hansmcp.gms : Hansen's Activity Analysis Example - MCP
Hansen's Activity Analysis Example
Reference:
- Scarf, H, and Hansen, T, The Computation of Economic Equilibria. Yale University Press, 1973.
Small Model of Type: MCP
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$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.
$Offtext
sets c commodities
/ agric, food, textiles, hserv, entert, houseop, capeop, steel,
coal, lumber, housbop, capbop, labor, exchange/
h consumers
/ agent1, agent2, agent3, agent4 /
s sectors
/ dom1, dom2, dom3, dom4, dom5, dom6, dom7,
dom8, dom9, dom10, dom11, dom12,
imp1, imp2, imp3, imp4, imp5, imp6, imp7,
exp1, exp2, exp3, exp4, exp5, exp6, 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;
alpha(c,h) = d(c,h) / sum(cc, d(cc,h));
parameter a(c,s) activity analysis matrix;
a(c,s) = data("output",c,s) - data("input",c,s);
positive
variables
p(c) commodity price,
y(s) production,
i(h) income;
equations
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) ne 1),
(i(h)/sum(cc, alpha(cc,h) * p(cc)**(1-esub(h)))) *
alpha(c,h) * (1/p(c))**esub(h)) +
sum(h$(esub(h) eq 1),
i(h) * alpha(c,h) / p(c));
profit(s).. -sum(c, a(c,s) * p(c)) =g= 0;
income(h).. i(h) =g= sum(c, p(c) * e(c,h));
model hansen / mkt.p, profit.y, income.i/;
p.l(c) = 1;
y.l(s) = 1;
i.l(h) = 1;
p.lo(c) = 0.00001$(smax(h, alpha(c,h)) gt eps);
* fix the price of numeraire commodity:
p.fx(c)$(ord(c) eq 1) = 1;
solve hansen using mcp;
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