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TEL> Vol.5 No.6, December 2015
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On the Application of the Laplace Transform in the Study of Phillips-Type Stabilization Policy

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DOI: 10.4236/tel.2015.56080    3,072 Downloads   3,846 Views   Citations
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Satoru Kageyama

Affiliation(s)

Graduate School of Economics, Osaka University, Osaka, Japan.

ABSTRACT

This paper provides a reformulation of Phillips’s multiplier-accelerator model with stabilization policy in terms of the Laplace transform. Applying the Laplace transform, the differential equations of the economy are transformed into the algebraic ones on a complex variable. The transfer functions of economic variables are defined by these algebraic equations. With this representation, we show the effects of Phillips-type policy on equilibrium level and derive the necessary and sufficient condition for asymptotic stability.

KEYWORDS

Stabilization Policy, Multiplier-Accelerator Policy, Transfer Function, Laplace Transform

Cite this paper

Kageyama, S. (2015) On the Application of the Laplace Transform in the Study of Phillips-Type Stabilization Policy. Theoretical Economics Letters, 5, 691-696. doi: 10.4236/tel.2015.56080.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Phillips, A.W. (1954) Stabilisation Policy in a Closed Economy. The Economic Journal, 64, 290-323. http://dx.doi.org/10.2307/2226835
[2] Hansen, L. and Sargent, T. (2008) Robustness. Princeton University Press, Princeton.
[3] Bromwich, T.I. (1917) Normal Coordinates in Dynamical Systems. Proceedings of the London Mathematical Society, 2, 401-448. http://dx.doi.org/10.1112/plms/s2-15.1.401
[4] Carson, J. (1926) The Heaviside Operational Calculus. Bulletin of the American Mathematical Society, 32, 43-68. http://dx.doi.org/10.1090/S0002-9904-1926-04162-8
[5] Allen, R.G.D. (1966) Mathematical Economics. Macmillan, London.
[6] Allen, R.G.D. (1967) Macroeconomic Theory: A Mathematical Treatment. Macmillan, London.
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[8] Bakshi, U.A. and Bakshi, V.U. (2010) Control Systems. Technical Publications.
[9] Gantmacher, F. (1959) The Theory of Matrices. Chelsea, New York.
[10] Samuelson, P.A. (1947) Foundations of Economic Analysis. Harvard University Press, Cambridge.

  
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