*W. M. Gorman*

*C. Blackorby and A. F. Shorrocks (eds)*

- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198285212
- eISBN:
- 9780191596322
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198285213.003.0018
- Subject:
- Economics and Finance, Microeconomics

This is an unpublished paper on the problem of capital aggregation in vintage models, which was presented at the First World Congress of the Econometric Society in Rome in 1965. At the beginning of ...
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This is an unpublished paper on the problem of capital aggregation in vintage models, which was presented at the First World Congress of the Econometric Society in Rome in 1965. At the beginning of his investigation, Gorman set out the problem in the primal with constant‐returns‐to‐scale technologies, but after some work he recognized that the solution is related to a concept that he had encountered in differential geometry––the edge of regression, and this led him to reformulate the problem in the dual. The Appendix contains a very detailed treatment of duality and the relationship between production functions and profit functions (Gorman uses the negative of the profit function, which he calls the loss function. Theorem 1 (in the Appendix) is a general equivalence between production and profit functions, while Theorem 2 extends this to production functions with fixed factors and gross profit functions; this leaves, as is usual in these arguments, a certain asymmetry in the duality, as quantities are usually non‐negative whereas prices are positive. Theorem 3 uses a boundedness assumption to establish a full duality.Less

This is an unpublished paper on the problem of capital aggregation in vintage models, which was presented at the First World Congress of the Econometric Society in Rome in 1965. At the beginning of his investigation, Gorman set out the problem in the primal with constant‐returns‐to‐scale technologies, but after some work he recognized that the solution is related to a concept that he had encountered in differential geometry––the edge of regression, and this led him to reformulate the problem in the dual. The Appendix contains a very detailed treatment of duality and the relationship between production functions and profit functions (Gorman uses the negative of the profit function, which he calls the loss function. Theorem 1 (in the Appendix) is a general equivalence between production and profit functions, while Theorem 2 extends this to production functions with fixed factors and gross profit functions; this leaves, as is usual in these arguments, a certain asymmetry in the duality, as quantities are usually non‐negative whereas prices are positive. Theorem 3 uses a boundedness assumption to establish a full duality.

*W. M. Gorman*

*C. Blackorby and A. F. Shorrocks (eds)*

- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198285212
- eISBN:
- 9780191596322
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198285213.003.0019
- Subject:
- Economics and Finance, Microeconomics

This paper appeared in the Hicks Festschrift in 1968 (Value, Capital and Growth: Essays in Honour of Sir John Hicks, ed. J. N. Wolfe. Edinburgh: Edinburgh University Press). It is a substantial ...
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This paper appeared in the Hicks Festschrift in 1968 (Value, Capital and Growth: Essays in Honour of Sir John Hicks, ed. J. N. Wolfe. Edinburgh: Edinburgh University Press). It is a substantial generalization of ’Capital aggregation in vintage models’ (Ch. 18) and is mathematically somewhat more elegant. This time the problem is posed in terms of gross profit functions and technology sets. In addition, the problem is solved for arbitrary numbers of aggregates––a problem only touched upon in Ch. 18.Less

This paper appeared in the Hicks Festschrift in 1968 (*Value, Capital and Growth: Essays in Honour of Sir John Hicks*, ed. J. N. Wolfe. Edinburgh: Edinburgh University Press). It is a substantial generalization of ’Capital aggregation in vintage models’ (Ch. 18) and is mathematically somewhat more elegant. This time the problem is posed in terms of gross profit functions and technology sets. In addition, the problem is solved for arbitrary numbers of aggregates––a problem only touched upon in Ch. 18.

*W. M. Gorman*

*C. Blackorby and A. F. Shorrocks (eds)*

- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198285212
- eISBN:
- 9780191596322
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198285213.003.0021
- Subject:
- Economics and Finance, Microeconomics

This paper was published in 1990 in Measurement and Modelling in Economics (ed. G. D. Myles. Amsterdam: North Holland), and in many ways is the culmination of Gorman's aggregation project, which ...
More

This paper was published in 1990 in Measurement and Modelling in Economics (ed. G. D. Myles. Amsterdam: North Holland), and in many ways is the culmination of Gorman's aggregation project, which began in 1953. The problem is cast as a capital aggregation problem, but can also be used in other contexts (labour, food). This time the aggregation question concerns the existence of a set of aggregates, where each aggregate can, in principle, depend upon all types of capital. The discussion in Sect. 1 is cast in terms of fixed factors and profit functions, and with appropriate changes can also be applied to vector social welfare, vector income measures, and so on. Sect. 2 performs the same exercise on net supply functions, Sect. 3 considers the case in which the aggregates are independent of prices, Sect. 4 presents an alternative characterization of the solution, and Sect. 5 presents an argument permitting the functions to be converted to partial derivatives; three appendices address further issues.Less

This paper was published in 1990 in *Measurement and Modelling in Economics* (ed. G. D. Myles. Amsterdam: North Holland), and in many ways is the culmination of Gorman's aggregation project, which began in 1953. The problem is cast as a capital aggregation problem, but can also be used in other contexts (labour, food). This time the aggregation question concerns the existence of a set of aggregates, where each aggregate can, in principle, depend upon all types of capital. The discussion in Sect. 1 is cast in terms of fixed factors and profit functions, and with appropriate changes can also be applied to vector social welfare, vector income measures, and so on. Sect. 2 performs the same exercise on net supply functions, Sect. 3 considers the case in which the aggregates are independent of prices, Sect. 4 presents an alternative characterization of the solution, and Sect. 5 presents an argument permitting the functions to be converted to partial derivatives; three appendices address further issues.