*Francesco Caselli*

- Published in print:
- 2016
- Published Online:
- January 2018
- ISBN:
- 9780691146027
- eISBN:
- 9781400883608
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691146027.003.0004
- Subject:
- Economics and Finance, Development, Growth, and Environmental

This chapter examines the efficiency with which the aggregate labor input and, respectively, the aggregate capital input are used in production. To this end, it uses an equation that takes into ...
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This chapter examines the efficiency with which the aggregate labor input and, respectively, the aggregate capital input are used in production. To this end, it uses an equation that takes into account coefficients that operate as augmentation coefficients for “natural capital equivalents,” that is, the capital input expressed in efficiency units of natural capital, and “unskilled-labor equivalents,” or the labor input in efficiency units of unskilled labor. After inferring augmentation coefficients for labor and capital, the chapter estimates variable capital shares and introduces a broader measure of labor inputs. The results reveal an imperfect elasticity of substitution between natural and reproducible capital.Less

This chapter examines the efficiency with which the aggregate labor input and, respectively, the aggregate capital input are used in production. To this end, it uses an equation that takes into account coefficients that operate as augmentation coefficients for “natural capital equivalents,” that is, the capital input expressed in efficiency units of natural capital, and “unskilled-labor equivalents,” or the labor input in efficiency units of unskilled labor. After inferring augmentation coefficients for labor and capital, the chapter estimates variable capital shares and introduces a broader measure of labor inputs. The results reveal an imperfect elasticity of substitution between natural and reproducible capital.

*Neil Tennant*

- Published in print:
- 2017
- Published Online:
- October 2017
- ISBN:
- 9780198777892
- eISBN:
- 9780191823367
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198777892.003.0010
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Ironically Anderson and Belnap argue for the rejection of Disjunctive Syllogism by means of an argument that appears to employ it. We aim to establish a ‘variable-sharing’ result for Classical Core ...
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Ironically Anderson and Belnap argue for the rejection of Disjunctive Syllogism by means of an argument that appears to employ it. We aim to establish a ‘variable-sharing’ result for Classical Core Logic that is stronger than any such result for any other system. We define an exigent relevance condition R(X,A) on the premise-set X and the conclusion A of any proof, exploiting positive and negative occurrences of subformulae. This treatment includes first-order proofs. Our main result on relevance is that for every proof of A from X in Classical Core Logic, we have R(X,A). R(X,A) is a best possible explication of the sought notion of relevance. Our result is optimal, and challenges relevantists in the Anderson–Belnap tradition to identify any strengthening of the relation R(X,A) that can be shown to hold for some subsystem of Anderson–Belnap R but that can be shown to fail for Classical Core Logic.Less

Ironically Anderson and Belnap argue for the rejection of Disjunctive Syllogism by means of an argument that appears to employ it. We aim to establish a ‘variable-sharing’ result for Classical Core Logic that is stronger than any such result for any other system. We define an exigent relevance condition R(X,A) on the premise-set X and the conclusion A of any proof, exploiting positive and negative occurrences of subformulae. This treatment includes first-order proofs. Our main result on relevance is that for every proof of A from X in Classical Core Logic, we have R(X,A). R(X,A) is a best possible explication of the sought notion of relevance. Our result is optimal, and challenges relevantists in the Anderson–Belnap tradition to identify any strengthening of the relation R(X,A) that can be shown to hold for some subsystem of Anderson–Belnap **R** but that can be shown to fail for Classical Core Logic.