1
$\begingroup$

I am trying to solve this equation for kss with mathematical but the system is failing and so I am hoping to get some pointers here.

EulSS= B * Css^(-G)*(1 - D + A* kss^(1-A)) == Css^(-G) 

When I try Solve[EulSS, kss, Reals] it fails. When I try Reduce[{EulSS && Css > 0 && G > 0 && A > 0 && A < 1 && B > 0 && B < 1 && G > 0}, kss, Reals]it just goes into a constant loop.

I will appreciate the help.

$\endgroup$
3
  • $\begingroup$ I'm guessing it is too difficult for Reduce to sort out solutions in real space subject to the parameter constraints. You might instead solve with no restrictions. In[36]:= EulSS = B*Css^(-G)*(1 - D + A*kss^(1 - A)) == Css^(-G); Solve[EulSS, kss] During evaluation of In[36]:= Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. Out[37]= {{kss -> (-((Css^G (-Css^-G + B Css^-G - B Css^-G D))/( A B)))^(1/(1 - A))}} $\endgroup$ Jan 5 at 23:36
  • $\begingroup$ First: divide both sides by Css^(-G). Then, replace the derivative operator D with d. $\endgroup$ Jan 5 at 23:43
  • $\begingroup$ Thanks a lot for the proposal. I initially figured that mathematical would be able to work out the division from the information I provided. $\endgroup$ Jan 6 at 1:15

1 Answer 1

1
$\begingroup$
  1. Divide both sides by Css^(-G)
  2. Replace the derivative operator D by variable d
  3. Replace upper-case letters (which conflict with Mathematica's internal names) with lower-case symbols
  4. Ensure $0 < a < 1$

Then

Assuming[0<a<1,
Solve[k^(1 - a) == (1/b - 1 + d)/a, k,Reals]]

$$k = a^{\frac{1}{a-1}} \left(\frac{b}{b d-b+1}\right)^{\frac{1}{a-1}}$$

with constraints.

$\endgroup$
3
  • $\begingroup$ Thanks a lot for the proposal. I initially figured that mathematical would be able to work out the division from the information I provided. $\endgroup$ Jan 6 at 1:14
  • $\begingroup$ But your D was as inappropriate as an isolated Sin or Factor or ... $\endgroup$ Jan 6 at 18:14
  • $\begingroup$ I reworded it with the A, B and so for. I was using greek letters in mathematica and couldn't copy and paste that here. But again, thanks a lot for the suggestion and clarifications. $\endgroup$ Jan 7 at 1:36

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.