MCP infeasible

GAMS
1

Hi all,

I’m using MCP to solve firm’s profit maximization as recommended by a paper.

output(t).. Y(t)=e=(kappa*[epsilon*K(t)**(1-1/sigma)+(1-epsilon)*L(t)**(1-1/sigma)]**[1/(1-1/sigma)])-0.5*psi*power(I(t)/K(t)-(n+delta),2)*K(t);
wage(t).. (1+cr)*w(t)=e=((1-epsilon)*kappa*L(t)**(-1/sigma)*(epsilon*K(t)**(1-1/sigma)+(1-epsilon)*L(t)**(1-1/sigma))**(-1+(1/(1-1/sigma))));
cost_accumulation(t).. q(t+1)=e=1+psi*(I(t)/K(t)-(n+delta));
cost(t).. r*q(t)=e=(epsilon*K(t)**(-1/sigma)*kappa*(epsilon*K(t)**(1-1/sigma)+(1-epsilon)*L(t)**(1-1/sigma))**(-1+(1/(1-1/sigma))))+0.5*psi*[power(I(t)/K(t),2)-power(n+delta,2)]+(1-delta)*q(t+1)-q(t);
capital_accumulation(t).. I(t)=e=K(t+1)-(1-delta)*K(t);

model a /output.Y wage.w cost_accumulation.q cost.I capital_accumulation.K /;
solve a using mcp;

I am having problems with the equation cost_accumulation(t) and cost(t), perhaps due to it being t+1. Equation cost(t) includes q(t+1) from cost_accumulation(t).

I appreciate any help to solve this

Thank,
Fabio

aa.gms (1.01 KB)

2

Hi Fabio

Some suggestions:

  • You should also take a close look at your equations and their derivations: the first two equations are just assignments as w(t) and y(t) appear only once (they are not used in any other equation), so you could drop them and find their values by using the solution.
  • Try to solve for only one period (surely not for 150). If I do that and take away the lower bounds, I get a solution with I<0. Does that make sense?
  • If you have all the parameters and a paper, you should be able to derive or take the capital stock in the first period as well as Q(“1”). Setting these values to the start values and setting the iteration limit to zero should point you to problems in the equations.
    Cheers
    Renger