You have defined x to be a function of Pn only, but in fact, it is dependent on several other parameters and you are not passing those values into the function. So, they are global. But inside Manipulate, they are local control variables. One way to address this is to make sure all of your functions pass in all of the parameter values:

x[Pn_, h_, d_] := (h (d/Pn)^d)^(1/(1 - d));

nx[Pn_, h_, d_] := d/Pn x[Pn, h, d];

Bx[Pn_, h_, d_] := (1 - d)*x[Pn, h, d];

f[z_] := -0.0003*z^3 + 0.006*z^2 - 0.1*z + 1;

n[Pn_, k_, h_, d_] := k f[x[Pn, h, d]];

Bn[Pn_, k_, h_, d_] := Pn n[Pn, k, h, d];

r[Pn_, k_, h_, d_] := Bx[Pn, h, d] + Bn[Pn, k, h, d];

xc[Pn_, a_, k_, h_, d_] := a r[Pn, k, h, d];

nc[Pn_, a_, k_, h_, d_] := (1 - a)/Pn r[Pn, k, h, d];

eq[Pn_, k_, a_, h_, d_] := 
  n[Pn, k, h, d] - nc[Pn, a, k, h, d] - nx[Pn, h, d];

Manipulate[
 FindRoot[eq[Pn, k, a, h, d] == 0, {Pn, 0.5966337871664869`}], {h, 4, 
  5}, {d, 0.3, 2}, {a, 0.5, 1}, {k, 20, 100}]

Here are some improvement suggestions: 1) you should use Definition if it is really a definition to be evaluated later on. f[Z_] is not proper in your code and you should write it as f[Z] instead because you use simple assignment rule. 2) do not use single Capital letters for variable names as they may interfere with Mathematica global variables 3) use single Simplify command to reduce the number of equations in one simple equations={eq1, eq2, ...eq13}//Simplify 4) Manipulate[ FindRoot[equations, ...], followed by parameter sliders

Hope this helps

Jones

the problem is that I have not managed to run me otherwise, everything works perfectly but fails to work me without using the OUT [%] also would eliminate all that and the program work without placing me Simplify[]

Thx