vonthmcp.gms : General Equilibrium Variant of the von Thunen Model
General Equilibrium Variant of the von Thunen Model
Reference:
- Rowse, Mackinnon, J, Samuelson, and von Thunen, General Equilibrium Variant of the von Thunen Model.
Small Model of Type: MCP
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$title General Equilibrium Variant of the Vonthunen Model (VONTHMCP,SEQ=136)
$Ontext
General Equilibrium Variant of the von Thunen Model
Rowse, Mackinnon, Samuelson, and von Thunen, General Equilibrium Variant
of the von Thunen Model.
$Offtext
set r regions /r1*r12/,
c commodities /wheat, rice, corn, barley/,
h households /worker, owner, porter/;
scalar ltot labor endowment /30/,
trns transport endowment /20/;
parameter d(r) distance to region r,
a(r) area of region r,
t(c) transport requirement
phi(c) cost function scale parameter
beta(c) cost function share parameter,
alpha(*,h) demand function share;
d(r) = 5 * (2 * ord(r) - 1);
a(r) = 2 * 3.1415 * d(r);
table misc(*,*)
wheat rice corn barley leisure
phi 1 2 3 4
beta 0.9 0.7 0.5 0.3
t 0.015 0.006 0.004 0.01
worker 0.2 0.3 0.1 0.3 0.1
owner 0.3 0.3 0.2 0.2
porter 0.6 0.2 0.1 0.1;
phi(c) = misc("phi",c);
beta(c) = misc("beta",c);
t(c) = misc("t",c);
alpha(c,h) = misc(h,c);
alpha("leisure",h) = misc(h,"leisure");
positive variables
cst(r,c) unit cost function
y(r,c) output level
ip(r) intervention purchase
pk(r) rental rate
wp porter wage
wl worker wage
p(c) market price;
equation def_cst(r,c)
prf_y(r,c)
pkbnd(r)
mkt_k(r)
mkt_t
mkt_l
mkt_g(c);
def_cst(r,c).. phi(c) * cst(r,c) =g=
(wl/beta(c))**beta(c) * (pk(r)/(1-beta(c)))**(1-beta(c));
prf_y(r,c).. cst(r,c) + t(c) * d(r) * wp =g= p(c);
pkbnd(r).. pk(r) =g= 0.0001 * wl;
mkt_k(r).. a(r) - ip(r) =g=
sum(c, y(r,c) * (1-beta(c)) * cst(r,c)) / pk(r) ;
mkt_t.. trns =g= sum((r,c), t(c) * d(r) * y(r,c));
mkt_l.. wl * ltot =g= sum((r,c), y(r,c) * beta(c) * cst(r,c))
+ alpha("leisure","porter") * ltot;
mkt_g(c).. p(c) * sum(r, y(r,c)) =g=
alpha(c,"porter") * trns * wp
+ alpha(c,"worker") * ltot * wl
+ alpha(c,"owner") * sum(r, pk(r) * (a(r) - ip(r)));
p.lo(c) = 0.1;
pk.lo(r) = 0.001;
model vonthun / def_cst.cst,
prf_y.y,
pkbnd.ip,
mkt_k.pk,
mkt_t.wp,
mkt_l.wl,
mkt_g.p /;
cst.l(r,c) = 1;
y.l(r,c) = 1;
ip.l(r) = 0;
pk.l(r) = 1;
wp.l = 1;
wl.l = 1;
p.l(c) = 1;
* use the labor wage as numeraire:
wl.fx = 1;
solve vonthun using mcp;
display y.l, cst.l;
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