Economic Equilibrium Modeling with GAMS

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1. An Overview
This document describes a mathematical programming system for general equilibrium
analysis named MPSGE which operates as a subsystem to the mathematical programming
language GAMS. MPSGE is a library of function and Jacobian evaluation routines which
facilitates the formulation and analysis of AGE models. MPSGE simpli es the modelling
process and makes AGE modelling accessible to any economist who is interested in the
application of these models. In addition to solving speci c modelling problems, the system
serves a didactic role as a structured framework in which to think about general equilibrium
systems.
MPSGE separates the tasks of model formulation and model solution, thereby freeing
model builders from the tedious task of writing model-speci c function evaluation subroutines.
All features of a particular model are communicated to GAMS/MPSGE through a
tabular input format. To use MPSGE, a user must learn the syntax and conventions of
this model de nition language.
The present paper is intended for students who have completed two semesters of study in
microeconomics. The purpose of this presentation is to give students a practical perspective
on microeconomic theory. The diligent student who works through all of the examples
provided here should be capable of building small models \from scratch" to illustrate
basic theory. This is a rst step to acquiring a set of useable tools for applied work.
The remainder of this paper is organized as follows. Section 2 provides practical tips on
how to get started with GAMS/MPSGE. Section 3 reviews basic ideas from the theory of
the consumer. Section 4 introduces the modelling framework with three models illustrating
the representation of consumer demand within the MPSGE language. Section 5 reviews
the pure exchange model, and Section 5 presents two MPSGE models of exchange. Each
of the model-oriented sections present exercises based on the models which give students
a chance to work through the material on their own. Section 6 provides solutions to
exercises from this paper. Additional introductory examples for self-study can be found in
Jim Markusen's library of MPSGE examples, as well as in the GAMS model library (look
for models with names ending in \MGE").
The level of presentation and diagrammatic exposition adopted here is based on Hal
Varian's undergraduate microeconomics textbook ( Intermediate Microeconomics: A Modern
Approach, Third Edition, W. W. Norton & Company, Inc., 1993).
The ultimate objective of this piece is to remind students of some theory which they
have already seen and illustrate how these ideas can be used to build numerical models
using GAMS with MPSGE. It is not my intention to provide a graduate level presentation
of this material. So far as possible, I have avoided calculus and even algebra. The objective
here is to demonstrate that what matters are economic ideas. With the proper tools, it is
possible to do concrete economic modeling without a lot of mathematical formalism.
2. Getting Started
(i) In order to use GAMS/MPSGE, you need to know how to create and edit text les.
There are several methods for doing this. One approach is to use NOTEPAD, the standard
text editor under Windows 95. It is also possible to use a text processor such as Microsoft
Word as a text editor. If you take this approach, you will need to remember to always save
the edited le in a text format. A nal approach, one which I suggest to graduate students