Dynamic Keynesian Model of Economic Growth with Memory and Lag

A mathematical model of economic growth with fading memory and continuous distribution of delay time is suggested. This model can be considered as a generalization of the standard Keynesian macroeconomic model. To take into account the memory and gamma-distributed lag we use the Abel-type integral a...

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Bibliographic Details
Published in:Mathematics (Basel) 2019-02, Vol.7 (2), p.178
Main Authors: Tarasov, Vasily, Tarasova, Valentina
Format: Article
Language:English
Subjects:
Abel-type integral
Asymptotic properties
Calculus
Consumption
Delay time
Differential equations
distributed lag
Distributed memory
Economic development
Economic growth
Economic models
Electromagnetism
Expenditures
fractional derivative
fractional differential equations
gamma distribution
Government spending
Growth models
Income
Keynesian model
Macroeconomics
Mathematical models
Mathematics
Operators (mathematics)
Power
Propensity to consume
Random variables
Response time
time delay
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Summary:A mathematical model of economic growth with fading memory and continuous distribution of delay time is suggested. This model can be considered as a generalization of the standard Keynesian macroeconomic model. To take into account the memory and gamma-distributed lag we use the Abel-type integral and integro-differential operators with the confluent hypergeometric Kummer function in the kernel. These operators allow us to propose an economic accelerator, in which the memory and lag are taken into account. The fractional differential equation, which describes the dynamics of national income in this generalized model, is suggested. The solution of this fractional differential equation is obtained in the form of series of the confluent hypergeometric Kummer functions. The asymptotic behavior of national income, which is described by this solution, is considered.
ISSN:2227-7390
2227-7390
DOI:10.3390/math7020178