Table Of ContentBestMasters
Springer awards „BestMasters“ to the best master’s theses which have been com-
pleted at renowned universities in Germany, Austria, and Switzerland.
Th e studies received highest marks and were recommended for publication by
supervisors. Th ey address current issues from various fi elds of research in natural
sciences, psychology, technology, and economics.
Th e series addresses practitioners as well as scientists and, in particular, off ers guid-
ance for early stage researchers.
Markus Merz
Scarce Natural
Resources, Recycling,
Innovation and Growth
Markus Merz
Tübingen, Germany
BestMasters
ISBN 978-3-658-12054-2 ISBN 978-3-658-12055-9 (eBook)
DOI 10.1007/978-3-658-12055-9
Library of Congress Control Number: 2015955646
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Contents
ListofFigures VII
ListofSymbols IX
1 Introduction 1
2 AnIntroductiontoEconomicGrowthTheoryandtheOilMarket 3
3 TheDasgupta-HealModel 11
3.1 AClosed-FormSolution . . . . . . . . . . . . . . . . . . . . . . 20
3.2 CriticalAssessment . . . . . . . . . . . . . . . . . . . . . . . . . 21
4 RecyclingasaSourceofRegeneration 25
4.1 TheEconomicSystemandtheEnvironment . . . . . . . . . . . . 27
4.2 RecyclingUnderaMaterialBalanceConstraint . . . . . . . . . . 29
4.3 IncompleteRecycling . . . . . . . . . . . . . . . . . . . . . . . . 34
5 TechnologicalProgress 37
5.1 ExogenousTechnologicalProgress . . . . . . . . . . . . . . . . 39
5.2 UncertainTechnologicalProgress . . . . . . . . . . . . . . . . . 45
5.3 TheKamien-SchwartzModel . . . . . . . . . . . . . . . . . . . . 52
6 DiscussionandConclusions 67
VI Contents
Appendix:ASketchofSolutions
A TheDasgupta-HealModel 71
A.1 StarvationofMankind . . . . . . . . . . . . . . . . . . . . . . . 74
A.2 PhaseDiagram . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
B AClosed-formSolutionoftheDasgupta-HealModel 79
C RecyclingUnderaMaterialBalanceConstraint 83
C.1 Long-runEquilibriumoftheEconomy . . . . . . . . . . . . . . . 86
D ExogenousTechnologicalProgress 89
D.1 PhaseDiagram . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
E UncertainTechnologicalProgress 97
E.1 ACertaintyEquivalentSolution . . . . . . . . . . . . . . . . . . 101
F TheKamien-SchwartzModel 103
F.1 PhaseDiagram . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
F.2 ConditionalProbabilityofCompletion . . . . . . . . . . . . . . . 110
References 113
ListofFigures
2.1 RealPriceofOil,1861-2015 . . . . . . . . . . . . . . . . . . . . 4
2.2 GrowthForecastfromtheLimitstoGrowth . . . . . . . . . . . . 6
2.3 GlobalUsageofOil . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 NetDifferenceBetweenAnnualReservesAdditionsandAnnual
Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1 CIESUtilityFunctions . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 ConsumptionPath. . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Dasgupta-Heal:PhaseDiagraminC/K-F/K Space . . . . . . . . 19
3.4 BehaviorofCapital,Output,andConsumption . . . . . . . . . . 21
4.1 TheEconomicSystemandtheEnvironment . . . . . . . . . . . . 28
5.1 ExogenousTechnologicalProgress:PhaseDiagraminC/K-F/K
Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.2 Exogenous Technological Progress: Phase Diagram inC/K−V
Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.3 ConsumptionPathOverTimeinCaseofaBackstop-Technology . 51
5.4 BehaviorofC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.5 Behaviorofm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.6 TimePatternforF ≤rhoatt =0andt >0 . . . . . . . . . . 62
K m m
5.7 OptimalPathfortheCaseofF ≤rhoatt >0 . . . . . . . . . . . 63
K m
VIII ListofFigures
5.8 Temporal Pattern for F > ρ at t , When Consumption Peaks
K m
BeforeR&DEffort . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.9 TemporalPatternforF >ρ att ,WhenR&DEffortPeaksBefore
K m
Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
ListofSymbols
A Technologicalprogressparameter
C Consumption
c Consumptioninefficiencyunits
c˜ Consumptioninefficiencyunitsadjustedbytheresourceinput
D Stockofwaste
F(·) Productiontechnology
F Marginalproductofcapital
K
F Marginalproductoftheexhaustibleresource
R
g Growthrate
H Hamiltonianoperator
h(z) Conditionalprobabilityofcompletion
I Investment
J Flowofsecondarymaterialinput(recyclableresource)
K Capital
k Capitalinefficiencyunits
k˜ Capitalinefficiencyunitsadjustedbyresourceinput
L Labor
MRS Marginalrateofsubstitution
m EffortinR&D
N Constantextractionofthedurablecommodity
P(·) Alternativeproductiontechnology
Q Inventoryofthedurablecommodity
