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By Prof. Dr. Horst Siebert (auth.)

ISBN-10: 3662031272

ISBN-13: 9783662031278

ISBN-10: 3662031299

ISBN-13: 9783662031292

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Additional resources for Economics of the Environment: Theory and Policy

Sample text

Only if the product of the cross derivatives as defined in Eq. 7 is smaller than the product of the derivatives as defined in Eq. 6, will the transformation function be concave. The Arrow-Enthoven theorem makes less stringent demands for the existence of a global maximum. 2 The A. C. Chiang, Fundamental Methods oj Mathematical Economics, 3rd ed. (New York: McGraw-Hill, 1984). 2 Production Theory and Transformation Space 41 production, abatement, and damage functions are concave and thereby quasiconcave too.

In order to develop our argument, we first characterize the competitive equilibrium. In a second step, we have to relate optimal allocation to competitive equilibrium. 5 4 Rewrite Eq. F' = WfFj +H,FjAs AQ2F2 W{F2+H2F2 AS On a general equilibrium with explicit consideration of the environment also compare DudenhOffer (1983), Maler (1985) and Pethig (1979). 5 Optimal Environmental Use 53 Competitive Equilibrium A competitive equilibrium is defined as an allocation A and a price vector P so that for [A, P] 1.

An alternative (more intuitive) approach for verifying the concavity of U = ¢J (QI, Q2) runs as follows. The transformation space U = ¢J (QI, Q2) is concave if every restriction is concave. The production, abatement, and damage functions are concave. The resource restriction is linear and hence concave (and convex). The emission function is linear for Hi' = 0 (and thus concave and convex). If we assume that H/, = 0, the transformation space U = ¢J (QI, Q2) is concave because all single restrictions which define it are concave.

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Economics of the Environment: Theory and Policy by Prof. Dr. Horst Siebert (auth.)

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