(*********************************************************************** 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[ 1543456, 35021]*) (*NotebookOutlinePosition[ 1544192, 35047]*) (* CellTagsIndexPosition[ 1544148, 35043]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Expected Utility: Varying the degree of risk aversion when the insurance \ contract has a positive expected profit\ \>", "Section"], Cell[TextData[{ "In this case the exponent in the utility function varies from .15 to .9 \ (i.e., \[Alpha] =.15, ", Cell[BoxData[ \(\[Alpha]\^\[Prime]\)]], "= .9). The probability of landing in the bad state of the world is held \ constant at ", Cell[BoxData[ \(\[Pi]\_B = .3\)]], ". The insurance contract has a positive expected profit, meaning \[Gamma] \ > ", Cell[BoxData[ \(TraditionalForm\`\[Pi]\_B\)]], ". In this case \[Gamma] =.25. The utility function is\n\t ", Cell[BoxData[ \(TraditionalForm\`\(\ u(c\_\(B\ \), c\_G, \[Pi]\_\(B\ \), 1 - \ \[Pi]\_B\ ) = \[Pi]\_B\ c\_B\%\[Alpha] + c\_G\%\[Alpha]\ \((1 - \[Pi]\_B)\)\)\)]], ".\nNote that with an unfair insurance contract, the consumer equilibrium \ occurs at less than full insurance (i.e., to the left the 45 degree line \ where the consumer has the same consumption in both the good and bad states \ of the world ). As the person becomes more risk averse, the equilibrium moves \ down the budget line--closer to full insurance." }], "Text"], Cell[CellGroupData[{ Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1.96 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 0.0238095 0.952381 0.0466667 0.952381 [ [ 0 0 0 0 ] [ 1 1.96 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.96 L 0 1.96 L closepath clip newpath % Start of user PostScript /mathtops { gsave MBeginOrig moveto MEndOrig currentpoint grestore } bind def /MAtocoords { mathtops 4 2 roll mathtops 4 copy pop pop 3 -1 roll sub /arry exch def exch sub /arrx exch def arrx dup mul arry dup mul add sqrt /arrl exch def translate } bind def /MAarrowhead1 { gsave MAtocoords arrl 0. eq { 0 0 Mdot } { [ arrx arrl div arry arrl div 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