Estrategias de inversión y acumulación de capital en horizonte infinito: Enfoque de control óptimo en tiempo continuo
Abstract
El objetivo general de la presente investigación es analizar la trayectoria óptima de inversión y acumulación de capital en horizonte infinito, bajo un enfoque teórico–analítico sustentado en la teoría del control óptimo en tiempo continuo y en los principios de la programación dinámica. El modelo de crecimiento con externalidades de capital físico muestra que la acumulación de capital de cada firma no solo incrementa su propia producción, sino que genera derrames positivos sobre la productividad del resto de la economía, de modo que, cuando a nivel agregado se cumple que la suma entre la elasticidad privada del capital y la intensidad de la externalidad es igual o superior a uno, la tecnología efectiva se aproxima a un esquema tipo AK con rendimientos constantes o crecientes al factor acumulable y desaparece el estado estacionario neoclásico típico del modelo de Solow. Este modelo aporta a los estudios relacionados con los modelos de crecimiento endógeno y explica por qué la acumulación de capital genera crecimiento sostenido sin tecnología exógena dominante. Se concluye que la investigación respalda la aplicación de subsidios a la inversión, incentivos a la acumulación de capital, y de transformaciones institucionales que promueven la asimilación parcial de esos beneficios externos.
Downloads
Download data is not yet available.
References
Agusalim, L., Anggraeni, L., y Pasaribu, S. H. (2022). The economy of Indonesia: Driven by physical or human capital? JEJAK: Journal of Economics and Policy, 15(1), 10-28. https://doi.org/10.15294/jejak.v15i1.34418
Akalpler, E., y Adil, H. (2017). The impact of foreign direct investment on economic growth in Singapore between 1980 and 2014. Eurasian Economic Review, 7, 435-450. https://doi.org/10.1007/s40822-017-0071-3
Ali, S., Chaudhry, I. S., y Farooq, F. (2012). Human capital formation and economic growth in Pakistan. Pakistan Journal of Social Sciences, 32(1), 229-240. https://pjss.bzu.edu.pk/index.php/pjss/article/view/147
Amir-ud-Din, R., Usman, M., Abbas, F., y Javed, S. A. (2019). Human versus physical capital: issues of accumulation, interaction and endogeneity. Economic Change and Restructuring, 52, 351-382. https://doi.org/10.1007/s10644-017-9225-2
Barro, R. J., y SalaiMartin, X. (2004). Economic Growth. The MIT Press.
Boamah, J., Adongo, F. A., Essieku, R., y Lewis, J. A. (2018). Financial depth, gross fixed capital formation and economic growth: Empirical analysis of 18 Asian economies. International Journal of Scientific and Education Research, 2(4), 120-130. http://dx.doi.org/10.2139/ssrn.3424688
Chi, W. (2008). The role of human capital in China’s economic development: Review and new evidence. China Economic Review, 19(3), 421-436. https://doi.org/10.1016/j.chieco.2007.12.001
Chiang, A. C., y Wainwright, K. (2006). Métodos fundamentales de economía matemática. McGraw-Hill/ Interamericana Editores S.A. de C.V.
Dawood, S. S., Haidar, B. K., y Ghazi, M. (2024). The effect of fixed capital formation rate on gross domestic product in Iraq. Public and Municipal Finance, 13(2), 56-69.http://dx.doi.org/10.21511/pmf.13(2).2024.06
Galor, O., y Moav, O. (2004). From physical to human capital accumulation: Inequality and the process of development. Review of Economic Studies, 71(4), 1001-1026. https://doi.org/10.1111/0034-6527.00312
Ghosh, S. (2019). Foreign direct investment, female education, capital formation, and economic growth in Japan and South Korea. International Economic Journal, 33(3), 509-536. https://doi.org/10.1080/10168737.2019.1600155
Gibescu, O. (2010). Does the gross fixed capital formation represent a factor for supporting the economic growth? MPRA Paper No. 50135. https://mpra.ub.uni-muenchen.de/50135/1/MPRA_paper_50135.pdf
Greiner, A., y Semmler, W. (2002). Externalities of investment, education and economic growth. Economic Modelling, 19(5), 709-724. https://doi.org/10.1016/S0264-9993(01)00076-1
Inada, K.-I. (1963). On a two-sector model of economic growth: Comments and a generalization. The Review of Economic Studies, 30(2), 119-127. https://doi.org/10.2307/2295809
Khatoon Ali, R., Javed, I., y Hayat, M. M. (2021). Impact of human capital on economic growth: A case study of Pakistan. Journal of Social Sciences Advancement, 2(2), 64-69. https://doi.org/10.52223/JSSA21-020202-15
Kuznets, S., y Jenks, E. (1961). Capital in the American economy; its function and Financing. Princeton University Press.
Labarca, N. J., y Panchana, A. M. (2022). Crecimiento económico en América Latina: Algunos determinantes desde la perspectiva austriaca. Revista de Ciencias Sociales (Ve), XXVIII(1), 216-233. https://doi.org/10.31876/rcs.v28i1.37686
Li, Y., Wang, X., Westlund, H., y Liu, Y. (2015). Physical capital, human capital, and social capital: The Changing Roles in China’s Economic Growth. Growth Change, 46(1), 133-149. https://doi.org/10.1111/grow.12084
Lucas, R. E. (1988). On the mechanics of economic development. Journal of Monetary Economics, 22(1), 3-42. https://doi.org/10.1016/0304-3932(88)90168-7
Mankiw, N. G., Romer, D., y Weil, D. N. (1992). A contribution to the empirics of economic growth. Quarterly Journal of Economics, 107(2), 407-437. https://eml.berkeley.edu/~dromer/papers/MRW_QJE1992.pdf
Meyer, D. F., y Sanusi, K. A. (2019). A causality analysis of the relationships between gross fixed capital formation, economic growth and employment in South Africa. Studia Universitatis Babeș-Bolyai Oeconomica, 64(1), 33-44. https://doi.org/10.2478/subboec-2019-0003
Oyinlola, M. A., Adedeji, A. A., y Onitekun, O. (2021). Human capital, innovation, and inclusive growth in sub-Saharan Africa Region. Economic Analysis and Policy, 72, 609-625.https://doi.org/10.1016/j.eap.2021.10.003
Pomi, S. S., Sarkar, S. M., y Dhar, B. K. (2021). Human or physical capital, which influences sustainable economic growth most? A study on Bangladesh. Canadian Journal of Business and Information Studies, 3(5), 101-108. https://doi.org/10.34104/cjbis.021.01010108
Raheem, I., Isah, K., y Adedeji, A. (2018). Inclusive growth, human capital development and natural resource rent in SSA. Economic Change and Restructuring, 51(1), 29-48. https://doi.org/10.1111/joes.12211
Rani, R., y Kumar, N. (2019). Panel data analysis of financial development, trade openness, and economic growth: Evidence from BRICS countries. Emerging Economy Studies, 4(1), 1-18. https://doi.org/10.1177/2394901518767023
Romer, P. M. (1986). Increasing returns and long-run growth. Journal of Political Economy, 94(5), 1002-1037. https://paulromer.net/speeding-up-and-missed-opportunities-evidence/IncreasingReturns.pdf
Romer, P. M. (1990). Endogenous technological change. Journal of Political Economy, 98(5, Pt. 2), S71-S102. https://web.stanford.edu/~klenow/Romer_1990.pdf
Sarel, M. (1996). Nonlinear effects of inflation on economic growth. IMF Staff Papers, 43(1), 199-215. https://doi.org/10.2307/3867357
Shuaib, I. M., y Ndidi, D. E. (2015). Capital formation: Impact on the economic development of Nigeria 1960-2013. European Journal of Business, Economics and Accountancy, 3(3), 23-40. https://www.idpublications.org/wp-content/uploads/2015/03/CAPITAL-FORMATION-IMPACT-ON-THE-ECONOMIC-DEVELOPMENT-OF-NIGERIA-1960-2013.pdf
Solow, R. M. (1956). A contribution to the theory of economic growth. Quarterly Journal of Economics, 70(1), 65-94. http://piketty.pse.ens.fr/les/Solow1956.pdf
Solow, R. M. (1962). Technical progress, capital formation, and economic growth. American Economic Review, 52(2), 76-86. https://www.jstor.org/stable/1910871
Swan, T. W. (1956). Economic Growth and Capital Accumulation. Economic Record, 32(2), 334-361. https://doi.org/10.1111/j.1475-4932.1956.tb00434.x
Tahir, M., Burki, U., y Hayat, A. (2022). Natural resources and economic growth: evidence from Brunei Darussalam. International Journal of Emerging Markets, 18(10): 4252-4269. https://doi.org/10.1108/IJOEM-05-2021-0762
Uzawa, H. (1965). Optimum technical change in an aggregative model of economic growth. International Economic Review, 6(1), 18-31.https://doi.org/10.2307/2525621
Vergil, H., y Saidy, S. (2025). Examining foreign capital inflows and growth in The Gambia: A dual-gap approach. South African Journal of Economic and Management Sciences, 28(1), a6031. https://doi.org/10.4102/sajems.v28i1.6031
Wang, Q., y Ma, Z. (2024). The measurement of China’s provincial physical capital stock based on the improved method and indicators. PLoS ONE, 19(8), e0307946. https://doi.org/10.1371/journal.pone.0307946
Akalpler, E., y Adil, H. (2017). The impact of foreign direct investment on economic growth in Singapore between 1980 and 2014. Eurasian Economic Review, 7, 435-450. https://doi.org/10.1007/s40822-017-0071-3
Ali, S., Chaudhry, I. S., y Farooq, F. (2012). Human capital formation and economic growth in Pakistan. Pakistan Journal of Social Sciences, 32(1), 229-240. https://pjss.bzu.edu.pk/index.php/pjss/article/view/147
Amir-ud-Din, R., Usman, M., Abbas, F., y Javed, S. A. (2019). Human versus physical capital: issues of accumulation, interaction and endogeneity. Economic Change and Restructuring, 52, 351-382. https://doi.org/10.1007/s10644-017-9225-2
Barro, R. J., y SalaiMartin, X. (2004). Economic Growth. The MIT Press.
Boamah, J., Adongo, F. A., Essieku, R., y Lewis, J. A. (2018). Financial depth, gross fixed capital formation and economic growth: Empirical analysis of 18 Asian economies. International Journal of Scientific and Education Research, 2(4), 120-130. http://dx.doi.org/10.2139/ssrn.3424688
Chi, W. (2008). The role of human capital in China’s economic development: Review and new evidence. China Economic Review, 19(3), 421-436. https://doi.org/10.1016/j.chieco.2007.12.001
Chiang, A. C., y Wainwright, K. (2006). Métodos fundamentales de economía matemática. McGraw-Hill/ Interamericana Editores S.A. de C.V.
Dawood, S. S., Haidar, B. K., y Ghazi, M. (2024). The effect of fixed capital formation rate on gross domestic product in Iraq. Public and Municipal Finance, 13(2), 56-69.http://dx.doi.org/10.21511/pmf.13(2).2024.06
Galor, O., y Moav, O. (2004). From physical to human capital accumulation: Inequality and the process of development. Review of Economic Studies, 71(4), 1001-1026. https://doi.org/10.1111/0034-6527.00312
Ghosh, S. (2019). Foreign direct investment, female education, capital formation, and economic growth in Japan and South Korea. International Economic Journal, 33(3), 509-536. https://doi.org/10.1080/10168737.2019.1600155
Gibescu, O. (2010). Does the gross fixed capital formation represent a factor for supporting the economic growth? MPRA Paper No. 50135. https://mpra.ub.uni-muenchen.de/50135/1/MPRA_paper_50135.pdf
Greiner, A., y Semmler, W. (2002). Externalities of investment, education and economic growth. Economic Modelling, 19(5), 709-724. https://doi.org/10.1016/S0264-9993(01)00076-1
Inada, K.-I. (1963). On a two-sector model of economic growth: Comments and a generalization. The Review of Economic Studies, 30(2), 119-127. https://doi.org/10.2307/2295809
Khatoon Ali, R., Javed, I., y Hayat, M. M. (2021). Impact of human capital on economic growth: A case study of Pakistan. Journal of Social Sciences Advancement, 2(2), 64-69. https://doi.org/10.52223/JSSA21-020202-15
Kuznets, S., y Jenks, E. (1961). Capital in the American economy; its function and Financing. Princeton University Press.
Labarca, N. J., y Panchana, A. M. (2022). Crecimiento económico en América Latina: Algunos determinantes desde la perspectiva austriaca. Revista de Ciencias Sociales (Ve), XXVIII(1), 216-233. https://doi.org/10.31876/rcs.v28i1.37686
Li, Y., Wang, X., Westlund, H., y Liu, Y. (2015). Physical capital, human capital, and social capital: The Changing Roles in China’s Economic Growth. Growth Change, 46(1), 133-149. https://doi.org/10.1111/grow.12084
Lucas, R. E. (1988). On the mechanics of economic development. Journal of Monetary Economics, 22(1), 3-42. https://doi.org/10.1016/0304-3932(88)90168-7
Mankiw, N. G., Romer, D., y Weil, D. N. (1992). A contribution to the empirics of economic growth. Quarterly Journal of Economics, 107(2), 407-437. https://eml.berkeley.edu/~dromer/papers/MRW_QJE1992.pdf
Meyer, D. F., y Sanusi, K. A. (2019). A causality analysis of the relationships between gross fixed capital formation, economic growth and employment in South Africa. Studia Universitatis Babeș-Bolyai Oeconomica, 64(1), 33-44. https://doi.org/10.2478/subboec-2019-0003
Oyinlola, M. A., Adedeji, A. A., y Onitekun, O. (2021). Human capital, innovation, and inclusive growth in sub-Saharan Africa Region. Economic Analysis and Policy, 72, 609-625.https://doi.org/10.1016/j.eap.2021.10.003
Pomi, S. S., Sarkar, S. M., y Dhar, B. K. (2021). Human or physical capital, which influences sustainable economic growth most? A study on Bangladesh. Canadian Journal of Business and Information Studies, 3(5), 101-108. https://doi.org/10.34104/cjbis.021.01010108
Raheem, I., Isah, K., y Adedeji, A. (2018). Inclusive growth, human capital development and natural resource rent in SSA. Economic Change and Restructuring, 51(1), 29-48. https://doi.org/10.1111/joes.12211
Rani, R., y Kumar, N. (2019). Panel data analysis of financial development, trade openness, and economic growth: Evidence from BRICS countries. Emerging Economy Studies, 4(1), 1-18. https://doi.org/10.1177/2394901518767023
Romer, P. M. (1986). Increasing returns and long-run growth. Journal of Political Economy, 94(5), 1002-1037. https://paulromer.net/speeding-up-and-missed-opportunities-evidence/IncreasingReturns.pdf
Romer, P. M. (1990). Endogenous technological change. Journal of Political Economy, 98(5, Pt. 2), S71-S102. https://web.stanford.edu/~klenow/Romer_1990.pdf
Sarel, M. (1996). Nonlinear effects of inflation on economic growth. IMF Staff Papers, 43(1), 199-215. https://doi.org/10.2307/3867357
Shuaib, I. M., y Ndidi, D. E. (2015). Capital formation: Impact on the economic development of Nigeria 1960-2013. European Journal of Business, Economics and Accountancy, 3(3), 23-40. https://www.idpublications.org/wp-content/uploads/2015/03/CAPITAL-FORMATION-IMPACT-ON-THE-ECONOMIC-DEVELOPMENT-OF-NIGERIA-1960-2013.pdf
Solow, R. M. (1956). A contribution to the theory of economic growth. Quarterly Journal of Economics, 70(1), 65-94. http://piketty.pse.ens.fr/les/Solow1956.pdf
Solow, R. M. (1962). Technical progress, capital formation, and economic growth. American Economic Review, 52(2), 76-86. https://www.jstor.org/stable/1910871
Swan, T. W. (1956). Economic Growth and Capital Accumulation. Economic Record, 32(2), 334-361. https://doi.org/10.1111/j.1475-4932.1956.tb00434.x
Tahir, M., Burki, U., y Hayat, A. (2022). Natural resources and economic growth: evidence from Brunei Darussalam. International Journal of Emerging Markets, 18(10): 4252-4269. https://doi.org/10.1108/IJOEM-05-2021-0762
Uzawa, H. (1965). Optimum technical change in an aggregative model of economic growth. International Economic Review, 6(1), 18-31.https://doi.org/10.2307/2525621
Vergil, H., y Saidy, S. (2025). Examining foreign capital inflows and growth in The Gambia: A dual-gap approach. South African Journal of Economic and Management Sciences, 28(1), a6031. https://doi.org/10.4102/sajems.v28i1.6031
Wang, Q., y Ma, Z. (2024). The measurement of China’s provincial physical capital stock based on the improved method and indicators. PLoS ONE, 19(8), e0307946. https://doi.org/10.1371/journal.pone.0307946
Published
2026-05-11
How to Cite
Urdaneta Montiel, A. J., Huaita Acha, D. M., Vento, J. F., & Luza Castillo, F. F. (2026). Estrategias de inversión y acumulación de capital en horizonte infinito: Enfoque de control óptimo en tiempo continuo. Revista De Ciencias Sociales, 32(2), 356-372. https://doi.org/10.31876/rcs.v32i2.45580
Issue
Section
Artículos
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
1.jpg)
1.jpg)
