Composition of functions not working [closed]

Question

I am trying to set a function within a function. What I do is to first create a function with two arguments. Then I would like to set a new function with the same two arguments, in which the previous function is inside the new one. However, when I do this, it seems that it does not read it properly.

I would appreciate it if sb could tell me what I am doing wrong.

See code below.

    Subscript[p, 1][Subscript[q, 1] _, Subscript[q, 2] _] := 
 Subscript[α, 1] + γ Subscript[q, 2] + 
  Subscript[q, 1] Subscript[β, 1]
Subscript[Π, 1][Subscript[q, 1] _, 
  Subscript[q, 
   2] _] := (Subscript[p, 1][Subscript[q, 1], Subscript[q, 2]] - 
    Subscript[w, 1])*Subscript[q, 1]
Subscript[Π, 1][Subscript[q, 1] _, Subscript[q, 2] _]

And see the picture for help

Answer 1

You must use Symbolize of the built-in Notation` package to use Subscripts as symbols.

Note: I symbolized both p and q below but you only need to symbolize q for the below to work.

Only symbols can be used as parameter names for function definitions. However, your subscripted expressions are not symbols.

Head @ Subscript[q, 1]

Subscript

With the Notation package and its helpful palette you can Symbolize these expressions.

Needs["Notation`"]
Symbolize[NotationTemplateTag[Subscript[p, _]]]
Symbolize[NotationTemplateTag[Subscript[q, _]]]

Subscripted p and q are now parsed as symbols.

Head @ Subscript[q, 1]

Symbol

One final step is we must use the Optional syntax when using these Symbolized symbols as parameter names.

Subscript[p, 1][Subscript[q, 1] : _, Subscript[q, 2] : _] := 
 Subscript[α, 1] + γ Subscript[q, 2] + Subscript[q, 1] Subscript[β, 1]

Notebook view below; easier to read.

You also have the ability to assign values to your symbolized subscripted symbols.

Subscript[q, 1] = 5;
Subscript[\[CapitalPi], 1][Subscript[q, 1], Subscript[q, 2]]

Symbolized symbols can be removed with RemoveSymbolize; also in the palette.

RemoveSymbolize[NotationTemplateTag[Subscript[p, _]] ]
RemoveSymbolize[NotationTemplateTag[Subscript[q, _]] ]

Hope this helps.