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G. Feichtinger, D. Grass, Y. Yegorov, F. Wirl, M. Eigruber:
"On the Matthew Effect on Individual Investments in Skills in Arts, Sports and Science";
Research Reports (Vienna University of Technology, Institute of Statistics and Mathematical Methods in Economics, Operations Research and Control Systems), 2020-05 (2020), 05; 38 S.

he paper describes the process of capital accumulation subject to the fol-lowing characteristics: (i) convex returns to (human) capital; (ii) the needto self-finance the investment. This setup is applicable to explain somepeculiarities in arts, sports and science, inter alia, the "Matthew effect"coined in Merton (1968) to explain why prominent researchers get dispro-portional credit for their work. The potential young artist´s (sportsman´s orscientist´s) optimal strategies include quitting, or continuing and even ex-panding one´s human capital in a profession. Both outcomes are separatedby a threshold level in human capital. In addition, it can be optimal to stayin business although consumption falls and stays at the subsistence levelforever (we call this outcome a "Sisyphus point"). This possibility is alsointeresting from a theoretical point of view, as the optimal control problemmay turn "abnormal", i.e., the objective does not enter the Hamiltonian.

Human capital accumulation, Abnormal control problem, Convex returns, Threshold, Matthew effect, Sisyphus point.

https://publik.tuwien.ac.at/files/publik_289717.pdf