Complex Economics

Complex Economics

DOI: 10.4018/978-1-6684-4935-6.ch006
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Abstract

When the real commodity function X and the imaginary money function Y are combined as complex economic function Z = X + iY and both X and Y link with price level P and output quantity Q, a framework of complex economics is set up, characterized by the Cauchy-Riemann equation and the Laplace equation. The economic complex analysis can characterize economic equilibrium and economic stability, providing a mathematical description of ideal economic situation. The author develops economic complex analysis in this chapter.
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Introduction

Complex Number with its Implications in Economics

In economics, the economic equilibrium is a state where economic forces such as demand, and supply are balanced and the equilibrium values of economic variables will not change in the absence of external influences. Economic stability refers to an absence of excessive fluctuations. An economy with fairly constant output growth and low and stable inflation would be considered economically stable, and the equilibrium is just the outcome of the stability.

To approach economic equilibrium and economic stability, the general equilibrium theories have been developed in both microeconomics (Arrow & Debreu, 1954) and macroeconomics (Fleming, 1962; Mundell, 1962, 1963; Tobin, 1969). Moreover, the general equilibrium and economic analysis are core topics in economics, particularly in monetary economics which also concerns economic stability and monetary mechanism (Samuelson, 1947; Friedman, 1948, 1956, 1966, 1970; Friedman & Hahn, 1990; Hahn, 1960; Modigliani, 1963). Following the framework of complex economics (Ye, 2017), we can develop economic complex analysis as follows, and we expect to benefit and enrich economic analysis as well as economic theories.

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