(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing 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[ 23350, 976]*) (*NotebookOutlinePosition[ 107323, 3812]*) (* CellTagsIndexPosition[ 107279, 3808]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[StyleBox["Choice under Uncertainty", FontSize->24]], "Text"], Cell[BoxData[ \(<< Utilities`Notation`\)], "Input"], Cell[BoxData[ RowBox[{"Symbolize", "[", TagBox[\(p\_1\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}]], "Input"], Cell[BoxData[ RowBox[{"Symbolize", "[", TagBox[\(p\_2\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}]], "Input"], Cell[BoxData[ RowBox[{"Symbolize", "[", TagBox[\(u\_1\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}]], "Input"], Cell[BoxData[ RowBox[{"Symbolize", "[", TagBox[\(u\_2\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}]], "Input"], Cell[BoxData[ RowBox[{"Symbolize", "[", TagBox[\(w\_1\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}]], "Input"], Cell[BoxData[ RowBox[{"Symbolize", "[", TagBox[\(w\_2\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}]], "Input"], Cell[TextData[StyleBox["Example 1: Insurance", FontSize->18]], "Text"], Cell[TextData[{ StyleBox["Definitions: ", FontVariations->{"Underline"->True}], "\nw = current wealth\nL = loss in case of adverse event\np = probability \ of adverse event\nq = insurance rate (cost of insurance per dollar of \ coverage)\n\[Alpha] = amount of coverage purchased\n\n", "The following Clear[] command is for your convenience. It deletes all \ numerical associations to the symbols in []. Use it whenever you get stuck \ and want to start from the beginning. " }], "Text"], Cell[BoxData[ \(Clear[u, r, w, W, L, p, q]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(u[w_] = \@w\)], "Input"], Cell[BoxData[ \(\@w\)], "Output"] }, Open ]], Cell["\<\ First check on the curvature properties of u[w]. Is this utility function \ concave over money?\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \({check1, check2} = Simplify[{D[u[x], x], D[u[x], x, x]}]\)], "Input"], Cell[BoxData[ \({1\/\(2\ \@x\), \(-\(1\/\(4\ x\^\(3/2\)\)\)\)}\)], "Output"] }, Open ]], Cell["\<\ Yes- we have a positive slope and a negative second derivative over all x>0. \ Next, compute the Arrow-Pratt coefficient of absolute risk aversion, and the \ coefficient of relative risk aversion.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \({r\_A, r\_R} = Simplify[{\(-D[u[x], x, x]\)/D[u[x], x], \(-x\)* D[u[x], x, x]/D[u[x], x]}]\)], "Input"], Cell[BoxData[ \({1\/\(2\ x\), 1\/2}\)], "Output"] }, Open ]], Cell["\<\ In words: u[x] exhibits \"decreasing absolute risk aversion\", and constant \ \"relative risk aversion\".\ \>", "Text"], Cell["Solve for optimal amount of insurance coverage", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(EU = p*u[w - L - \[Alpha]*q + \[Alpha]] + \((1 - p)\)* u[w - \[Alpha]*q]\)], "Input"], Cell[BoxData[ \(\((1 - p)\)\ \@\(w - q\ \[Alpha]\) + p\ \@\(\(-L\) + w + \[Alpha] - q\ \[Alpha]\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(FOC = D[EU, \[Alpha]]\)], "Input"], Cell[BoxData[ \(\(-\(\(\((1 - p)\)\ q\)\/\(2\ \@\(w - q\ \[Alpha]\)\)\)\) + \(p\ \((1 - \ q)\)\)\/\(2\ \@\(\(-L\) + w + \[Alpha] - q\ \[Alpha]\)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(sol = \(Solve[FOC \[Equal] 0, \[Alpha]]\)[\([1]\)]\)], "Input"], Cell[BoxData[ \({\[Alpha] \[Rule] \(\(-L\)\ q\^2 + 2\ L\ p\ q\^2 - L\ p\^2\ q\^2 - p\^2\ \ w + 2\ p\^2\ q\ w + q\^2\ w - 2\ p\ q\^2\ w\)\/\(\((p\^2 + q - 2\ p\ q)\)\ \ \((\(-q\) + q\^2)\)\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[%]\)], "Input"], Cell[BoxData[ \({\[Alpha] \[Rule] \(\(-L\)\ \((\(-1\) + p)\)\^2\ q\^2 + \((q\^2 - 2\ p\ \ q\^2 + p\^2\ \((\(-1\) + 2\ q)\))\)\ w\)\/\(\((\(-1\) + q)\)\ q\ \((p\^2 + q \ - 2\ p\ q)\)\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\[Alpha]\^*\) = \[Alpha] /. %\)], "Input"], Cell[BoxData[ \(\(\(-L\)\ \((\(-1\) + p)\)\^2\ q\^2 + \((q\^2 - 2\ p\ q\^2 + p\^2\ \ \((\(-1\) + 2\ q)\))\)\ w\)\/\(\((\(-1\) + q)\)\ q\ \((p\^2 + q - 2\ p\ \ q)\)\)\)], "Output"] }, Open ]], Cell["Let's work with actual numbers to make things more explicit", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \({w = 1000, L = 800, p = .5, q = .6}\)], "Input"], Cell[BoxData[ \({1000, 800, 0.5`, 0.6`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\[Alpha]\^*\)\)], "Input"], Cell[BoxData[ \(366.6666666666669`\)], "Output"] }, Open ]], Cell["\<\ This implies we under-insure - the standard result for actuarilly unfair \ contracts (q>p). Verify that expected utility is higher under insurance than \ non-insurance\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(EUi = p*u[w - L - \[Alpha]*q + \[Alpha]] + \((1 - p)\)* u[w - \[Alpha]*q] /. \[Alpha] -> \(\[Alpha]\^*\)\)], "Input"], Cell[BoxData[ \(23.27373340628157`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(EUn = p*u[w - L] + \((1 - p)\)*u[w] /. \[Alpha] -> \(\[Alpha]\^*\)\)], "Input"], Cell[BoxData[ \(22.882456112707374`\)], "Output"] }, Open ]], Cell["\<\ At this coverage, what is the insurance premium (i.e. the amount paid to the \ insurance company)?\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Pr = \(\[Alpha]\^*\)*q\)], "Input"], Cell[BoxData[ \(220.00000000000014`\)], "Output"] }, Open ]], Cell[TextData[StyleBox["How would these results change under fair odds?", FontSize->14]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \({w = 1000, L = 800, p = .5, q = .5}\)], "Input"], Cell[BoxData[ \({1000, 800, 0.5`, 0.5`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\[Alpha]\^*\)\)], "Input"], Cell[BoxData[ \(800.`\)], "Output"] }, Open ]], Cell["Full insurance, as expected.", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(EUi = p*u[w - L - \[Alpha]*q + \[Alpha]] + \((1 - p)\)* u[w - \[Alpha]*q] /. \[Alpha] -> \(\[Alpha]\^*\)\)], "Input"], Cell[BoxData[ \(24.49489742783178`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(EUn = p*u[w - L] + \((1 - p)\)*u[w] /. \[Alpha] -> \(\[Alpha]\^*\)\)], "Input"], Cell[BoxData[ \(22.882456112707374`\)], "Output"] }, Open ]], Cell["\<\ The differences in EU has increased - insurance has become relatively more \ attractive.\ \>", "Text"], Cell[TextData[{ "At these odds, what is the highest premium and the highest insurance rate \ the individual will pay for ", StyleBox["full", FontWeight->"Bold"], " insurance? To answer this question, we need to find the certainty \ equivalent to a \"no insurance\" gamble." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Solve[u[c] \[Equal] EUn, c]\)[\([1]\)] /. \[Alpha] -> \(\[Alpha]\^*\)\)], "Input"], Cell[BoxData[ \({c \[Rule] 523.606797749979`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Prmax = w - c /. %\)], "Input"], Cell[BoxData[ \(476.393202250021`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(qmax = Prmax/\(\[Alpha]\^*\)\)], "Input"], Cell[BoxData[ \(0.5954915028125263`\)], "Output"] }, Open ]], Cell["\<\ Compare this certainty equivalent to the expected value of a \"no insurance\" \ gamble.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(EVn = p*\((w - L)\) + \((1 - p)\)*w /. \[Alpha] -> \(\[Alpha]\^*\)\)], "Input"], Cell[BoxData[ \(600.`\)], "Output"] }, Open ]], Cell["So c < EVn, another indication of risk aversion.", "Text"], Cell[TextData[StyleBox["Example 2: Risk Premium (=\"Probability Premium\")", FontSize->18]], "Text"], Cell["\<\ Find the generic expression for the risk premium for the utility function \ u[x]=Log[x].\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Solve[ u[x] == \((1/2 + rp)\)*u[x + \[Epsilon]] + \((1/2 - rp)\)* u[x - \[Epsilon]], rp]\)[\([1]\)]\)], "Input"], Cell[BoxData[ \({rp \[Rule] \(\(-2\)\ \@x + \@\(x - \[Epsilon]\) + \@\(x + \[Epsilon]\)\ \)\/\(2\ \((\@\(x - \[Epsilon]\) - \@\(x + \[Epsilon]\))\)\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(rp = rp /. %\)], "Input"], Cell[BoxData[ \(\(\(-2\)\ \@x + \@\(x - \[Epsilon]\) + \@\(x + \[Epsilon]\)\)\/\(2\ \((\ \@\(x - \[Epsilon]\) - \@\(x + \[Epsilon]\))\)\)\)], "Output"] }, Open ]], Cell["\<\ Assume the individual starts with wealth = w (from above). Somebody proposes \ an investment that may lead to a loss or gain of \[Epsilon]=800 with some \ probability p, and (1-p), respectively. How much lower than 1/2 must p be \ (or, equivalently, how much better than 50% must the chance of winning be) \ for the individual to accept the gamble?\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(N[rp /. {x \[Rule] w, \[Epsilon] \[Rule] 800}]\)], "Input"], Cell[BoxData[ \(0.11803398874989493`\)], "Output"] }, Open ]], Cell[BoxData[ \(Clear[c, rp, p, q, w, L]\)], "Input"], Cell[TextData[StyleBox["Example 4: Exercise: MC 6.C.18", FontSize->18]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(u[x_] = \@x\)], "Input"], Cell[BoxData[ \(\@x\)], "Output"] }, Open ]], Cell["Part (a)", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \({r\_A, r\_R} = {\(-D[u[x], x, x]\)/D[u[x], x], \(-x\)* D[u[x], x, x]/D[u[x], x]}\)], "Input"], Cell[BoxData[ \({1\/\(2\ x\), 1\/2}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \({r\_A, r\_R} /. x \[Rule] 5\)], "Input"], Cell[BoxData[ \({1\/10, 1\/2}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \({W, L, p\_1, p\_2} = {16, 4, 1/2, 1/2}\)], "Input"], Cell[BoxData[ \({16, 4, 1\/2, 1\/2}\)], "Output"] }, Open ]], Cell["Part (b) ", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(EU = p\_1*u[W] + p\_2*u[L]\)], "Input"], Cell[BoxData[ \(3\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Solve[u[c] \[Equal] EU, c]\)[\([1]\)]\)], "Input"], Cell[BoxData[ \({c \[Rule] 9}\)], "Output"] }, Open ]], Cell["Compare to expected VALUE of the lottery:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(EV = p\_1*W + p\_2*L\)], "Input"], Cell[BoxData[ \(10\)], "Output"] }, Open ]], Cell["\<\ For the risk premium part, we need to start at a wealth level that is \ equidistant from 16 and 4, i.e x = EV in this case.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Solve[u[x] == \((1/2 + rp)\)*u[W] + \((1/2 - rp)\)*u[L], rp]\)[\([1]\)] /. x \[Rule] 10\)], "Input"], Cell[BoxData[ \({rp \[Rule] 1\/2\ \((\(-3\) + \@10)\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(N[%]\)], "Input"], Cell[BoxData[ \({rp \[Rule] 0.08113883008418976`}\)], "Output"] }, Open ]], Cell["Part (c)", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \({W, L, p\_1, p\_2} = {36, 16, 1/2, 1/2}\)], "Input"], Cell[BoxData[ \({36, 16, 1\/2, 1\/2}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(EU = p\_1*u[W] + p\_2*u[L]\)], "Input"], Cell[BoxData[ \(5\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Solve[u[c] \[Equal] EU, c]\)[\([1]\)]\)], "Input"], Cell[BoxData[ \({c \[Rule] 25}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(EV = p\_1*W + p\_2*L\)], "Input"], Cell[BoxData[ \(26\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Solve[u[x] == \((1/2 + rp)\)*u[W] + \((1/2 - rp)\)*u[L], rp]\)[\([1]\)] /. x \[Rule] 26\)], "Input"], Cell[BoxData[ \({rp \[Rule] 1\/2\ \((\(-5\) + \@26)\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(N[%]\)], "Input"], Cell[BoxData[ \({rp \[Rule] 0.049509756796392246`}\)], "Output"] }, Open ]], Cell["\<\ In both cases, EV-c = 1, but r is larger for the first case. This is because \ u[x] exhibits constant relative risk aversion and (therefore) decreasing \ absolute risk aversion. (see item (iv) under Proposition 6.C.3 on p. 193.\ \>", "Text"], Cell[BoxData[ \(Clear[rp, c, W, L, p\_1, p\_2, u]\)], "Input"], Cell[TextData[StyleBox["Example 5: Exercise MC 6.C.16", FontSize->18]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(u[x_] = \@x\)], "Input"], Cell[BoxData[ \(\@x\)], "Output"] }, Open ]], Cell["Part (a)", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \({G, B, w, p} = {10, 5, 10, 0.7}\)], "Input"], Cell[BoxData[ \({10, 5, 10, 0.7`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(EU = p*u[w + G] + \((1 - p)\)*u[w + B]\)], "Input"], Cell[BoxData[ \(4.292390172361931`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Solve[u[c] \[Equal] EU, c]\)[\([1]\)]\)], "Input"], Cell[BoxData[ \({c \[Rule] 18.42461339178929`}\)], "Output"] }, Open ]], Cell[TextData[{ "So the owner is indifferent between \"owning\" the lottery and a ", StyleBox["sure wealth", FontWeight->"Bold"], " of c. Thus, he would sell the lottery for no less than " }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(p\_s = c - w /. %\)], "Input"], Cell[BoxData[ \(8.42461339178929`\)], "Output"] }, Open ]], Cell["Part (b)", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(EU = p*u[w + G - pb] + \((1 - p)\)*u[w + B - pb]\)], "Input"], Cell[BoxData[ \(0.30000000000000004`\ \@\(15 - pb\) + 0.7`\ \@\(20 - pb\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[\(Solve[u[c] \[Equal] EU, c]\)[\([1]\)]]\)], "Input"], Cell[BoxData[ \({c \[Rule] \(\(11.149999999999997`\)\(\[InvisibleSpace]\)\) + 0.42`\ \@\(\(\(15.`\)\(\[InvisibleSpace]\)\) - 1.`\ pb\)\ \ \@\(\(\(20.`\)\(\[InvisibleSpace]\)\) - 1.`\ pb\) - 0.58`\ pb}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(cb = c /. %\)], "Input"], Cell[BoxData[ \(\(\(11.149999999999997`\)\(\[InvisibleSpace]\)\) + 0.42`\ \@\(\(\(15.`\)\(\[InvisibleSpace]\)\) - 1.`\ pb\)\ \ \@\(\(\(20.`\)\(\[InvisibleSpace]\)\) - 1.`\ pb\) - 0.58`\ pb\)], "Output"] }, Open ]], Cell["\<\ The buyer is indifferent between \"owning\" the lottery (by buying it at \ price pb) and a sure wealth of cb. Since the purchase must make him at least \ as well off as no purchase, maximum pb can be derived as \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Solve[u[w] \[Equal] u[cb], pb]\)[\([1]\)]\)], "Input"], Cell[BoxData[ RowBox[{\(Solve::"ifun"\), \(\(:\)\(\ \)\), "\<\"Inverse functions are \ being used by \\!\\(Solve\\), so some solutions may not be found; use Reduce \ for complete solution information. \ \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", ButtonStyle->\\\"RefGuideLinkText\ \\\", ButtonFrame->None, ButtonData:>\\\"Solve::ifun\\\"]\\)\"\>"}]], \ "Message"], Cell[BoxData[ \({pb \[Rule] 8.35371376374779`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(pb\^*\) = pb /. %\)], "Input"], Cell[BoxData[ \(8.35371376374779`\)], "Output"] }, Open ]], Cell["Double-check:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(EU = p*u[w + G - pb] + \((1 - p)\)*u[w + B - pb] /. pb \[Rule] \(pb\^*\)\)], "Input"], Cell[BoxData[ \(3.1622776601683795`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(u[cb] /. pb \[Rule] \(pb\^*\)\)], "Input"], Cell[BoxData[ \(3.1622776601683795`\)], "Output"] }, Open ]], Cell[TextData[StyleBox["How would these results change for a \"riskier\" \ lottery with p=0.3.?", FontSize->16]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \({G, B, w, p} = {10, 5, 10, 0.3}\)], "Input"], Cell[BoxData[ \({10, 5, 10, 0.3`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(EU = p*u[w + G] + \((1 - p)\)*u[w + B]\)], "Input"], Cell[BoxData[ \(4.0527291288450655`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Solve[u[c] \[Equal] EU, c]\)[\([1]\)]\)], "Input"], Cell[BoxData[ \({c \[Rule] 16.424613391789283`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(p\_s = c - w /. %\)], "Input"], Cell[BoxData[ \(6.424613391789283`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(EU = p*u[w + G - pb] + \((1 - p)\)*u[w + B - pb]\)], "Input"], Cell[BoxData[ \(0.7`\ \@\(15 - pb\) + 0.3`\ \@\(20 - pb\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[\(Solve[u[c] \[Equal] EU, c]\)[\([1]\)]]\)], "Input"], Cell[BoxData[ \({c \[Rule] \(\(9.149999999999999`\)\(\[InvisibleSpace]\)\) + 0.42`\ \@\(\(\(15.`\)\(\[InvisibleSpace]\)\) - 1.`\ pb\)\ \ \@\(\(\(20.`\)\(\[InvisibleSpace]\)\) - 1.`\ pb\) - 0.58`\ pb}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(cb = c /. %\)], "Input"], Cell[BoxData[ \(\(\(9.149999999999999`\)\(\[InvisibleSpace]\)\) + 0.42`\ \@\(\(\(15.`\)\(\[InvisibleSpace]\)\) - 1.`\ pb\)\ \ \@\(\(\(20.`\)\(\[InvisibleSpace]\)\) - 1.`\ pb\) - 0.58`\ pb\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Solve[u[w] \[Equal] u[cb], pb]\)[\([1]\)]\)], "Input"], Cell[BoxData[ RowBox[{\(Solve::"ifun"\), \(\(:\)\(\ \)\), "\<\"Inverse functions are \ being used by \\!\\(Solve\\), so some solutions may not be found; use Reduce \ for complete solution information. \ \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", ButtonStyle->\\\"RefGuideLinkText\ \\\", ButtonFrame->None, ButtonData:>\\\"Solve::ifun\\\"]\\)\"\>"}]], \ "Message"], Cell[BoxData[ \({pb \[Rule] 6.38043426902122`}\)], "Output"] }, Open ]], Cell["\<\ As expected, the price of the lottery decreases for both sides.\ \>", "Text"], Cell[BoxData[ \(Clear[u, c, cb, pb, w, G, B, p]\)], "Input"], Cell["Example 6: Comparing Risk Aversion", "Text", FontSize->18], Cell["Two individuals 1, 2 have the following utility functions:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(u\_1[w_] = 27 + Log[w] - Exp[\(-w\)] + w\^\(-5\)*Sin[w]\)], "Input"], Cell[BoxData[ \(27 - \[ExponentialE]\^\(-w\) + Log[w] + Sin[w]\/w\^5\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(u\_2[w_] = 35 + 3*Log[w] - 3*Exp[\(-w\)] + 3*w\^\(-5\)*Sin[w]\)], "Input"], Cell[BoxData[ \(35 - 3\ \[ExponentialE]\^\(-w\) + 3\ Log[w] + \(3\ Sin[w]\)\/w\^5\)], "Output"] }, Open ]], Cell["\<\ Both have initial wealth w=3. They are offered a gamble that wins $1 with \ probability p, and loses $1 with prob. (1-p). Use p=0.7.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \({w, p} = {3, 0.7}\)], "Input"], Cell[BoxData[ \({3, 0.7`}\)], "Output"] }, Open ]], Cell["Find out if person 1 will accept the gamble. ", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(EU\_1 = p*u\_1[w + 1] + \((1 - p)\)*u\_1[w - 1]\)], "Input"], Cell[BoxData[ \(28.132935992679524`\)], "Output"] }, Open ]], Cell["In comparison, the utility of current wealth is ", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(N[u\_1[w]]\)], "Input"], Cell[BoxData[ \(28.049405961074157`\)], "Output"] }, Open ]], Cell["\<\ Person 1 will accept, as EU of the gample > utility of current wealth. \ Another way to answer this question is to see whether the certainty \ equivalent wealth level correspondning to the gamble is higher than current \ wealth. However, the u-function is too non-linear for \"Solve: to work, so \ we'll skip this alternative approach.\ \>", "Text"], Cell[TextData[{ "Does knowing that person 1 acepts the gamble tell us anything about the \ chances that person 2 will? Note that ", Cell[BoxData[ \(TraditionalForm\`u\_\(\(2\)\(\ \)\)\)]], "is an ", StyleBox["affine (linear) transformation", FontWeight->"Bold"], " of ", Cell[BoxData[ \(TraditionalForm\`u\_1\)]], " ", Cell[BoxData[ \(TraditionalForm\`\((u\_2 = 3*u\_1 - 43)\)\)]], " so both functions represent ", StyleBox["identical prefences over lotteries", FontWeight->"Bold"], ". Thus, we would expect person 2 to also accept the gamble. let's check:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(EU\_2 = p*u\_2[w + 1] + \((1 - p)\)*u\_2[w - 1]\)], "Input"], Cell[BoxData[ \(38.39880797803857`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(N[u\_2[w]]\)], "Input"], Cell[BoxData[ \(38.14821788322246`\)], "Output"] }, Open ]], Cell["\<\ Compare the Arrow-Pratt measure of absolute risk aversion for both \ individuals at arbitrary wealth levels. 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ImageMargins->{{30, Inherited}, {Inherited, 0}}, Magnification->0.8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], LanguageCategory->None, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontColor->RGBColor[0.269993, 0.308507, 0.6]], Cell[StyleData["CellLabel", "Presentation"], FontSize->12], Cell[StyleData["CellLabel", "Condensed"], FontSize->9], Cell[StyleData["CellLabel", "SlideShow"]], Cell[StyleData["CellLabel", "Printout"], FontFamily->"Courier", FontSize->8, FontSlant->"Italic", FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["FrameLabel"], LanguageCategory->None, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9], Cell[StyleData["FrameLabel", "Presentation"], FontSize->12], Cell[StyleData["FrameLabel", "Condensed"], FontSize->9], Cell[StyleData["FrameLabel", "SlideShow"]], Cell[StyleData["FrameLabel", "Printout"], FontFamily->"Courier", FontSize->8, FontSlant->"Italic", FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Inline Formatting", "Section"], Cell["\<\ These styles are for modifying individual words or letters in a cell \ exclusive of the cell tag.\ \>", "Text"], Cell[StyleData["RM"], StyleMenuListing->None, FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["BF"], StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["IT"], StyleMenuListing->None, FontSlant->"Italic"], Cell[StyleData["TR"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["TI"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["TB"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["TBI"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Bold", FontSlant->"Italic"], Cell[StyleData["MR"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["MO"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["MB"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["MBO"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Italic"], Cell[StyleData["SR"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["SO"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["SB"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["SBO"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Italic"], Cell[CellGroupData[{ Cell[StyleData["SO10"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->10, FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["SO10", "Printout"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->7, FontWeight->"Plain", FontSlant->"Italic"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["InlineFormula"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", ScriptLevel->1, SingleLetterItalics->True], Cell[StyleData["InlineFormula", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["InlineFormula", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}, FontSize->11], Cell[StyleData["InlineFormula", "SlideShow"]], Cell[StyleData["InlineFormula", "Printout"], CellMargins->{{2, 0}, {6, 6}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{60, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", ScriptLevel->0, SingleLetterItalics->True, UnderoverscriptBoxOptions->{LimitsPositioning->True}], Cell[StyleData["DisplayFormula", "Presentation"], LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["DisplayFormula", "Condensed"], LineSpacing->{1, 1}, FontSize->11], Cell[StyleData["DisplayFormula", "SlideShow"]], Cell[StyleData["DisplayFormula", "Printout"], FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Program"], CellFrame->{{0, 0}, {0.5, 0.5}}, CellMargins->{{60, 4}, {0, 8}}, CellHorizontalScrolling->True, Hyphenation->False, LanguageCategory->"Formula", ScriptLevel->1, FontFamily->"Courier"], Cell[StyleData["Program", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["Program", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}, FontSize->11], Cell[StyleData["Program", "SlideShow"]], Cell[StyleData["Program", "Printout"], CellMargins->{{2, 0}, {6, 6}}, FontSize->9] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Outline Styles", "Section"], Cell[CellGroupData[{ Cell[StyleData["Outline1"], CellMargins->{{60, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 50}, ParagraphIndent->-38, CounterIncrements->"Outline1", CounterAssignments->{{"Outline2", 0}, {"Outline3", 0}, {"Outline4", 0}}, FontSize->18, FontWeight->"Bold", CounterBoxOptions->{ CounterFunction:>Utilities`Notation`Private`CapitalRomanNumeral}], Cell[StyleData["Outline1", "SlideShow"]], Cell[StyleData["Outline1", "Printout"], CounterBoxOptions->{ CounterFunction:>Utilities`Notation`Private`CapitalRomanNumeral}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Outline2"], CellMargins->{{90, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 60}, ParagraphIndent->-27, CounterIncrements->"Outline2", CounterAssignments->{{"Outline3", 0}, {"Outline4", 0}}, FontSize->15, FontWeight->"Bold", CounterBoxOptions->{CounterFunction:>(Part[ CharacterRange[ "A", "Z"], #]&)}], Cell[StyleData["Outline2", "SlideShow"]], Cell[StyleData["Outline2", "Printout"], CounterBoxOptions->{CounterFunction:>(Part[ CharacterRange[ "A", "Z"], #]&)}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Outline3"], CellMargins->{{120, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 70}, ParagraphIndent->-21, CounterIncrements->"Outline3", CounterAssignments->{{"Outline4", 0}}, FontSize->12, CounterBoxOptions->{CounterFunction:>Identity}], Cell[StyleData["Outline3", "SlideShow"]], Cell[StyleData["Outline3", "Printout"], CounterBoxOptions->{CounterFunction:>Identity}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Outline4"], CellMargins->{{150, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 80}, ParagraphIndent->-18, CounterIncrements->"Outline4", FontSize->10, CounterBoxOptions->{CounterFunction:>(Part[ CharacterRange[ "a", "z"], #]&)}], Cell[StyleData["Outline4", "SlideShow"]], Cell[StyleData["Outline4", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext ButtonBoxes. The \ \"Hyperlink\" style is for links within the same Notebook, or between \ Notebooks.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonFrame->"None", ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"], FontSize->16], Cell[StyleData["Hyperlink", "Condensed"], FontSize->11], Cell[StyleData["Hyperlink", "SlideShow"]], Cell[StyleData["Hyperlink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line help \ system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Presentation"], FontSize->16], Cell[StyleData["MainBookLink", "Condensed"], FontSize->11], Cell[StyleData["MainBookLink", "SlideShow"]], Cell[StyleData["MainBookLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Presentation"], FontSize->16], Cell[StyleData["AddOnsLink", "Condensed"], FontSize->11], Cell[StyleData["AddOnsLink", "SlideShow"]], Cell[StyleData["AddOnsLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"], FontSize->16], Cell[StyleData["RefGuideLink", "Condensed"], FontSize->11], Cell[StyleData["RefGuideLink", "SlideShow"]], Cell[StyleData["RefGuideLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLinkText"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLinkText", "Presentation"], FontSize->16], Cell[StyleData["RefGuideLinkText", "Condensed"], FontSize->11], Cell[StyleData["RefGuideLinkText", "SlideShow"]], Cell[StyleData["RefGuideLinkText", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Presentation"], FontSize->16], Cell[StyleData["GettingStartedLink", "Condensed"], FontSize->11], Cell[StyleData["GettingStartedLink", "SlideShow"]], Cell[StyleData["GettingStartedLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DemosLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "Demos", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["DemosLink", "SlideShow"]], Cell[StyleData["DemosLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["TourLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "Tour", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["TourLink", "SlideShow"]], Cell[StyleData["TourLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"], FontSize->16], Cell[StyleData["OtherInformationLink", "Condensed"], FontSize->11], Cell[StyleData["OtherInformationLink", "SlideShow"]], Cell[StyleData["OtherInformationLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["MasterIndexLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MasterIndex", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MasterIndexLink", "SlideShow"]], Cell[StyleData["MasterIndexLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headers and Footers", "Section"], Cell[StyleData["Header"], CellMargins->{{0, 0}, {4, 1}}, DefaultNewInlineCellStyle->"None", LanguageCategory->"NaturalLanguage", StyleMenuListing->None, FontSize->10, FontSlant->"Italic"], Cell[StyleData["Footer"], CellMargins->{{0, 0}, {0, 4}}, DefaultNewInlineCellStyle->"None", LanguageCategory->"NaturalLanguage", StyleMenuListing->None, FontSize->9, FontSlant->"Italic"], Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Times", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell["Palette Styles", "Section"], Cell["\<\ The cells below define styles that define standard ButtonFunctions, for use \ in palette buttons.\ \>", "Text"], Cell[StyleData["Paste"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, Placeholder]}]&)}], Cell[StyleData["Evaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["EvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionMove[ FrontEnd`InputNotebook[ ], All, Cell, 1], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}] }, Closed]], Cell[CellGroupData[{ Cell["Placeholder Styles", "Section"], Cell["\<\ The cells below define styles useful for making placeholder objects in \ palette templates.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Placeholder"], Placeholder->True, StyleMenuListing->None, FontSlant->"Italic", FontColor->RGBColor[0.890623, 0.864698, 0.384756], TagBoxOptions->{Editable->False, Selectable->False, StripWrapperBoxes->False}], Cell[StyleData["Placeholder", "Presentation"]], Cell[StyleData["Placeholder", "Condensed"]], Cell[StyleData["Placeholder", "SlideShow"]], Cell[StyleData["Placeholder", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["PrimaryPlaceholder"], StyleMenuListing->None, DrawHighlighted->True, FontSlant->"Italic", Background->RGBColor[0.912505, 0.891798, 0.507774], TagBoxOptions->{Editable->False, Selectable->False, StripWrapperBoxes->False}], Cell[StyleData["PrimaryPlaceholder", "Presentation"]], Cell[StyleData["PrimaryPlaceholder", "Condensed"]], Cell[StyleData["PrimaryPlaceholder", "SlideShow"]], Cell[StyleData["PrimaryPlaceholder", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["FormatType Styles", "Section"], Cell["\<\ The cells below define styles that are mixed in with the styles of most \ cells. If a cell's FormatType matches the name of one of the styles defined \ below, then that style is applied between the cell's style and its own \ options. This is particularly true of Input and Output.\ \>", "Text"], Cell[StyleData["CellExpression"], PageWidth->Infinity, CellMargins->{{6, Inherited}, {Inherited, Inherited}}, ShowCellLabel->False, ShowSpecialCharacters->False, AllowInlineCells->False, Hyphenation->False, AutoItalicWords->{}, StyleMenuListing->None, FontFamily->"Courier", FontSize->12, Background->GrayLevel[1]], Cell[StyleData["InputForm"], InputAutoReplacements->{}, AllowInlineCells->False, Hyphenation->False, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["OutputForm"], PageWidth->Infinity, TextAlignment->Left, LineSpacing->{0.6, 1}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["StandardForm"], InputAutoReplacements->{ "->"->"\[Rule]", ":>"->"\[RuleDelayed]", "<="->"\[LessEqual]", ">="->"\[GreaterEqual]", "!="->"\[NotEqual]", "=="->"\[Equal]", Inherited}, "TwoByteSyntaxCharacterAutoReplacement"->True, LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["TraditionalForm"], InputAutoReplacements->{ "->"->"\[Rule]", ":>"->"\[RuleDelayed]", "<="->"\[LessEqual]", ">="->"\[GreaterEqual]", "!="->"\[NotEqual]", "=="->"\[Equal]", Inherited}, "TwoByteSyntaxCharacterAutoReplacement"->True, LineSpacing->{1.25, 0}, SingleLetterItalics->True, TraditionalFunctionNotation->True, DelimiterMatching->None, StyleMenuListing->None], Cell["\<\ The style defined below is mixed in to any cell that is in an inline cell \ within another.\ \>", "Text"], Cell[StyleData["InlineCell"], LanguageCategory->"Formula", ScriptLevel->1, StyleMenuListing->None], Cell[StyleData["InlineCellEditing"], StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216]] }, Closed]], Cell[CellGroupData[{ Cell["Automatic Styles", "Section"], Cell["\<\ The cells below define styles that are used to affect the display of certain \ types of objects in typeset expressions. For example, \"UnmatchedBracket\" \ style defines how unmatched bracket, curly bracket, and parenthesis \ characters are displayed (typically by coloring them to make them stand out).\ \ \>", "Text"], Cell[StyleData["UnmatchedBracket"], StyleMenuListing->None, FontColor->RGBColor[0.760006, 0.330007, 0.8]], Cell[StyleData["Completions"], StyleMenuListing->None, FontFamily->"Courier"] }, Closed]], Cell[CellGroupData[{ Cell["Styles from HelpBrowser", "Section"], Cell[CellGroupData[{ Cell[StyleData["MathCaption"], CellFrame->{{0, 0}, {0, 0.5}}, CellMargins->{{66, 12}, {2, 24}}, PageBreakBelow->False, CellFrameMargins->{{8, 8}, {8, 2}}, CellFrameColor->GrayLevel[0.700008], CellFrameLabelMargins->4, LineSpacing->{1, 1}, ParagraphSpacing->{0, 8}, StyleMenuListing->None, FontColor->GrayLevel[0.2]], Cell[StyleData["MathCaption", "Presentation"], FontSize->18], Cell[StyleData["MathCaption", "SlideShow"]], Cell[StyleData["MathCaption", "Printout"], CellMargins->{{39, 0}, {0, 14}}, Hyphenation->True, FontSize->9, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ObjectName"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["ObjectName", "Presentation"], FontSize->18], Cell[StyleData["ObjectName", "SlideShow"]], Cell[StyleData["ObjectName", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Usage"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["Usage", "Presentation"], FontSize->18], Cell[StyleData["Usage", "SlideShow"]], Cell[StyleData["Usage", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Notes"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["Notes", "Presentation"], FontSize->18], Cell[StyleData["Notes", "SlideShow"]], Cell[StyleData["Notes", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["InlineOutput"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["InlineOutput", "Presentation"], FontSize->18], Cell[StyleData["InlineOutput", "SlideShow"]], Cell[StyleData["InlineOutput", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell["Emphasis Boxes and Pictures", "Subsection"], Cell[CellGroupData[{ Cell[StyleData["Box"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->1}], 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