Dynamic Model of the Human Capital Growth in Heterogeneous Group of Students
DOI:
https://doi.org/10.17308/econ.2026.1/13610Keywords:
optimal control theory, learning strategies, educational capitalAbstract
Subject and Purpose of the Study. The paper examines the problem of optimal educational policy required to equalize the educational capital for students with different abilities through the careful selection of teaching efforts. Teaching is considered in a heterogeneous group of students consisting of individuals of two types.
Methodology. To study the problem, we use microeconomic modeling. The constructed general mathematical model takes into account the dynamics of capital of students with different learning abilities and takes the form of differential equations containing control from the teacher, who chooses teaching efforts. In addition, the teacher’s objective functional, defined over a finite time horizon, includes terms that reflect the educational policy imposed by the administration.
Results. Within the formulated general model, we specified the functions included in the model and showed that the simpler problem reduces to an optimal control problem. We also integrated the first-order conditions derived from the Hamiltonian, thereby establishing the capital growth trajectories Along with the terminal values of capital, the effort levels in the two groups are found. Thus, the stated problem is fully solved. As the main result of the study, we established that the educational policy aimed at bringing the accumulation trajectories of the two groups closer together has a solution. When incentivizing an equalizing policy, the administrator primarily takes into account differences in student abilities.
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References
Barkley, A., & Coffey, B. K. (2018). An Economic Model of Student Learning. Journal of Agricultural and Applied Economics, 50(4), 503-525. DOI: 10.1017/aae.2018.13
Becker, G. (1994). Human Capital: A Theoretical and Empirical Analysis, with Special Reference to Education, 3rd Edition. Chicago: University of Chicago Press.
Benabou, R. (1996). Equity and Efficiency in Human Capital Investment: The Local Connection. The Review of Economic Studies, 63(2), 237-264. DOI:10.2307/2297851
Bosworth, R., & Caliendo, F. (2007). Educational Production and Teacher Preferences. Economics of Education Review, 26(4), 487-500. DOI: 10.1016/j.econedurev.2005.04.004
Brevik, L. M., Gunnulfsen, A. E., & Renzulli, J. S. (2018). Student Teachers’ Practice and Experience with Differentiated Instruction for Students with Higher Learning Potential. Teaching and Teacher Education, 71, 34-45. DOI: 10.1016/j.tate.2017.12.003
Collins, M., & Lindstedt, J. (2024). The Effects of More Informative Grading on Student Outcomes. Journal of Economic Behavior & Organization, 218, 514-549. DOI: 10.1016/j.jebo.2023.12.001
Csikszentmihalyi, M. (1990). Flow: The Psychology of Optimal Experience. New York: Harper and Row.
Cunha, F., & Heckman, J. (2007). The Technology of Skill Formation. American Economic Review, 97(2), 31-47. DOI: 10.3386/w12840
De Paola, M., Gioia, F., & Scoppa, V. (2023). Online Teaching, Procrastination and Students’ Achievement. Economics of Education Review, 94, 102378. DOI: 10.1016/j.econedurev.2023.102378
Di Tomasso, M. L., Contini, D., De Rosa, D., Ferrara, F., Piazzalunga, D., & Robutti, O. (2024). Tackling the Gender Gap in Mathematics with Active Learning Methodologies. Economics of Education Review, 100, 102538. DOI: 10.1016/j.econedurev.2024.102538
Hermann, Z., Horvath, H., & Kisfalusi, D. (2024). Are Separate Classrooms Inherently Unequal? The Effect of Within-school Sorting on the Socioeconomic Test Score Gap in Hungary. Economics of Education Review, 103, 102582. DOI: 10.1016/j.econedurev.2024.102582
Huynh, Q. (2024). Paying (and Paving) My Way: Extra-class Participation and Rent Extraction. Labor Economics, 91, 102616. DOI: 10.1016/j.labeco.2024.102616
Kalinowski, E., Westphal, A., Jurczok, A., & Vock, M. (2024). The Essential Role of Teacher Efficacy and Enthusiasm for Differentiated Instruction. Teaching and Teaching Education, 148, 104663. DOI: 10.1016/j.tate.2024.104663
Van Lent, M. (2025). Peer Creativity and Academic Achievement. Economics of Education Review, 106, 102649. DOI: 10.1016/j.econedurev.2025.102649
Röhl, S., Davison, K., & Bardach, L. (2025). Heterogeneity in Students’ Perceptions of Teaching Quality: A Marker of Adaptive Teaching? Learning and Instruction, 101, 102245. DOI: 10.31219/osf.io/mbntz_v2
Tanaka, R., & Wang, T. (2025). How Do Classmates Matter for the Class-size Effects? Economics of Education Review, 108, 102689. DOI: 10.1016/j.econedurev.2025.102689
Theeuwes, B., Saab, N., Denessen, E., & Admiraal, W. (2025). Unravelling Teachers’ Intercultural Competence when Facing a Simulated Multicultural Classroom. Teaching and Teaching Education, 162, 105053. DOI: 10.1016/j.tate.2025.105053
Webb, N. M. (1989). Peer Interaction and Learning in Small Groups. International Journal of Educational Research, 13(1), 21-39. DOI: 10.1016/0883-0355(89)90014-1
Weingarden, M., Karsenty, R., & Koichu, B. (2026). Realistic Visual Representations as Mediators between Everyday and Mathematical Discourses in Heterogeneous Classrooms. The Journal of Mathematical Behavior, 81, 101300. DOI: 10.1016/j.jmathb.2025.101300
Zohar, A., Degani, A., & Vaaknin, E. (2001). Teachers’ Beliefs about Low-achieving Students and Higher Order Thinking. Teaching and teacher education, 17(4), 469-485. DOI: 10.1016/s0742-051x(01)00007-5
Zou, J. (2024). The Peer Effect of Persistence on Student Achievement. Economics of Education Review, 102, 102574. DOI: 10.1016/j.econedurev.2024.102574
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