Model pertumbuhan pengeluaran publik dengan pendekatan fungsi logistik

Abstract

Economic growth can be detected from increasing ratio between public expenditure with national income. Some theories can be applied to explain this ratio level as well as public expenditure per capita, i.e. Wagner’s Law and Pigou’s Conjecture. Wagner’s Law is an exponential model of growth process from ratio between public expenditure with national income. While Pigou’s Conjecture describes that tax excess could act as a brake for public commodity supplies. The economic growth will be modeled in this paper by combining Wagner’s Law and Pigou’s Conjecture. The model is a nonlinear differential equation of the ratio. This equation is also known as Verhulst’s logistic equation. Logistic equation is an equation that describes population growth in an environment with considering environment’s limited support capability. Integration of Verhulst’s equation produces an S-curve. Further more, Wagner’s Law and Pigou’s Conjecture are combined and applied to illustrate the economic growth model of some developed countries (America, Italy, Germany, France, and England) as well as Indonesia. The resulted models are in the form of S-curve described earlier, which tends to increase and converge to a certain level. Therefore, combination of Wagner’s Law and Pigou’s Conjecture is suitable to model the data being observed and can be used to analyze dynamics of public expenditure.