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Graphics - Production Possibility Frontier

Posted 10 years ago

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:
POSTED BY: Edo Nomics
Posted 10 years ago

Here's the best I can come up with:

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)}}]}, {Line[{{{0,
          185}, {9, 182}, {18, 177}, {27, 170}, {33, 163}, {40, 
         152.5}, {45, 143}, {50.5, 129}, {56, 112}, {60, 96}, {62.5, 
         83}, {65, 68}, {67, 50}, {69, 20}, {70, 0}}}]}}], {{a, 30}, 
  0, 50}, {{b, .6}, .0000001, 1}, {{X, 90}, 0, 100}]

I plotted the production possibility curve with the

Line[{{0, 185}, {9, 182}, {18, 177}, {27, 170}, {33, 163}, {40, 152.5}, {45, 143}, {50.5, 129}, {56, 112}, {60, 96}, {62.5, 83}, {65, 68}, {67, 50}, {69, 20}, {70, 0}}]

Any ideas how to make this simpler? Any ideas how make the curve smoother?

POSTED BY: Edo Nomics
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