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Exact Discretization of an Economic Accelerator and Multiplier with Memory

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Lomonosov Moscow State University Business School, Lomonosov Moscow State University, Moscow 119991, Russia
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Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia
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Fractal Fract 2017, 1(1), 6; https://doi.org/10.3390/fractalfract1010006
Received: 31 July 2017 / Revised: 7 September 2017 / Accepted: 7 September 2017 / Published: 11 September 2017
Fractional differential equations of macroeconomics, which allow us to take into account power-law memory effects, are considered. We describe an economic accelerator and multiplier with fading memory in the framework of discrete-time and continuous-time approaches. A relationship of the continuous- and discrete-time fractional-order equations is considered. We propose equations of the accelerator and multiplier for economic processes with power-law memory. Exact discrete analogs of these equations are suggested by using the exact fractional differences of integer and non-integer orders. Exact correspondence between the equations with finite differences and differential equations lies not so much in the limiting condition, when the step of discretization tends to zero, as in the fact that mathematical operations, which are used in these equations, satisfy in many cases the same mathematical laws. View Full-Text
Keywords: fractional derivative; fractional integral; multiplier; accelerator; macroeconomics; dynamic memory; power-law memory; exact difference; fractional difference; exact discretization fractional derivative; fractional integral; multiplier; accelerator; macroeconomics; dynamic memory; power-law memory; exact difference; fractional difference; exact discretization
MDPI and ACS Style

Tarasova, V.V.; Tarasov, V.E. Exact Discretization of an Economic Accelerator and Multiplier with Memory. Fractal Fract 2017, 1, 6.

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