A complete characterization of equilibrium paths in a labour-less two-sector model of optimal growth

Guerrazzi, Marco (2025): A complete characterization of equilibrium paths in a labour-less two-sector model of optimal growth.

Abstract

In this paper, I develop a two-sector growth model in which the output of each industry is obtained only by means of capital. From a theoretical perspective, this setting reveals that the determinacy of the equilibrium path is possible even when the production technology available in the industry of consumption goods is not necessarily convex. Moreover, form a numerical point of view, I show that whenever the first-best solution of the model is tailored on the US economy, such a theoretical framework relaxes the complementarity between the propensities to consume and to save and it is also consistent with the observed countercyclical pattern of the relative price of capital goods.

• Item Type: MPRA Paper
• Language: English
• Keywords: Capital accumulation; Investment; Consumption; Two-sector growth model; Relative price of capital goods.
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E21 - Consumption ; Saving ; Wealth; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E22 - Investment ; Capital ; Intangible Capital ; Capacity; O - Economic Development, Innovation, Technological Change, and Growth > O1 - Economic Development > O11 - Macroeconomic Analyses of Economic Development

References

Benhabib, J., Farmer, R. E. A. (1996), Indeterminacy and Sector-Specific Externalities, Journal of Monetary Economics, Vol. 37, No. 3, pp. 421-442.

Benhabib, J., Farmer, R. E. A. (1994), Indeterminacy and Increasing Returns, Journal of Economic Theory, Vol. 63, No. 1, pp. 19-41.

Benhabib, J., Nishimura, K. (1998), Indeterminacy and Sunspots with Constant Returns, Journal of Economic Theory, Vol. 81, No. 1, pp. 58-96.

Cai, D. (2006), A Two-Sector Economic Growth Model with Optimal Labor and Capital Allocation, Applied Mathematics and Computation, Vol. 183, No. 2, pp. 1359-1377.

Cass, D. (1965), Optimum Growth in an Aggregative Model of Capital Accumulation, Review of Economic Studies, Vol. 32, No. 3, pp. 233-240.

Christiano, L. J., Fisher, J. D. M. (2003), Stock Market and Investment Goods Prices: Implications for Macroeconomics, NBER Working Paper Series, No. 10031.

Collins, W. J., Williamson, J. G. (2001), Capital-Goods Prices and Investment, 1870-1950, Journal of Economic History, Vol. 61, No. 1, pp. 59-94.

Ferreira, P. C., de Abreu Pessoa, A., Veloso, F. A. (2014), Distortions in the Investment Goods Sector and Productivity Decline, FGV EPGE Economics Working Papers, No. 755.

Fisher, J. D. M. (2006), The Dynamic Effects of Neutral and Investment-Specific Technology Shocks, Journal of Political Economy, Vol. 114, No. 3, pp. 413-451.

Harrison, S. H., Weder, M. (2002), Tracing Externalities as a Source of Indeterminacy, Journal of Economic Dynamics & Control, Vol. 26, No. 5, pp. 851-867.

Hergovich, P., Merz, M. (2018), The Price of Capital, Factor Substitutability, and Corporate Profits, IZA Discussion Papers, No. 11791.

Gabisch, G. (1973), Optimal Growth in the Two-Sector Neoclassical Growth Model, Journal of Economics - Zeitschrift für Nationalökonomie, Vol. 33, pp. 419-426.

Growiec, J. (2022), Automation, Partial and Full, Macroeconomic Dynamics, Vol. 26, No. 7, pp. 1731-1755.

Guerrazzi, M., Candido, G. (2025), The Determination of the Price of Capital Goods: A Differential Game Approach, Managerial and Decision Economics, Vol. 46, No. 1, pp. 222-234.

Hahn, F. H. (1965), On Two Sector Growth Models, Review of Economic Studies, Vol. 32, No. 4, pp. 339-346.

Hashimoto, H., Sakuragawa, M. (1999), A Characterization of the Dynamical System in a Two-Sector Overlapping-Generations Model: The Case of Unbounded Growth, Japanese Economic Review, Vol. 50, No. 2, pp. 138-147.

Hornstein, A., Prashinick, J. (1997), Intermediate Inputs and Sectoral Comovement in the Business Cycle, Journal of Monetary Economics, Vol. 40, No. 3, pp. 573-595.

Itskhoki, O., Moll, B. (2019), Optimal Development Policies with Financial Frictions, Econometrica, Vol 87, No. 1, pp. 139-173.

Justiniano, A., Primiceri, G. E., Tambalotti, A. (2011), Investment Shocks and the Relative Price of Investment, Review of Economic Dynamics, Vol. 14, No. 1, pp. 102-121.

Kydland, F. E., Prescott, E. C. (1982), Time to Build and Aggregate Fluctuations, Econometrica, Vol. 50, No. 6, pp. 1345-1370.

Lian, W., Novta, N., Pugacheva, E., Timmer, Y., Topalova, P. (2020), The Price of Capital Goods: A Driver of Investment Under Threat, IMF Economic Review, Vol. 68, No. 3, pp. 509-549.

Matsuo, M., Nishimura, K., Sakagami, T., Venditti, A. (2008), Characterization of Equilibrium Paths in a Two-Sector Economy with CES Production Functions and Sector-Specific Externality, HAL Working Papers, No. 00281642.

Meade, J. E. (1961), A Neo-Classical Theory of Economic Growth, London: Allen & Unwin.

Restuccia, D., Urrutia, C. (2001), Relative Prices and Investment Rates, Journal of Monetary Economics, Vol. 47, No. 1, pp. 93-121.

Senouci, M. (2011), Optimal Growth and the Golden Rule in a Two-Sector Model of Capital Accumulation, PSE Working Papers, No. 00572510.

Shell, K. (1966), Comparative Statics for the Two-Sector Model, Metroeconomica, Vol. 18, No. 2, pp. 117-124.

Uzawa, H. (1964), Optimal Growth in a Two-Sector Model of Capital Accumulation, Review of Economic Studies, Vol. 31, No. 1, pp. 1-24.

Uzawa, H. (1961), On a Two-Sector Model of Economic Growth, Review of Economic Studies, Vol. 29, No. 1, pp. 40-47.

Venditti, A. (2005), The Two Sector Overlapping Generations Model: A Simple Formulation, Research in Economics, Vol. 59, No. 2, pp. 164-188.

Zhang, W-B. (2005), A Two-Sector Model with Labour Supply, Australian Journal of Labour Economics, Vol. 8, No. 3, pp. 245-260.