A time-scale variational approach to inflation, unemployment and social loss

• Autorzy: Dryl M. , Malinowska A. B. , Torres D. F. M.
• Języki publikacji: EN

Abstrakty

EN

Both inflation and unemployment inflict social losses. When a tradeoff exists between the two, what would be the Best combination of inflation and unemployment? A well known approach in economics to address this question is writing the social loss as a function of the rate of inflation p and the rate of unemployment u, with different weights, and then, using known relations between p, u, and the expected rate of inflation π, to rewrite the social loss function as a function of π. The answer is achieved by applying the calculus of variations in order to find an optimal path π that minimizes Total social loss over a given time interval. Economists dealing with this question use a continuous or a discrete variational problem. Here we propose to use a time-scale model, unifying the results available in the literature. Moreover, the new formalism allows for obtaining new insights into the classical models when applied to real data of inflation and unemployment.

Słowa kluczowe

EN

calculus on time scales; calculus of variations; delta derivatives; dynamic model; inflation; unemployment

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2013
• Tom: Vol. 42, no. 2
• Strony: 399--418
• Opis fizyczny: Bibliogr. 17 poz., wykr.

Twórcy

autor

Dryl M.

• CIDMA — Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

autor

Malinowska A. B.

• Faculty of Computer Science, Bialystok University of Technology, 15-351 Białystok, Poland

autor

Torres D. F. M.

• CIDMA — Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Bibliografia

• 1. Almeida, R. and Torres, D. F. M. (2009) Isoperimetric problems on time scales with nabla derivatives. J. Vib. Control 15 (6), 951–958.
• 2. Bartosiewicz, Z. and Torres, D. F. M. (2008) Noether’s theorem on time scales. J. Math. Anal. Appl. 342 (2), 1220–1226.
• 3. Bohner, M. and Peterson, A. (2001) Dynamic equations on time scales. Birkhäuser Boston, Boston, MA.
• 4. Bohner, M. and Peterson, A. (2003) Advances in Dynamic Equations on Time Scales. Birkhäuser Boston, Boston, MA.
• 5. Chiang, A. C. (1992) Elements of Dynamic Optimization. McGraw-Hill, Inc., Singapore.
• 6. Ferreira, R. A. C., Malinowska, A. B. and Torres, D. F. M. (2011) Optimality conditions for the calculus of variations with higher-order delta derivatives. Appl. Math. Lett. 24 (1), 87–92.
• 7. Girejko, E., Malinowska, A. B. and Torres, D. F. M. (2010) A unified approach to the calculus of variations on time scales. Proceedings of 2010 CCDC, Xuzhou, China, May 26-28, 2010. In: IEEE Catalog Number CFP1051D-CDR, 2010, 595–600. DOI:10.1109/CCDC.2010.5498972
• 8. Girejko, E., Malinowska, A. B. and Torres, D. F. M. (2012) The contingent epiderivative and the calculus of variations on time scales. Optimization 61 (3), 251–264.
• 9. Hilger, S. (1997) Differential and difference calculus-unified! Nonlinear Anal. 30 (5), 2683–2694.
• 10. Inflationdata.com, Current inflation, Bureau of Labor Statistics, http://inflationdata.com/Inflation/Inflation_Rate/CurrentInflation.asp, date of retrieval: 31-Oct-2012.
• 11. Malinowska, A. B. and Torres, D. F. M. (2011) Euler-Lagrange equations for composition functionals in calculus of variations on time scales. Discrete Contin. Dyn. Syst. 29 (2), 577–593.
• 12. Malinowska, A. B. and Torres, D. F. M. (2012) Introduction to the Fractional Calculus of Variations. Imp. Coll. Press, London.
• 13. Martins, N. and Torres, D. F. M. (2011) Generalizing the variational theory on time scales to include the delta indefinite integral. Comput. Math. Appl. 61 (9), 2424–2435.
• 14. Mozyrska, D. and Torres, D. F. M. (2009) A study of diamond-alpha dynamic equations on regular time scales. Afr. Diaspora J. Math. (N.S.) 8 (1), 35–47.
• 15. Samuelson, P. A. and Nordhaus, W. D. (2004) Economics, 18th ed. McGraw-Hill/Irwin, Boston, MA.
• 16. Taylor, D. (1989) Stopping inflation in the Dornbusch model: Optimal monetary policies with alternate price-adjustment equations. Journal of Macroeconomics 11 (2), 199–216.
• 17. Unemploymentdata.com, Unemployment rate (Seasonally Adjusted U-3 Unemployment Rate), Bureau of Labor Statistics, http://unemploymentdata. com/unemployment-rate, date of retrieval: 31-Oct-2012.

Uwagi

PL

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