harmge.gms : Increasing returns with average cost pricing
MPSGE input file with an example from Kazuya Kamiya:
"Computation of Equilibria with Increasing Returns to Scale"
Discussion Paper Number 73, Faculty of Economics,
Osaka University, Tokyo, Japan.
Reference:
- Kamiya, K, Computation of Equilibria with Increasing Returns to Scale. Tech. rep., Faculty of Economics, Osaka University, ?.
Small Model of Types: MPSGE mcp
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$TITLE Increasing returns and average cost pricing (HARMGE,SEQ=148)
$Ontext
MPSGE input file with an example from Kazuya Kamiya:
"Computation of Equilibria with Increasing Returns to Scale"
Discussion Paper Number 73, Faculty of Economics,
Osaka University, Tokyo, Japan.
Kamiya, K, Computation of Equilibria with Increasing Returns to Scale.
Tech. rep., Faculty of Economics, Osaka University, ?.
$Offtext
SET G GOODS /X,Y/
F FACTORS /C,L/;
SCALAR A MARKUP PARAMETER /0/,
MCP FLAG FOR MARGINAL COST PRICING /1/;
PARAMETER NU(G) SCALE ELASTICITY FOR IRTS SECTORS /Y 0.3/
TABLE ALPHA(*,G) PRODUCTION TECHNOLOGY
X Y
L 0.4 0.46154
C 0.4 0.53846
K 0.2
PARAMETER BETA(G) PREFERENCE PARAMETERS /X 1, Y 1/;
PARAMETER ENDOW(*) Goods and factor endowments /
X 20
Y 20
C 20
L 20 /;
PARAMETER K(G) Specific capital stocks /
X 1 /;
$ONTEXT
$MODEL:KAMIYA
$SECTORS:
U ! UTILITY INDEX
Z(G) ! PRODUCTION OUTPUT
$COMMODITIES:
PU ! CONSUMPTION PRICE INDEX
P(G) ! OUTPUT PRICES
W(F) ! FACTOR PRICES
R(G)$ALPHA("K",G) ! SPECIFIC FACTORS IN NON-IRTS SECTORS
$CONSUMERS:
H ! REPRESENTATIVE AGENT
$AUXILIARY:
Q(G)$NU(G) ! QUANTITY ADJUSTMENT FOR IRTS SECTOR.
T(G)$NU(G) ! PRICING ADJUSTMENT FOR IRTS SECTOR.
*
* Utility index (Cobb-Douglas)
*
$PROD:U s:1.0
O:PU
I:P(G) Q:BETA(G)
*
* Increasing returns sector with endogenous pricing:
*
$PROD:Z(G) s:1.0
O:P(G) Q:1 A:H N:T(G)$NU(G)
I:W(F) Q:ALPHA(F,G)
I:R(G) Q:ALPHA("K",G)
* FINAL DEMAND:
$DEMAND:H
D:PU
E:P(G) Q:ENDOW(G)
E:W(F) Q:ENDOW(F)
E:R(G) Q:K(G)
E:P(G)$NU(G) Q:1.0 R:Q(G)
* Quantity adjustment:
*
$CONSTRAINT:Q(G)$NU(G)
Q(G) =E= Z(G)**(1+NU(G)) - Z(G);
* PRICING EQUATION:
$CONSTRAINT:T(G)$NU(G)
T(G) =E= 1 - ((1+NU(G)$MCP)/(1+A)) * Z(G)**NU(G);
$OFFTEXT
$SYSINCLUDE mpsgeset KAMIYA
* SPECIFY THAT T(G) AND Q(G) ARE FREE:
Q.LO(G)$NU(G) = -INF;
T.LO(G)$NU(G) = -INF;
$INCLUDE KAMIYA.GEN
SOLVE KAMIYA USING MCP;
SCALAR PNORM PRICE INDEX FOR NORMALIZATION;
PARAMETER PRICES(*,*) EQUILIBRIUM PRICES FOR VARIOUS PRICING RULES;
PNORM = SUM(G, P.L(G)) + SUM(F, W.L(F));
PRICES(G,"MCP") = P.L(G) / PNORM;
PRICES(F,"MCP") = W.L(F) / PNORM;
MCP = 0;
$INCLUDE KAMIYA.GEN
SOLVE KAMIYA USING MCP;
PNORM = SUM(G, P.L(G)) + SUM(F, W.L(F));
PRICES(G,"ACP") = P.L(G) / PNORM;
PRICES(F,"ACP") = W.L(F) / PNORM;
A=0.2;
$INCLUDE KAMIYA.GEN
SOLVE KAMIYA USING MCP;
PNORM = SUM(G, P.L(G)) + SUM(F, W.L(F));
PRICES(G,"A=0.2") = P.L(G) / PNORM;
PRICES(F,"A=0.2") = W.L(F) / PNORM;
A=0.5;
$INCLUDE KAMIYA.GEN
SOLVE KAMIYA USING MCP;
PNORM = SUM(G, P.L(G)) + SUM(F, W.L(F));
PRICES(G,"A=0.5") = P.L(G) / PNORM;
PRICES(F,"A=0.5") = W.L(F) / PNORM;
A=1.0;
$INCLUDE KAMIYA.GEN
SOLVE KAMIYA USING MCP;
PNORM = SUM(G, P.L(G)) + SUM(F, W.L(F));
PRICES(G,"A=1.0") = P.L(G) / PNORM;
PRICES(F,"A=1.0") = W.L(F) / PNORM;
A=5.0;
$INCLUDE KAMIYA.GEN
SOLVE KAMIYA USING MCP;
PNORM = SUM(G, P.L(G)) + SUM(F, W.L(F));
PRICES(G,"A=5.0") = P.L(G) / PNORM;
PRICES(F,"A=5.0") = W.L(F) / PNORM;
* DISPLAY THE RESULTS:
DISPLAY PRICES;
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