Battle for Climate and Scarcity Rents: Beyond the Linear-Quadratic Case

33 Pages Posted: 5 Nov 2014

See all articles by Mark Kagan

Mark Kagan

VU University Amsterdam

Rick van der Ploeg

University of Oxford

Cees Withagen

Free University of Amsterdam; Tilburg University

Date Written: October 24, 2014


The nature of oil demand influences the oil extraction rate and hence has implications for both the timing of oil exhaustion and optimal climate policy. We analyse what role oil demand specification plays in strategic interactions b between an oil-importing country producing final goods and wishing to mitigate global warming (Industria) and an oil-exporting country (Oilrabia) who buys final goods from the other country. Industria uses the carbon tax to impose an import tariff on oil and steal some of Oilrabia’s scarcity rent. We derive subgame-perfect and open-loop Nash equilibrium outcomes and obtain results about the relative speeds of oil extraction and carbon accumulation and compare these with the efficient and competitive outcomes. We show that for the most typical demand functions, open-loop oil price will always be initially higher resulting in delayed extraction. However, we demonstrate that for certain more complex demand specification, Oilrabia has an incentive to initially price oil lower than the efficient level, resulting in more oil extraction and more climate damages. We further show that using the carbon tax as a tariff may not be as beneficial as suggested by previous studies. For certain demand functions, Industria sets the tariff too high leading to a decrease in the consumers welfare that isn’t compensated by the higher tariff revenues.

Keywords: exhaustible resources, Hotelling rule, efficiency, carbon tax, climate rent, differential game, subgame-perfect Nash equilibrium

JEL Classification: C730, H300, Q320, Q370, Q540

Suggested Citation

Kagan, Mark and van der Ploeg, Frederick and Withagen, Cees A. M., Battle for Climate and Scarcity Rents: Beyond the Linear-Quadratic Case (October 24, 2014). CESifo Working Paper Series No. 5041. Available at SSRN:

Mark Kagan

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV

Frederick Van der Ploeg

University of Oxford ( email )

Manor Road Building
Manor Road
Oxford, OX1 3BJ
United Kingdom

Cees A. M. Withagen (Contact Author)

Free University of Amsterdam ( email )

Tinbergen Institute De Boelelaan 1105
1081 HV Amsterdam

Tilburg University ( email )

Postbus 90153
Tilburg, DC Noord-Brabant 5000 LE

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