and RenewableResources

Tietenberg and Lewis, Chapter 6

The Allocation of Depletable and Renewable Resources

Introduction

Three separate concepts are used to classify the stock ofdepletable resources:

1 Current Reserves: are known resources that can pro�tablybe extracted at current prices

2 Potential Reserves: The amount of reserves potentiallyavailable depends upon the price people are WTP for thoseresources

3 The Resource Endowment: It represents an upper limit onthe availability of terrestrial resources

The distinctions among these three concepts are signi�cant:Use data on current reserves as if they represent themaximum potential reserves.Assume that the entire resource endowment can bemade available as potential reserve.



Depletable recyclable resource

They can be augmented by economic replenishment, as well asby recycling.

Renewable Resource (RR)

Natural replenishment augments the �ow of RR at anon-negligible rate.



Managing renewable resources presents a di¤erent challengefrom managing depletable resources, though an equallysigni�cant one.

Depletable resources: Allocating Stocks among generationsRR: The maintenance of an e¢ cient, sustainable �ow.

E¢ cient Intertemporal Allocations

For a depletable, nonrecycable resource, this requires abalancing of the current and subsequent uses of the resource.



The Two-Period Model Revisited: Main Assumptions

1 Constant Marginal Extraction Cost (MExC)2 No Substitute Resource3 Total Marginal Cost: TMC= MUC + MExC4 Highest price anyone is willing to pay $8


The Two-Period Model Revisited



Transition to a Renewable Substitute: Assumptions

1 Constant Marginal Extraction Cost (MExC)2 Substitute Resource3 Marginal Extraction Cost of the renewable resource ($6)4 Marginal Extraction Cost of the depletable resource ($2)



TMC1

TMC2

MEC2

MEC1

The cheapest goodwould be consumed

Second Resource/ 1st

resource is exhausted

Transition from one constantCost Depletable resource to another

Time

T*

$

TMC of the two resources have to be equal at the time of transition

TMC are not equal in other periods.



Increasing Marginal Extraction Cost (MEC)



Di¤erences between Constant MEC and Increasing MEC are:

1 The behavior of the Marginal User Cost (MUC): In this casewe have that MUC declines over time until, at the time oftransition to the renewable resource, it goes to zero

2 In the increasing-cost case, the reserve is not exhausted someis left in the ground because it is too expensive to take out.



Exploration and Technology Progress:

The marginal cost of exploration is the marginal cost of �ndingadditional units of resource, should be expected to rise overtime, just as the MEC does.

Environmental Costs

the extraction of a natural resource imposes an environmentalcost on society not internalized by the producers.



Environmental Costs, Assumptions:

1 The extraction of the depletable resource caused somedamage to the environment not adequately re�ected in thecost faced by the extracting �rms

2 The environmental damage can be included by increasing theMC by $1.00 (MC=3+0.1Q)

On the demand side, the inclusion of environmental costsresults in higher prices, which tend to decrease demand.

The higher marginal cost also means that a smallercumulative amount of the depletable resource would beextracted in an e¢ cient allocation.

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