Abstract
Input-output (Leontief) production function is widely used in economic analysis. And diminishing marginal rate of return is a very well accepted economic fact. Leontief production function normally results in a linear production possibility frontier (PPF) due to its linear feature, whereas diminishing marginal rate of return implies a non-linear PPF. In this paper, the authors aim to fix this problem by considering multiple primary inputs in a simplified two-sector economy. The authors find that it is possible to curve a non-linear PPF by using Leontief production function when the authors add heterogeneous primary inputs. The authors also discuss the PPF using non-linear production function. Furthermore, the authors propose that three commonly used economic presumptions cannot hold in the same framework. These presumptions are “single primary input”, “fixed-proportion inputs” and “law of diminishing marginal returns”.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barthwal R, Industrial Economies: An Introductory Textbook, 3rd Edition, New Age International, 2010.
Anderson D A, Cracking the AP Economics Macro & Micro Exams, Vol. 9, Princeton Review, 2009.
Hall R E and Lieberman M, Macroeconomics: Principles and Applications, 6th Edition, Longman, 1989.
Brooke M Z and Buckley P J, Handbook of International Trade, Springer, New York, 2016.
Dorfman R, Samuelson P A, and Solow R M, Linear Programming and Economic Analysis, Dover Publications, New York, 1987.
Jones C I, Misallocation, economic growth, and input-output economics, NBER Working Paper No. 16742, National Bureau of Economic Research, 2011.
Acemoglu D, Introduction to Modern Economic Growth, Princeton University Press, Princeton, 2008.
Ljungqvist L and Sargent T J, Recursive Macroeconomic Theory, MIT Press, Massachusetts, US, 2018.
Arrow K J, Alternative proof of the substitution theorem for Leontief models in the general case, Activity Analysis of Production and Allocation, Ed. by Koopmans T C, Wiley, 1951, 155–164.
Koopmans T C, Alternative proof of the substitution theorem for Leontief models in the case of three industries, Activity Analysis of Production and Allocation, Ed. by Koopmans T C, Wiley, 1951, 147–154.
Levhari D, A Nonsubstitution theorem and switching of techniques, Quarterly Journal of Economics, 1965, 79(1): 98–105.
Samuelson P A, Abstract of a theorem concerning substitutability in open Leontief models, Activity Analysis of Production Allocation, 1951, 13: 142–146.
Stiglitz J E, Non-substitution theorems with durable capital goods, The Review of Economic Studies, 1970, 37(4): 543–553.
Jones C I, Intermediate goods and weak links in the theory of economic development, American Economic Journal: Macroeconomics, 2011, 3(2): 1–28.
Acknowledgements
The authors would like to thank Prof. Geoffrey J. D. Hewings, University of Illinois, Urbana, USA and Prof. Yang Cuihong, Chinese Academy of Sciences, for their useful comments. Of course, the authors are entirely responsible for all the remaining errors.
Author information
Authors and Affiliations
Corresponding author
Additional information
This paper was supported by China Postdoctoral Science Foundation under Grant No. 2020M671504, the National Social Science Foundation of China under Grant No. 14AZD085, and the National Natural Science Foundation of China under Grant Nos. 71373106, 71903186.
This paper was recommended for publication by Editor YANG Cuihong.
Rights and permissions
About this article
Cite this article
Jiang, W., Fan, J. & Tian, K. Input-Output Production Structure and Non-Linear Production Possibility Frontier. J Syst Sci Complex 34, 706–723 (2021). https://doi.org/10.1007/s11424-020-9079-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11424-020-9079-y