# Having Trouble Setting up a System...

• Aug 31st 2009, 02:15 PM
teddydraiman
Having Trouble Setting up a System...
...of DEs in regards to a written problem we've been given. Here it is, followed by a tentative 'stab' at what is meant to be in the equation.

"Suppose that the time rate of change (ROC) of a price M(t) of a product, minus inflation I(t) is proportional to the difference between Supply S(t) at time t and some equilbrium supply t.

(If $S>S_0$ the supply is too large and cost 'will' decrease. If $S supply is too low and price 'will' increase)

Also assume that the ROC in supply is proportional to the difference between the price P and some equilibrium $P_0$

(If $P>P_0$ the price is too high and supply will increase. If $P the price is too low and supply will decrease)

We've also got that F(t) = sinwt

Now, this is what I have scribbled down in an attempt to get some working out, but I highly doubt that it is anywhere near correct, as I'm having trouble moving the knowledge of DEs from just straight questions into drawing stuff out of problems.

$dy/dt(M(t) - I(t))(s(t) - S_0$) = 0
I(t) = sinwt

As I've, I'm well from confident about it :( Can anyone help out at all? TYVM
• Sep 2nd 2009, 11:24 AM
Coomast
Quote:

Originally Posted by teddydraiman
...of DEs in regards to a written problem we've been given. Here it is, followed by a tentative 'stab' at what is meant to be in the equation.

"Suppose that the time rate of change (ROC) of a price M(t) of a product, minus inflation I(t) is proportional to the difference between Supply S(t) at time t and some equilbrium supply t.

(If $S>S_0$ the supply is too large and cost 'will' decrease. If $S supply is too low and price 'will' increase)

Also assume that the ROC in supply is proportional to the difference between the price P and some equilibrium $P_0$

(If $P>P_0$ the price is too high and supply will increase. If $P the price is too low and supply will decrease)

We've also got that F(t) = sinwt

Now, this is what I have scribbled down in an attempt to get some working out, but I highly doubt that it is anywhere near correct, as I'm having trouble moving the knowledge of DEs from just straight questions into drawing stuff out of problems.

$dy/dt(M(t) - I(t))(s(t) - S_0$) = 0
I(t) = sinwt

As I've, I'm well from confident about it :( Can anyone help out at all? TYVM

Have you read your post again after posting it? You designate the price with variable M and with variable P. Then F(t)=sin(wt) seems to be inflation I(t), or not? So this becomes difficult to follow and moreover what is the exact question?

I assume you mean by the first part:

$\frac{dM}{dt}-I(t)=-K\cdot \left(S(t)-S_0 \right)$

K is a proportionality constant. And by the second part:

$\frac{dS}{dt}=M(t)-M_0$

And finally:

$I(t)=sin(wt)$

If this is correct you can substitute the second and last part in the first one and obtain a second order DE. Please check this and come back to shed some light on these dark postingshadows :-)

Coomast
• Sep 3rd 2009, 02:09 AM
teddydraiman
Gah. I did mean that I(T) = sinwt, rather than F(T). And grud knows why I've switched between P and M for price.
All the rest is correctly interpreted. Very sorry for the confusion.
• Sep 6th 2009, 08:46 AM
Coomast
Quote:

Originally Posted by teddydraiman
Gah. I did mean that I(T) = sinwt, rather than F(T). And grud knows why I've switched between P and M for price.
All the rest is correctly interpreted. Very sorry for the confusion.

No problem I'm happy everything is sorted out with the question. OK, so can you write down the second order DE and solve it? It should look familiar....

coomast