Economic Equilibrium Modeling with GAMS

8
A MPSGE model speci cation is always listed between $ONTEXT and $OFFTEXT statements.
The rst statement within an MPSGE model-description assigns a name to the
model. The model name must begin with a letter and must have 10 or fewer characters.
$ONTEXT
$MODEL:DEMAND
The model speci cation begins by declaring variables for the model. In a standard
model, there are three types of variables: commodity prices, sectoral activity levels, and
consumer incomes. The end of each line may conclude with a \!", followed by a variable
description.
N.B. The variables associated with commodities are prices, not quantities. (In this and
subsequent models, I use P as the rst letter for each of the commodity variables to remind
us that these variables are prices.)
N.B. The variable associated with a consumer is an income level,notawelfare index.
$SECTORS:
X ! ACTIVITY LEVEL FOR X = DEMAND FOR GOOD X
Y ! ACTIVITY LEVEL FOR Y = DEMAND FOR GOOD Y
$COMMODITIES:
PX ! PRICE OF X WHICH WILL EQUAL PL
PY ! PRICE OF Y WHICH WILL EQUAL 2 PL
PL ! PRICE OF THE ARTIFICIAL FACTOR L
$CONSUMERS:
RA ! REPRESENTATIVE AGENT INCOME
Function speci cations follow the variable declarations. In this model, our rst declarations
correspond to the two production sectors. In this model, the production structures
are particularly simple. Each of the sectors has one input and one output. In the MPSGE
syntax, I: denotes an input and O: denotes an output. The output quantity coe cients
for both sectors are unity (Q:1). This means that the level values for x and y equal the
quantities produced.
The nal function speci ed in the model represents the utility function and endowments
for the single consumer. In this function, the E: entries correspond to endowments and the
D: entries are demands. Reference demands, reference prices and the substitution elasticity
(s:1) characterize preferences.
The demand entries shown here are consistent with a Cobb-Douglas utility function in
which the budget share for y is twice the budget share for x (i.e. the MRS at (1,1) equals
1/2):
$PROD:X