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 $\displaystyle S>S_0$ the supply is too large and cost 'will' decrease. If $\displaystyle S<S_0$ 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 $\displaystyle P_0$

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

We've also got that F(t) = sin*wt*

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.

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

I(t) = sin*wt*

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