Abstract
This paper presents the mathematical and computational details which provide the bases of a new methodology for production analysis, void of the standard but empirically dubious assumptions of production theory, but able to assess the level and the evolution of intra-industry heterogeneity and to measure industry and firm-level productivity change. In particular, in this work, we show how geometry can be an effective tool to tackle some relevant issues in economics and how, with new computational methods, it is possible to switch from continuous models to discrete ones, the latter requiring a much smaller set of assumptions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
The interested reader can refer to Ziegler (1995) for a survey on Zonotopes.
References
Baily MN, Hulten C, Campbell D (1992) Productivity dynamics in manufacturing establishments. Brook Pap Econ Act Microecon 4:187–249
Baldwin E, Klemperer P (2015) Understanding preferences: “demand types”, and the existence of equilibrium with indivisibilities. http://www.nuff.ox.ac.uk/users/klemperer/tropical.pdf. Accessed 18 June 2015
Baldwin JR, Rafiquzzaman M (1995) Selection versus evolutionary adaptation: learning and post-entry performance. Int J Ind Org 13(4):501–522
Bartelsman EJ, Doms M (2000) Understanding productivity: lessons from longitudinal microdata. J Econ Lit 38(2):569–594
Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2:429–444
Daraio C, Simar L (2007) Conditional nonparametric frontier models for convex and nonconvex technologies: a unifying approach. J Prod Anal 28(1):13–32
Dosi G (2007) Statistical regularities in the evolution of industries. a guide through some evidence and challenges for the theory. In: Malerba F, Brusoni S (eds) Perspectives on innovation. Cambridge University Press, Cambridge
Dosi G (2004) A very reasonable objective still beyond our reach: Economics as an empirically disciplined social science. In: Augier M, March JG (eds) Models of a man, essays in memory of Herbert A. MIT Press, Simon
Dosi G, Grazzi M, Tomasi C, Zeli A (2012) Turbulence underneath the big calm? The micro-evidence behind Italian productivity dynamics. Small Bus Econ 39(4):1043–1067
Dosi G, Grazzi M, Marengo L, Settepanella S (2013) Production theory: accounting for firm heterogeneity and technical change. LEM working paper no. 22
Farrell MJ (1957) The measurement of productive efficiency. J R Stat Soc Ser A (Gen) 120(3):253–290
Hildenbrand W (1981) Short-run production functions based on microdata. Econometrica 49(5):1095–1125
Koopmans TC (1977) Examples of production relations based on microdata. In: Harcour GC (ed) The Microeconomic foundations of macroeconomics. Macmillan Press, London
Koshevoy G (1995) Multivariate lorenz majorization. Soc Choice Welf 12:93–102
Koshevoy G (1998) The lorenz zonotope and multivariate majorizations. Soc Choice Welf 15:1–14
Savaglio E (2002) Multidimensional inequality: a survey. U of Siena, economics working paper no. 362
Schmedders K, Renner PJ (2015) A polynomial optimization approach to principal-agent problems. Econometrica 83(2):729–769
Shiozawa Y (2015) Trade theory and exotic algebra. Evolut Inst Econ Rev 12
Simar L, Zelenyuk V (2011) Stochastic FDH/DEA estimators for frontier analysis. J Prod Anal 36(1):1–20
Syverson C (2011) What determines productivity? J Econ Lit 49(2):326–65
Tran NM (2015) The perron-rank family. Evolut Inst Econ Rev 12
Ziegler GM (1995) Lectures on polytopes. In: Graduate texts in mathematics. Springer, Berlin
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Settepanella, S., Dosi, G., Grazzi, M. et al. A discrete geometric approach to heterogeneity and production theory. Evolut Inst Econ Rev 12, 223–234 (2015). https://doi.org/10.1007/s40844-015-0014-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40844-015-0014-1