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Comparative Statics - System of Equations

Posted 8 years ago
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Hello,
I have a system of 13 equations (13 endogenous variables, linear and nonlinear equations), and I try to compute various comparative statics. I have done it before for a different project but now I am stuck with an error message.

The error message is ""Power::infy: "Infinite expression 1/0 encountered."" as it enters equation g9 as 0.

Any help or proposals for efficient computations of comparative statics would be very appreciated.
 (* Endogenous variables: c, L, n, k, m, u, d, q, h, \[Delta], Vl, Vc *)
 ClearAll
 g1 = T - c - L - P    
 g2 = P*A - L*(\[Rho]* m + u)  
 g3 = - f + n*k - G[n] - F[m] - 
   D[F[m], m]*( (r + \[Delta])/D[\[Delta], m]) - (r*h*Vl)/(r + h) 
 g4 = (P*A*\[CapitalPi])/(L*n) - k
 g5 = D[G[n], n] - k
 g6 = c - n*L
g7 = D[F[m], m] -
  D[F[m], {m, 2}]*((r + \[Delta])/D[\[Delta], m]) - (\[Rho]*
    s)/(\[Alpha]*T)*\[Psi]
g8 = n - m - u - d
g9 = (D[\[Delta], m])^2 - D[\[Delta], {m, 2}]*(r + \[Delta])
g10 = \[Delta] - Pr[q , m]
g11 = h - \[Delta]/(n + \[Delta])
g12 = Vc - ((1 + r)*h*Vl)/(r + h)
g13 = Vl - (k*n - G[n] - D[F[m], m]*((r + \[Delta])/D[\[Delta], m]) -
    f )*(r + h)/(r*h)

All equations are written as gi = 0 - i=1,...,13.

Thank you!
POSTED BY: Tom G
Answer
3 Replies
Points needing clarification:

Do you mean that Delta is an undefined scalar variable?   D[ undefined variable, anything ] is zero.

My understanding from 5 minutes of study is that endogenous variables come from
within the system.  It looks like the symbols you labled as endogenous variables
are set outside this set of equations. Maybe we just need to see the whole program.

Please read the documentation for ClearAll.  The way you included it does nothing.
Posted 8 years ago
In[12]:= D[\[Delta], m]

Out[12]= 0

Differentiating one unknown variable with respect to another variable gives zero and that is in your denominator. That is the reason for this error message.
Posted 8 years ago
Thanks.
\Delta is a probability that follows from the probability function Pr(.) with arguments q and m. Hence, D[\Delta, m] should show the change in the probability function and therefore the change in the probability when varying m.

A change in an exogenous variable should affect q and m and therefore also the probability \Delta.

The approach works for this:
u = f[x]
D[u, x]
POSTED BY: Tom G
Answer
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