Quantitative Justification for the Gravity Model in Economics

The gravity model in economics describes the trade flow between two countries as a function of their Gross Domestic Products (GDPs) and the distance between them. This model is motivated by the qualitative similarity between the desired dependence and the dependence of the gravity force (or potential energy) between the two bodies on their masses and on the distance between them. In this paper, we provide a quantitative justification for this economic formula. 1 Gravity Model in Economics: A Brief Introduction What is gravity model. It is known that, in general: • neighboring countries trade more than distant ones, and • countries with larger Gross Domestic Product (GDP) g have a higher volume of trade than countries with smaller GDP. Thus, in general, the trade flow ti j between the two countries i and j: • increases when the GDPs gi and g j increase and • decreases with the distance ri j increases. A qualitatively similar phenomenon occurs in physics: the gravity force fi j between the two bodies: • increases when their masses mi and m j increase and • decreases with the distance between then increases. Vladik Kreinovich Department of Computer Science, University of Texas at El Paso, 500 W. University, El Paso, Texas 79968, USA, e-mail: [email protected] Songsak Sriboonchitta Faculty of Economics, Chiang Mai University, Chiang Mai 50200 Thailand, e-mail: [email protected]