Fluctuations of aggregated production capacity near balanced growth path. (English) Zbl 1521.90057
Olenev, Nicholas (ed.) et al., Optimization and applications. 13th international conference, OPTIMA 2022, Petrovac, Montenegro, September 26–30, 2022. Revised selected papers. Cham: Springer. Lect. Notes Comput. Sci. 13781, 192-204 (2023).
Summary: The differential equation for the total production capacity in the vintage capacity model with age limit contains a delay. A characteristic solution to this equation is not only a balanced growth path, but also various kinds of oscillations near this path. The paper presents a multivalued solution for a special case of a fixed age limit and a given value of the share of new capacities. The state of such a system is determined by a whole segment of the trajectory.
For the entire collection see [Zbl 1516.90004].
For the entire collection see [Zbl 1516.90004].
MSC:
| 90B30 | Production models |
Keywords:
aggregated production capacity; vintage capacity model; age limit; balanced growth path; fluctuationsReferences:
| [1] | Bellen, A.; Zennaro, M., Numerical Methods for Delay Differential Equations (2003), Oxford: Clarendon Press, Oxford · Zbl 1038.65058 · doi:10.1093/acprof:oso/9780198506546.001.0001 |
| [2] | Bellman, R.; Cooke, KL, Differential-Difference Equations (1963), New York, London: Academic Press, New York, London · Zbl 0105.06402 |
| [3] | Boivin, A.; Zhong, H., Completeness of systems of complex exponentials and the Lambert W functions, Trans. Am. Math. Soc., 359, 1829-1849 (2007) · Zbl 1210.42046 · doi:10.1090/S0002-9947-06-03950-X |
| [4] | Corless, RM; Gonnet, GH; Hare, DEG; Jeffrey, DJ; Knuth, DE, On the Lambert W function, Adv. Comput. Math., 5, 329-359 (1996) · Zbl 0863.65008 · doi:10.1007/BF02124750 |
| [5] | Hale, J., Theory of Functional Differential Equations (1977), New York: Springer, New York · Zbl 0352.34001 · doi:10.1007/978-1-4612-9892-2 |
| [6] | Heffernan, JM; Corless, RM, Solving some delay differential equations with computer algebra, Math. Sci., 31, 21-34 (2006) · Zbl 1115.34074 |
| [7] | Johansen, L., Production functions and the concept of capacity, Collect. Econ. Math. Econom., 2, 49-72 (1968) |
| [8] | Johansen, L., Substitution versus fixed production coefficients in the theory of economic growth: a synthesis, Econometrica, 27, 2, 157-176 (1959) · Zbl 0124.12202 · doi:10.2307/1909440 |
| [9] | Kantorovich, LV; Gorkov, LI, On some functional expressions that arise in the analysis of a single-product economic model, Doklady AN SSSR, 129, 4, 732-735 (1959) · Zbl 0115.37603 |
| [10] | Kolmanovskii, V.; Myshkis, A., Applied Theory of Functional Differential Equations (1992), Dordrecht: Kluwer, Dordrecht · Zbl 0917.34001 · doi:10.1007/978-94-015-8084-7 |
| [11] | Olenev, N.: Identification of an aggregate production function for the economy of Turkey. In: New Trends in Economics and Administrative Sciences. Proceedings of the Izmir International Congress on Economics and Administrative Sciences (IZCEAS 2018), pp. 1761-1770. Detay Yayincilik, Izmir (2018) |
| [12] | Olenev, NN, Identification of a production function with age limit for production capacities, Math. Model. Comput. Simul., 12, 4, 482-491 (2020) · doi:10.1134/S2070048220040134 |
| [13] | Olenev, N.; Jaćimović, M.; Khachay, M.; Malkova, V.; Posypkin, M., Golden rule saving rate for an endogenous production function, Optimization and Applications, 267-279 (2020), Cham: Springer, Cham · doi:10.1007/978-3-030-38603-0_20 |
| [14] | Olenev, N.N., Petrov, A.A., Pospelov, I.G.: Model of change processes of production capacity and production function of industry. In: Samarsky, A.A., Moiseev, N.N., Petrov, A.A. (eds.) Mathematical Modelling: Processes in Complex Economic and Ecologic Systems, pp. 46-60. Nauka, Moscow (1986). doi:10.13140/RG.2.1.3938.8880. (in Russian) |
| [15] | Protter, MH; Morrey, CB; Protter, MH; Morrey, CB, Differentiation under the integral sign. Improper integrals. The Gamma function, Intermediate Calculus, 421-426 (1985), New York: Springer, New York · doi:10.1007/978-1-4612-1086-3_8 |
| [16] | Skubachevskii, AL, Elliptic Functional Differential Equations and Applications (1996), Basel: Birkhäuser, Basel · Zbl 0876.35124 · doi:10.1007/978-3-0348-9033-5 |
| [17] | Solow, RM, A contribution to the theory of economic growth, Q. J. Econ., 70, 1, 65-94 (1956) · doi:10.2307/1884513 |
| [18] | Solow, R.M.: Investment and technical progress. In: Mathematical Methods in the Social Sciences, pp. 48-93. Stanford University Press, Stanford (1960) · Zbl 0124.36603 |
| [19] | Yi, S.; Nelson, PW; Ulsoy, AG, Time-Delay Systems: Analysis and Control Using the Lambert W Function (2010), Singapore: World Scientific, Singapore · Zbl 1209.93002 · doi:10.1142/7759 |
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