This has done serious injury to your code, but I believe it has also fixed some serious errors. For example, the expression to be displayed now appears before all the manipulate controls. That is as the documentation for Manipulate shows. The code appears to work now.

Manipulate[
 Subscript[k, 11] = (Subscript[\[Alpha], 1]/(1 - Subscript[\[Alpha], 1]))*Subscript[r, 1];
 Subscript[\[Eta], 11] = 1/(-1 + Subscript[\[Alpha], 1])/(E^(-Subscript[\[Alpha], 1]*Subscript[g1, 0])*
    (1/(Subscript[r, 1]*(1 - Subscript[\[Alpha], 1])))^-Subscript[\[Alpha], 1]);
 Subscript[y, 11] = (1 - Subscript[\[Eta], 11])*E^((1 - Subscript[\[Alpha], 1])*Subscript[g1, 0])*
   Subscript[k, 11]^Subscript[\[Alpha], 1];
 Subscript[g1, 1] = Subscript[\[Alpha], 1]*Subscript[g1, 0];
 Subscript[r, 2] = Subscript[\[Alpha], 1]*((1 - Subscript[\[Eta], 11])/(1 - 2*Subscript[\[Eta], 11]));
 Subscript[k, 12] = (Subscript[\[Alpha], 1]/(1 - Subscript[\[Alpha], 1]))*Subscript[r, 2];
 Subscript[\[Eta], 12] = 1/(-1 + Subscript[\[Alpha], 1])/(E^(-Subscript[\[Alpha], 1]*Subscript[g1, 1])*
    (1/(Subscript[r, 2]*(1 - Subscript[\[Alpha], 1])))^-Subscript[\[Alpha], 1]);
 Subscript[y, 12] = (1 - Subscript[\[Eta], 12])*E^((1 - Subscript[\[Alpha], 1])*Subscript[g1, 1])*
    Subscript[k, 12]^Subscript[\[Alpha], 1];
 Subscript[g1, 2] = Subscript[\[Alpha], 1]*Subscript[g1, 1];
 Subscript[r, 3] = Subscript[\[Alpha], 1]*((1 - Subscript[\[Eta], 12])/(1 - 2*Subscript[\[Eta], 12]));
 Subscript[k, 13] = (Subscript[\[Alpha], 1]/(1 - Subscript[\[Alpha], 1]))*Subscript[r, 3];
 Subscript[\[Eta], 13] = 1/(-1 + Subscript[\[Alpha], 1])/(E^(-Subscript[\[Alpha], 1]*Subscript[g1, 2])*
    (1/(Subscript[r, 3]*(1 - Subscript[\[Alpha], 1])))^-Subscript[\[Alpha], 1]);
 Subscript[y, 13] = (1 - Subscript[\[Eta], 13])*E^((1 - Subscript[\[Alpha], 1])*Subscript[g1, 2])*
    Subscript[k, 13]^Subscript[\[Alpha], 1];
 Subscript[g1, 3] = Subscript[\[Alpha], 1]*Subscript[g1, 2];
 Subscript[r, 4] = Subscript[\[Alpha], 1]*((1 - Subscript[\[Eta], 13])/(1 - 2*Subscript[\[Eta], 13]));
 ListLinePlot[{{Subscript[\[Eta], 11], Subscript[\[Eta], 12], Subscript[\[Eta], 13]},
     {Subscript[y, 11], Subscript[y, 12], Subscript[y, 13]}}],
 {{Subscript[\[Alpha], 1], 0.4, "\[Alpha]1"}, 0.1, 1, Appearance -> "Labeled"},
 {{Subscript[r, 1], 1, "r"}, 1, 5, Appearance -> "Labeled"},
 {{Subscript[g1, 0], 1, "g1"}, 1, 5, Appearance -> "Labeled"}]

Perhaps you can try making one small change at a time to make the code look more like your original and see if it continues to work after each change or try to understand why the change makes it no longer work.