[?] Solve a simple equation using RSolve?

Questions
,
1

I have the following two equations:

I. Subscript[Q, t] == Subscript[EE, t]*Subscript[NN, t] + 
  Subscript[FF, t]*Subscript[MM, t]

II. Subscript[FF, t] == Subscript[EE, t] - 1

I would like to solve it for Q_t so that II. in I. :

Subscript[Q, t] == Subscript[EE, t]*Subscript[NN, t] + 
      (Subscript[EE, t] - 1)*Subscript[MM,t]

How I can I do this in Mathematica?
Using RSolve gives me the following error:

RSolve::deqx: Supplied equations are not difference equations of the given functions.

I would also like to learn how to properly apply the RSolve function with symbolic equations.

2

You don’t have a recurrence equation where you can use RSolve. In your’s case:

    Eliminate[{Subscript[Q, t] == 
        Subscript[EE, t]*Subscript[NN, t] + 
         Subscript[FF, t]*Subscript[MM, t], 
       Subscript[FF, t] == Subscript[EE, t] - 1}, 
      Subscript[FF, t]] // Simplify

    % // TeXForm
\left(\text{EE}_t-1\right) \text{MM}_t+\text{EE}_t \text{NN}_t=Q_t
3

Would this be a recurrence problem?

I.

`Subscript[X, t] == (1 - \[Theta])*Sum[\[Theta]^(k - 1)*(Subscript[P, t - k] - Subscript[P, t - k - 1]),`

II.

`<{k, 1, t - 1}] + \[Theta]^(t - 1)*1,`

III. `

Subscript[NN, t] == Subscript[X, t]/(\[Gamma]*\[Sigma]^2),`

IV.

`Subscript[M, t] == (Subscript[D, t] - (T - t - 1)*\[Gamma]*\[Sigma]^2*Q - Subscript[P, t])/(\[Gamma]* \[Sigma]^2),

V.

EE*Subscript[NN, t] + FF*Subscript[MM, t] == Q,

V. `

EE == FF - 1`

I would like to solve this for Subscript[P, t]

4

Possible duplicate Question