TITLE:
Recommended Methods to Re-Calculate Regional and Total Economic Surpluses after Solving Spatial Equilibrium Models by the Non-Linear Programming Method
AUTHORS:
Phan Sy Hieu, Steve Harrison, Dominic Smith
KEYWORDS:
Producer Surplus, Consumer Surplus, Negative Intercepts, Integrals of Supply and Demand
JOURNAL NAME:
Modern Economy,
Vol.6 No.5,
May
14,
2015
ABSTRACT: The current non-linear programming
method does not derive regional economic surpluses and may derive an imprecise
maximized value of the total economic surplus. The main reason is that the
integrals for supply functions will automatically take regional non-economic
producer surpluses into account if any intercepts of supply functions is
negative. Consequently, the derived values are always lower than the real
regional and total economic surpluses. The unknown regional economic surpluses
and the imprecise total economic surplus will limit the suitable application of
the model for broader contexts including game theory analysis, international
trade policy analysis, and even GDP calculation. This paper recommends two
formulae applied for two types of functions, namely original and inverse supply
and demand functions, to calculate the regional and total economic surpluses of
commodities. The two methods can be converted to each other conveniently, for
example by using an inverse matrix of coefficients of original supply and
demand functions to solve coefficients of inverse supply and demand functions.
A numerical example is used to illustrate the spatial equilibrium model for 2
products and 3 regions with original linear supply and demand functions.