scarfmcp.gms : Scarf's Activity Analysis Example
Scarf's Activity Analysis Example
Reference:
- Scarf, H, and Hansen, T, The Computation of Economic Equilibria. Yale University Press, 1973.
Small Model of Type: MCP Includes: scarfdata.inc
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$title Scarf's Activity Analysis Example (SCARFMCP,SEQ=132)
$Ontext
Scarf's Activity Analysis Example
Scarf, H, and Hansen, T, The Computation of Economic Equilibria.
Yale University Press, 1973.
$Offtext
$include scarfdata.inc
positive
variables
p(c) commodity price,
y(s) production,
i(h) income;
equations
mkt(c) commodity market,
profit(s) zero profit,
income(h) income index;
* distinguish ces and cobb-douglas demand functions:
mkt(c).. sum(s, a(c,s) * y(s)) + sum(h, e(c,h)) =g=
sum(h$(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$(esub(h) eq 1),
i(h) * alpha(c,h) / p(c));
profit(s).. -sum(c, a(c,s) * p(c)) =g= 0;
income(h).. i(h) =g= sum(c, p(c) * e(c,h));
model scarf / mkt.p, profit.y, income.i/;
p.l(c) = 1;
y.l(s) = 1;
i.l(h) = sum(c, p.l(c) * e(c,h));
p.lo(c) = 0.00001$(smax(h, alpha(c,h)) gt eps);
* fix the price of numeraire commodity:
i.fx(h)$(ord(h) eq 1) = i.l(h);
solve scarf using mcp;
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