Economic Equilibrium Modeling with GAMS

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$MODEL:EXCHANGE
$COMMODITIES:
PX ! EXCHANGE PRICE OF GOOD X
PY ! EXCHANGE PRICE OF GOOD Y
$CONSUMERS:
A ! CONSUMER A
B ! CONSUMER B
$DEMAND:A s:SIGMA_A
E:PX Q:XA
E:PY Q:YA
D:PX Q:THETA_A
D:PY Q:(1-THETA_A)
$DEMAND:B s:SIGMA_B
E:PX Q:(1-XA)
E:PY Q:(1-YA)
D:PX Q:THETA_B
D:PY Q:(1-THETA_B)
$OFFTEXT
$SYSINCLUDE mpsgeset EXCHANGE
$INCLUDE EXCHANGE.GEN
SOLVE EXCHANGE USING MCP;
SCALAR
PRATIO EQUILIBRIUM PRICE OF X IN TERMS OF Y,
IRATIO EQUILIBRIUM RATIO OF CONSUMER INCOMES;
PRATIO = PX.L / PY.L;
IRATIO = A.L / B.L;
DISPLAY IRATIO, PRATIO;
The foregoing sets up the model and computes the competitive equilibrium. After
GAMS returns from the solver, we declare and compute some report values.
Absolute levels of income and price returned from a general equilibrium model are not
meaningful because a model determines only relative prices. For this reason, we report
equilibrium income and price levels in relative terms.
In the nal step, we compute an alternative e cient equilibrium, one in which the
income levels for A and B are equal. The purpose of this exercise is to demonstrate the
second welfare theorem. When incomes are both xed, the equilibrium remains e cient,
but the connection between market prices and endowment income is eliminated.