kehomge.gms : Multiple equilibria in a simple GE model
This is a simple general equilibrium model with multiple (three)
isolated equilibria. There are four commodities, two
Leontief production activities, and four consumers with Cobb-
Douglas preferences.
Reference:
- Kehoe, T, A Numerical Investigation of the Multiplicity of Equilibria. Mathematical Programming Study 23 (1985), 240-258.
Small Model of Types: MPSGE mcp
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$TITLE Multiple equilibria in a simple GE model (KEHOMGE,SEQ=149)
$Ontext
This is a simple general equilibrium model with multiple (three)
isolated equilibria. There are four commodities, two
Leontief production activities, and four consumers with Cobb-
Douglas preferences.
Kehoe, T, A Numerical Investigation of the Multiplicity of Equilibria.
Mathematical Programming Study 23 (1985), 240-258.
MILES may find any of the three equilibria depending
on the starting point.
$Offtext
SET G GOODS /G1*G4/
S SECTORS /S1,S2/
C CONSUMERS /C1*C4/
EQ EQUILIBRIA /EQ1*EQ3/;
TABLE SP(G,EQ) Starting points for finding various equilibria.
EQ1 EQ2 EQ3
G1 1 1 1
G2 1 1 0.8
G3 1 0.2 0.7
G4 0.2 1 1
TABLE E(G,C) Factor endowments
C1 C2 C3 C4
G1 5
G2 5
G3 40
G4 40
TABLE ALPHA(G,C) Budget shares
C1 C2 C3 C4
G1 0.52 0.86 0.50 0.06
G2 0.40 0.10 0.20 0.25
G3 0.04 0.02 0.2975 0.0025
G4 0.04 0.02 0.0025 0.6875
TABLE A(G,S) Activity analysis matrix
S1 S2
G1 6 -1
G2 -1 3
G3 -4 -1
G4 -1 -1
$ONTEXT
$MODEL:KEHOE
$SECTORS:
Y(S)
$COMMODITIES:
P(G)
$CONSUMERS:
H(C)
$DEMAND:H(C) s: 1.00
E:P(G) Q:E(G,C)
D:P(G) Q:ALPHA(G,C)
$PROD:Y(S)
O:P(G)$(A(G,S) GT 0) Q:A(G,S)
I:P(G)$(A(G,S) LT 0) Q:(-A(G,S))
$OFFTEXT
$SYSINCLUDE mpsgeset KEHOE
PARAMETER PRICES(G,EQ), LEVELS(S,EQ);
LOOP(EQ,
$INCLUDE KEHOE.GEN
P.L(G) = SP(G,EQ);
SOLVE KEHOE USING MCP;
PRICES(G,EQ) = P.L(G);
LEVELS(S,EQ) = Y.L(S);
);
DISPLAY PRICES, LEVELS;
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