Economic Equilibrium Modeling with GAMS

12
In an equilibrium, nal demand always equals endowments for both goods, because
these are the only sources of demand and supply. The model as parameterized demonstrates
that if we set endowments for this model equal to the demand function calibration point,
the model equilibrium price ratio equals the benchmark MRS.
This program begins with some GAMS statements in which three scalar parameters
are declared. These parameters will be used in the place of numbers within the MPSGE
model. The syntax for these GAMS statements is introduced in Chapter 2 of the GAMS
manual. In short, we declare x, y and MRS as scalar parameters and initialize the rst
two of these to unity. The MRS parameter is assigned a value following the solution of the
model.
SCALAR
X QUANTITY OF X FOR WHICH THE MRS IS TO BE EVALUATED /1/
Y QUANTITY OF Y FOR WHICH THE MRS IS TO BE EVALUATED /1/
MRS COMPUTED MARGINAL RATE OF SUBSTITUTION;
The remainder of the MPSGE program is, in fact, simpler than Example 1.
$ONTEXT
$MODEL:MRSCAL
$COMMODITIES:
PX ! PRICE INDEX FOR GOOD X
PY ! PRICE INDEX FOR GOOD Y
$CONSUMERS:
RA ! REPRESENTATIVE AGENT
$DEMAND:RA s:1
D:PX Q:1 P:(1/4)
D:PY Q:1 P:1
E:PX Q:X
E:PY Q:Y
$OFFTEXT
$SYSINCLUDE mpsgeset MRSCAL
$INCLUDE MRSCAL.GEN
SOLVE MRSCAL USING MCP;
Following the solution, we compute a function of the solution values, the ratio of the
price of x to the price of y. We do this using the GAMS syntax which references the
equilibrium level values of the PX and PY and storing this result in the scalar MRS. This
scalar value is then displayed in the listing le with 8 digits: