A Fuzzy Economic Dynamic Model

Abstract

In the study presented here, fuzzy logic was used to analyze the behavior of a model of economic dynamics that assumes income to be in equilibrium when it is composed of consumption and investment, that is, when savings and investment are equal. The study considered that consumption and savings depend on the income of the previous period through uncertain factors, and, at the same time, that investment is an uncertain magnitude across various periods, represented as a fuzzy number with a known membership function. Under these conditions, the model determines the factor of income growth and investments required to maintain equilibrium, as well as the uncertain values of income for the different periods, expressed through fuzzy numbers. The study also analyzes the conditions for their convergence and the fuzzy value that income represents in equilibrium.

Incorporating Fuzzy Logic in Harrod’s Economic Growth Model

“…Consequently, the modeling presented in this article expands the possibilities offered by the current Harrod's growth model [29][30][31], and continues along the path first followed with the proposal to use fuzzy numbers [11,12].…”

“…where we assume that a accepts all possible values given by the fuzzy number A = a , µ A (a)/a ∈ R and b all possible values given by the fuzzy number B = b , µ B (b)/b ∈ R . We then need to find all possible values of x, each with their own degrees of possibility, that satisfy any of Equation (12).…”

“…We must therefore study the possibility of this magnitude taking on a specific value x, considering that several combinations of possible values for a and b will exist so that f (a , b) = x. Each of the possible values of x fulfills some of the equations of the family (12).…”

“…As we have argued for the models of previous works [11,12], the use of fuzzy numbers to express the marginal propensity to save and the accelerator, makes subsequent calculations difficult, but it allows the possibility of studying the behavior of the model when we operate with uncertain values, thus obtaining more information and giving a wider range of applications of the model. By operating with fuzzy numbers, we will determine the values of income, investment and growth rate as fuzzy numbers under conditions of uncertainty defined through their α-cuts, as well as their function of theoretical membership from the approach and solution of the equation given by the model under conditions of fuzziness.…”

“…The incorporation of fuzzy logic into economic models has been addressed in a multitude of papers [8][9][10]. Following this line of research, in recent years the fuzzy logic perspective has been proposed for various growth models [11,12]. The present work, included in this current line of research, proposes the creation of a dynamic model of income behavior based on the classic Harrod model.…”