(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 2595062, 49594]*) (*NotebookOutlinePosition[ 2595903, 49623]*) (* CellTagsIndexPosition[ 2595859, 49619]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["\<\ The Indiffernce Map of a von Neuman-Morgenstern Utility Function\ \>", "Section"], Cell[TextData[{ "This animation shows the how the shape of the indiffernce map of the \ utility function\n\t\t", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"u", "(", RowBox[{ FormBox[\(c\_B\), "TraditionalForm"], ",", FormBox[\(c\_G\), "TraditionalForm"], ",", FormBox[\(\[Pi]\_B\), "TraditionalForm"]}], ")"}], "=", RowBox[{ RowBox[{ FormBox[\(\[Pi]\_B\), "TraditionalForm"], " ", SuperscriptBox[ FormBox[\(c\_B\), "TraditionalForm"], "\[Alpha]"]}], "+", RowBox[{"(", RowBox[{"1", "-", RowBox[{ FormBox[\(\[Pi]\_B\), "TraditionalForm"], " ", FormBox[\()\( c\_G\^\[Alpha]\)\), "TraditionalForm"]}]}]}]}]}], TraditionalForm]]], " \nchanges as the probability of the bad state of the world (", Cell[BoxData[ \(TraditionalForm\`\[Pi]\_B\)]], ") varies between zero and one. The exponent in the utility function is \ held constant at \[Alpha] = .6 in this image sequence. Note that as the bad \ state of the world becomes more likely the indifference curves become \ steeper. This means the consumer is willing to give up more consumption in \ the good state of the world to obtain some additional consumption in the bad \ state of the world. With a given insurance premium, such an individual would \ purchase more insurance as the hazard becomes more likely." }], "Text"], Cell[CellGroupData[{ Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0 0.05 0 0.05 [ [1.025 0 0 -7.5 ] [1.025 0 18 7.5 ] [0 1.025 -9.5 0 ] [0 1.025 9.5 15 ] [.5 1.0125 -50 0 ] [.5 1.0125 50 52 ] [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid 0 0 m 1 0 L s gsave 1.025 0 -61 -11.5 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23 translate 1 -1 scale 63.000000 14.625000 moveto %%IncludeResource: font Times-Bold %%IncludeFont: Times-Bold /Times-Bold findfont 14.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 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