-Michael
Code: Select all
Set
i 'regions' / A, B /;
Parameter
T(i) 'transportation cost' /A 1
B 1/
lambda(i) 'fraction of labourers in region' / A 0.4
B 0.6 /;
Scalar
delta 'fraction of income spent on manufactured goods' / 0.7 /
epsilon 'substitutability' / 1.5 /;
variables
z 'total income'
y(i) 'income level'
w(i) 'wage level'
p(i) 'price level';
Positive Variable y(i),w(i),p(i);
Equation
incomeEquation(i) 'income level in region i'
wageEquation(i) 'wage level in region i'
priceEquation(i) 'prive level in region i'
GDP 'total income of economy';
alias (i,i2);
GDP.. z =e= sum(i,y(i));
incomeEquation(i).. y(i) =e= (lambda(i)*delta*w(i) + 0.5*(1-delta));
wageEquation(i).. w(i) =e=(sum(i2,y(i2)*(T(i2)**(1-epsilon))*(p(i2)**(epsilon-1))))**(1/epsilon);
priceEquation(i).. p(i) =e= (sum(i2, lambda(i2)*(w(i2)**(1-epsilon))*(T(i2)**(1-epsilon))))**(1/(1-epsilon));
Model neecge / all /;
p.lo(i) = 1e-6;
w.lo(i) = 1e-6;
y.l(i) = 1;
p.l(i) = 1;
w.l(i) = 1;
solve neecge using nlp maximizing z;