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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:
 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?