*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This is an unpublished paper on the problem of capital aggregation in vintage models, which was presented at the First World Congress of the Econometric Society in Rome in 1965.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This is an unpublished paper on the problem of capital aggregation in vintage models, which was presented at the First World Congress of the Econometric Society in Rome in 1965.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This is an unpublished paper on the problem of capital aggregation in vintage models, which was presented at the First World Congress of the Econometric Society in Rome in 1965.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.

*Michael J. Harper*

- Published in print:
- 2007
- Published Online:
- February 2013
- ISBN:
- 9780226044491
- eISBN:
- 9780226044507
- Item type:
- chapter

- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226044507.003.0005
- Subject:
- Economics and Finance, Microeconomics

This chapter reexamines a well-known and conceptually difficult aspect of the vintage asset problem: the aggregation of different technological vintages of capital. The chapter is organized as ...
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This chapter reexamines a well-known and conceptually difficult aspect of the vintage asset problem: the aggregation of different technological vintages of capital. The chapter is organized as follows. Section 4.2 reviews relevant material on models of production, capital measurement, and quality adjustment. Section 4.3 develops a “model of production with machines”, in which the Solow vintage model is extended to individual machines. This machine model permits clearer definitions of key concepts such as deterioration and embodied and disembodied technical change. The machine model predicts that older vintages are preferentially discarded during a cyclical downturn. This realistic behavior is inconsistent with what is assumed in capital stock calculations. Section 4.4 examines the machine model in nominal terms. Section 4.5 considers the idea of real capital input. The machine model is used to clarify previous discussions of what the marginal product of capital is—the added output obtained from a collection of machines by adding one machine (not a machine hour) and without adding any labor. Section 4.6 discusses how quality adjustments to capital inputs could be overstated.Less

This chapter reexamines a well-known and conceptually difficult aspect of the vintage asset problem: the aggregation of different technological vintages of capital. The chapter is organized as follows. Section 4.2 reviews relevant material on models of production, capital measurement, and quality adjustment. Section 4.3 develops a “model of production with machines”, in which the Solow vintage model is extended to individual machines. This machine model permits clearer definitions of key concepts such as deterioration and embodied and disembodied technical change. The machine model predicts that older vintages are preferentially discarded during a cyclical downturn. This realistic behavior is inconsistent with what is assumed in capital stock calculations. Section 4.4 examines the machine model in nominal terms. Section 4.5 considers the idea of real capital input. The machine model is used to clarify previous discussions of what the marginal product of capital is—the added output obtained from a collection of machines by adding one machine (not a machine hour) and without adding any labor. Section 4.6 discusses how quality adjustments to capital inputs could be overstated.