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We \ start with the following inverse demand functions"], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "p1[x1_,x2_] := 10 - b1 x1 - c x2\np2[x1_,x2_] := 10 - b2 x2 - c x1"], "Input",\ AspectRatioFixed->True], Cell[TextData["The profit functions become"], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "profit1[x1_,x2_] := Evaluate[p1[x1,x2]*x1]\nprofit2[x1_,x2_] := \ Evaluate[p2[x1,x2]*x2]"], "Input", AspectRatioFixed->True], Cell[TextData["The reaction curves are determined by"], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "solution1=Solve[D[profit1[x1,x2],x1]==0,x1][[1]]\n\ solution2=Solve[D[profit2[x1,x2],x2]==0,x2][[1]]\nr1[x2_] := \ Evaluate[x1/.solution1]\nr2[x1_] := Evaluate[x2/.solution2]"], "Input", AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "If we fix the parameters, we can plot these isoprofit contours. We will \ set ", Evaluatable->False, AspectRatioFixed->True], StyleBox["c=b1", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[", so that the two goods are perfect substitutes.", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "b1=b2=c=1\nisoprofitLines=ContourPlot[profit1[x1,x2],\n\ {x1,0,7},{x2,0,7},ContourShading->False]"], "Input", AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "We can also plot the reaction curves. Here's a neat way to do it using ", Evaluatable->False, AspectRatioFixed->True], StyleBox["ParametricPlot", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[".", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "reactionCurves=ParametricPlot[{{r1[t],t},{t,r2[t]}},{t,0,7}]\n\ Show[isoprofitLines,reactionCurves]"], "Input", AspectRatioFixed->True]}, Open]], Cell[CellGroupData[{Cell[TextData["Stackelberg equilibrium"], "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "We derived the reaction curve for firm 2 above. 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