Description
Hansen's Activity Analysis Example.
Small Model of Type : MCP
Category : GAMS Model library
Main file : hansmcp.gms
$title Hansen's Activity Analysis Example (HANSMCP,SEQ=135)
$onText
Hansen's Activity Analysis Example.
Scarf, H, and Hansen, T, The Computation of Economic Equilibria.
Yale University Press, 1973.
Keywords: mixed complementarity problem, activity analysis, general equilibrium model,
social accounting matrix, european regional policy, impact analysis
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Set
c 'commodities' / agric, food, textiles, hserv, entert, houseop, capeop
steel, coal, lumber, housbop, capbop, labor, exchange /
h 'consumers' / agent1*agent4 /
s 'sectors' / dom1*dom12, imp1*imp7, exp1*exp7 /;
Alias (c,cc);
Table e(c,h) 'commodity endowments'
agent1 agent2 agent3 agent4
housbop 2 0.4 0.8
capbop 3 2 7.5
labor 0.6 0.8 1 0.6;
Table d(c,h) 'reference demands'
agent1 agent2 agent3 agent4
agric 0.1 0.2 0.3 0.1
food 0.2 0.2 0.2 0.2
textiles 0.1 0.1 0.3 0.1
hserv 0.1 0.1 0.1 0.1
entert 0.1 0.1 0.1 0.1
houseop 0.3 0.1 0.1
capeop 0.1 0.2 0.3;
Parameter esub(h) 'elasticities in demand' / agent1 1, agent2 1
agent3 1, agent4 1 /;
Table data(*,c,s) 'activity analysis matrix'
dom1 dom2 dom3 dom4 dom5
output.agric 5.00
output.food 5.00
output.textiles 2.00
output.hserv 2.00
output.entert 4.00
output.houseop 0.32
output.capeop 0.40 1.30 1.20
input .agric 3.50 0.10 0.70
input .food 0.90 0.10 0.80
input .textiles 0.20 0.50 0.10 0.10
input .hserv 1.00 2.00 2.00 2.00
input .steel 0.20 0.40 0.20 0.10
input .coal 1.00 0.10 0.10 1.00
input .lumber 0.50 0.40 0.30 0.30
input .housbop 0.40
input .capbop 0.50 1.50 1.50 0.10 0.10
input .labor 0.40 0.20 0.20 0.02 0.40
+ dom6 dom7 dom8 dom9 dom10
output.houseop 0.80
output.capeop 1.10 6.00 1.80 1.20 0.40
output.steel 2.00
output.coal 2.00
output.lumber 1.00
input .textiles 0.80 0.40 0.10 0.10 0.10
input .hserv 0.40 1.80 1.60 0.80 0.20
input .steel 1.00 2.00 0.50 0.20
input .coal 0.20 1.00 0.20
input .lumber 3.00 0.20 0.20 0.50
input .capbop 1.50 2.50 2.50 1.50 0.50
input .labor 0.30 0.10 0.10 0.40 0.40
+ dom11 dom12 imp1 imp2 imp3
output.agric 1.00
output.food 1.00
output.textiles 1.00
output.houseop 0.36
output.capeop 0.90
input .hserv 0.40 0.20 0.20
input .housbop 0.40
input .capbop 1.00 0.20 0.10 0.10
input .labor 0.04 0.02 0.02
input .exchange 0.50 0.40 0.80
+ imp4 imp5 imp6 imp7 exp1
output.capeop 1.00
output.steel 1.00
output.coal 1.00
output.lumber 1.00
output.exchange 0.50
input .agric 1.00
input .hserv 0.40 0.40 0.40 0.40 0.20
input .capbop 0.20 0.20 0.20 0.20 0.20
input .labor 0.04 0.04 0.04 0.04 0.04
input .exchange 1.20 0.60 0.70 0.40
+ exp2 exp3 exp4 exp5 exp6
output.exchange 0.40 0.80 1.20 0.60 0.70
input .food 1.00
input .textiles 1.00
input .hserv 0.20 0.20 0.40 0.40 0.40
input .capeop 1.00
input .steel 1.00
input .coal 1.00
input .capbop 0.10 0.10 0.20 0.20 0.20
input .labor 0.02 0.02 0.04 0.04 0.04
+ exp7
output.exchange 0.40
input .hserv 0.40
input .lumber 1.00
input .capbop 0.20
input .labor 0.04;
Parameter
alpha(c,h) 'demand function share parameter'
a(c,s) 'activity analysis matrix';
alpha(c,h) = d(c,h)/sum(cc, d(cc,h));
a(c,s) = data("output",c,s) - data("input",c,s);
Positive Variable
p(c) 'commodity price'
y(s) 'production'
i(h) 'income';
Equation
mkt(c) 'commodity market'
profit(s) 'zero profit'
income(h) 'income index';
* distinguish ces and cobb-douglas demand functions:
mkt(c).. sum(s, a(c,s)*y(s)) + sum(h, e(c,h))
=g= sum(h$(esub(h) <> 1), (i(h)/sum(cc, alpha(cc,h)*p(cc)**(1 - esub(h))))
* alpha(c,h)*(1/p(c))**esub(h))
+ sum(h$(esub(h) = 1), i(h)*alpha(c,h)/p(c));
profit(s).. -sum(c, a(c,s)*p(c)) =g= 0;
income(h).. i(h) =g= sum(c, p(c)*e(c,h));
Model hansen / mkt.p, profit.y, income.i /;
p.l(c) = 1;
y.l(s) = 1;
i.l(h) = 1;
p.lo(c) = 0.00001$(smax(h, alpha(c,h)) > eps);
* fix the price of numeraire commodity:
p.fx(c)$(ord(c) = 1) = 1;
solve hansen using mcp;