Hello,

How can I add a production possibility frontier (curve) to the attached code? The production possibility frontier is a smooth, bowed-out curve that is concave to the origin. It's position is fixed on the axes. Here's the code I have so far:

Manipulate[
 Plot[((a/(1 - b)) + (b/(1 - b))*X), {X, 0, 100}, 
  PlotRange -> {{0, 100}, {0, 300}}, AxesOrigin -> {0, 0}, 
  LabelStyle -> Directive[12], AxesLabel -> {"X-axis", "Y-axis"}, 
  Ticks -> {{{X/2, 
      X}}, {{((a/(1 - b)) + (b/(1 - b))*
         X/2), ((a/(1 - b)) + (b/(1 - b))*X)}}}, 
  Epilog -> {{Dashed, 
     Line[{{X/2, 
        0}, {X/2, ((a/(1 - b)) + (b/(1 - b))*X/2)}}]}, {Dashed, 
     Line[{{X/
         2, ((a/(1 - b)) + (b/(1 - b))*
           X/2)}, {0, ((a/(1 - b)) + (b/(1 - b))*X/2)}}]}}], {{a, 30},
   0, 50}, {{b, .6}, .0000001, 1}, {{X, 90}, 0, 100}]

I attached a PDF file to show what I have in mind. How can I add a production possibility frontier to this code?

Attachments: