0
$\begingroup$

I'm trying to solve a second order difference equation. But there's a stochastic term inside the equation, I was wondering what should the correct way of approaching this problem? Here's the 2nd order equation:

$P_{t}+\lambda\frac{\eta^{s}}{\eta^{d}}P_{t-1}+\frac{(1-\lambda)\eta^{s}}{\eta^{d}}P_{t-1}=\frac{q^{d}-q^{s}}{\eta^d}-\frac{1}{\eta^d}\epsilon_{t}$

Or we could simplify it as $P_{t}+AP_{t-1}+BP_{t-1}=C-D\epsilon_{t}$

where $\epsilon_{t}$ is in iid random variable with zero mean

Should I assume the term is zero or what? Thanks a lot!


Just for your interest, it's derived from the following set of equations by equating (1) with (2), and substitute in (3) eventually. In economics it's called Cobweb model of agricultural production.

System of equations: $Q_{t}^{d}=q^{d}-\eta^dQ_{t}$ ---(1) is the demand equation

$Q_{t}^{s}=q^{s}+\eta^sP_{t}^{d}$ ----(2) is the supply equation

$P_{e}^{t}=\lambda*P_{t-1}+(1-\lambda)E_{t-1}*P_{t}$ ---(3) is how prices adjust

$\endgroup$
  • $\begingroup$ By the way, can someone advise me how to make the equations appear? I think the latex code is correct right? Thanks! First time using it... $\endgroup$ – George Apr 25 '15 at 8:53
  • 1
    $\begingroup$ What does \eta^P_{t}^{d} mean? $\eta^P_{t}^{d}$ Should it be $\eta^dP_{t}$? $\endgroup$ – user228113 Apr 25 '15 at 9:04
  • 1
    $\begingroup$ Put the LaTeX within dollar signs! $\endgroup$ – Math1000 Apr 25 '15 at 9:05
  • 1
    $\begingroup$ Thanks @Math1000! Yes, you're right @G. Sassatelli $\endgroup$ – George Apr 25 '15 at 9:14
0
$\begingroup$

I think I get it. I should probably take expectations on the second order DE equation. The prices in expectations will be substituted by the price adjustment equation.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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