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{"sheet":"Menu","index":0,"n_rows":13,"n_cols":7,"rows_kept":13,"cut":false,"hidden":false,"merged":[]}
["These are the interactive Excel sheets of the paper entitled \"Teaching an insurance model: An interactive exercise\"."]
[]
[null,"Choose the option:",null,null,null,null,"Figura 1"]
[null,null,null,null,null,null,"Function 1"]
[null,null,null,null,null,null,"Log"]
[null,null,null,null,null,null,"CARA"]
[null,null,null,null,null,null,"DARA"]
[]
[]
[]
[]
["Note:  The option \"Utility function U(w)=w^α\" is used in Sections 3 and 4. The option \"Utility functions U(w)=ln(w)\" and \"U(w)=w^(1-σ)/(1-σ)\" are presented in Section 5."]
["The option \"Attitudes toward risk\" reproduces Figure A in the Appendix with different utility functions representing risk averse, neutral or risk lover agents. "]

{"sheet":"Figure A","index":1,"n_rows":87,"n_cols":26,"rows_kept":87,"cut":false,"hidden":true,"merged":[[2,2,2,3]]}
[]
[]
[null,null,"Parameters"]
[null,null,"w1",2]
[]
[null,null,"w2",16]
[]
[5,null,"p1",{"$f":"A8/10","v":0.5}]
[]
[null,null,"p2",{"$f":"1-D8","v":0.5}]
[5,null,"α",{"$f":"A11/10","v":0.5}]
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[null,null,null,null,null,null,null,"w","u(w)"]
[null,null,null,null,null,null,null,0,{"$f":"+H67^D$11","v":0}]
[null,null,null,null,null,null,null,1,{"$f":"+H68^D$11","v":1}]
[null,null,null,null,null,null,null,2,1.4142135623730951]
[null,null,null,null,null,null,null,3,1.7320508075688772]
[null,null,null,null,null,null,null,4,2]
[null,null,null,null,null,null,null,5,2.2360679774997898]
[null,null,null,null,null,null,null,6,2.4494897427831779,null,null,null,null,null,null,"(EL)","U(E(L))"]
[null,null,null,null,null,null,null,7,2.6457513110645907,null,null,null,null,"U(wi)",null,{"$f":"+P75","v":9},0,null,{"$f":"+P74","v":9},{"$f":"+Q75","v":3},null,{"$f":"+L75","v":2},0,null,{"$f":"+V74","v":2},{"$f":"+Y74^D11","v":1.4142135623730951}]
[null,null,null,null,null,null,null,8,2.8284271247461903,null,"w1",{"$f":"D4","v":2},0,{"$f":"+L75^D11","v":1.4142135623730951},null,{"$f":"+D4*D8+D6*D10","v":9},{"$f":"+P75^D11","v":3},null,0,{"$f":"+Q75","v":3},null,{"$f":"+V74","v":2},{"$f":"+V75^D11","v":1.4142135623730951},{"$f":"W75","v":1.4142135623730951},0,{"$f":"+Z74","v":1.4142135623730951}]
[null,null,null,null,null,null,null,9,3,null,"w2",{"$f":"D6","v":16},0,{"$f":"+L76^D11","v":4}]
[null,null,null,null,null,null,null,10,3.1622776601683795,null,null,null,null,null,null,{"$f":"+P75","v":9},0,null,{"$f":"+P77","v":9},{"$f":"+Q78","v":2.7071067811865475},null,{"$f":"+L76","v":16},0,null,{"$f":"+L76","v":16},{"$f":"+Y77^D11","v":4}]
[null,null,null,null,null,null,null,11,3.3166247903553998,null,null,null,null,null,null,{"$f":"+P75","v":9},{"$f":"+D8*N75+D10*N76","v":2.7071067811865475},"U(L)",0,{"$f":"+Q78","v":2.7071067811865475},null,{"$f":"+V77","v":16},{"$f":"+V78^D11","v":4},null,0,{"$f":"+Z77","v":4}]
[null,null,null,null,null,null,null,12,3.4641016151377544]
[null,null,null,null,null,null,null,13,3.6055512754639891]
[null,null,null,null,null,null,null,14,3.7416573867739413,null,null,null,null,null,null,{"$f":"+Q78^(1/D11)","v":7.3284271247461898},0,null,{"$f":"+P81","v":7.3284271247461898},{"$f":"+Q82","v":2.7071067811865475}]
[null,null,null,null,null,null,null,15,3.872983346207417,null,null,null,null,null,null,{"$f":"+P81","v":7.3284271247461898},{"$f":"+Q78","v":2.7071067811865475},null,0,{"$f":"+T81","v":2.7071067811865475}]
[null,null,null,null,null,null,null,16,4]
[null,null,null,null,null,null,null,17,4.1231056256176606]
[null,null,null,null,null,null,null,18,4.2426406871192848]
[null,null,null,null,null,null,null,19,4.358898943540674]
[null,null,null,null,null,null,null,20,4.4721359549995796]

{"sheet":"Figure B","index":2,"n_rows":167,"n_cols":27,"rows_kept":167,"cut":false,"hidden":true,"merged":[[2,2,3,3],[2,6,3,7]]}
[]
[]
[null,null,"Table I: Initial solution",null,null,null,"Table II: Comparative Analysis"]
[]
[null,null,"Parameters",null,null,null,"Parameters"]
[null,2,"π",{"$f":"B6/10","v":0.2},null,2,"π",{"$f":"+F6/10","v":0.2}]
[null,null,null,0.3]
[null,3,"p",{"$f":"B8/10","v":0.3},null,3,"p",{"$f":"F8/10","v":0.3}]
[]
[null,null,"w0",1000,null,null,"w0",1000]
[]
[null,3,"α",{"$f":"+B12/10","v":0.3},null,3,"α",{"$f":"+F12/10","v":0.3}]
[]
[null,null,"l",700,null,null,"l",700]
[]
[]
[null,null,"Variables",null,null,null,"Variables"]
[null,null,"w1",436.02351115535942,null,null,"w1",436.02350795537535]
[null,null,"w2",941.70420950484606,null,null,"w2",941.70421087628552]
[]
[null,null,"Constraints",null,null,null,"Constraints"]
[null,null,"p*w1+(1-p)*w2-w0+pl=0",{"$f":"+D8*D18+(1-D8)*D19-D10+D8*D14","v":0},null,null,"p*w1+(1-p)*w2-w0+pl=0",{"$f":"+H8*H18+(1-H8)*H19-H10+H8*H14","v":1.2505552149377763E-11}]
[null,null,"w0-l-w1≤0",{"$f":"+D10-D14-D18","v":-136.02351115535942},null,null,"w0-l-w1≤0",{"$f":"+H10-H14-H18","v":-136.02350795537535}]
[null,null,"wo-w1-p*l≥0",{"$f":"+D10-D18-D8*D14","v":353.97648884464058},null,null,"wo-w1-p*l≥0",{"$f":"+H10-H18-H8*H14","v":353.97649204462459}]
[null,null,"wo-pl-w2≤0",{"$f":"+D10-D8*D14-D19","v":-151.70420950484606},null,null,"wo-pl-w2≤0",{"$f":"+H10-H8*H14-H19","v":-151.70421087628552}]
[null,null,"w0-w2≥0",{"$f":"+D10-D19","v":58.295790495153938},null,null,"w0-w2≥0",{"$f":"+H10-H19","v":58.295789123714485}]
[]
[null,null,"Quantity of q",null,null,null,"Quantity of q"]
[null,null,"q=(w0-w2)/p",{"$f":"+(D10-D19)/D8","v":194.31930165051313},null,null,"q=(w0-w2)/p",{"$f":"+(H10-H19)/H8","v":194.31929707904828}]
[]
[null,null,"Expected utility function",null,null,null,"Expected utility function"]
[null,null,"π*w1^α+(1-π)*w2^α",{"$f":"+D6*D18^D12+(1-D6)*D19^D12","v":7.4796087811136154},null,null,"π*w1^α+(1-π)*w2^α",{"$f":"+H6*H18^H12+(1-H6)*H19^H12","v":7.4796087811136518}]
[]
[null,null,"Note: This option corresponds to the utility function used in Section 3 of the paper. Use the scroll bars to modify the parameters of the insurance problem."]
[null,null,"For example, use the scroll bar below the probability of a robbery  π in cell H6, adjusting it from π=0.2 to  π=0.4. Then call Solver and, click Solve in the Solver Parameters window. "]
[null,null,"Change the letter H for D in all cells of the Solver Parameters window if you modify the parameters of Table I."]
[null,null,"If Solver shows a message \"Solver encountered an error value in the Objective Cell or a Constraint cell\" just change the initial values of the variables to, for example 100."]
[null,null,"π=  probability of robbery"]
[null,null,"p=  insurance premium rate"]
[null,null,"w0=  initial wealth "]
[null,null,"α= parameter of the expected utility function "]
[null,null,"l= amount of wealth stolen if robbery"]
[null,null,"w1= agent’s wealth if robbery "]
[null,null,"w2= agent’s wealth if no robbery"]
[null,null,"q= amount of insurance"]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Initial solution",null,null,null,"Final solution"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,20,"w1","w1prime","w2budget","w2prime","C2utility",null,"w1","w1prime","C2utility"]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"β",1]
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[]
[]
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{"sheet":"Figure C","index":3,"n_rows":165,"n_cols":27,"rows_kept":165,"cut":false,"hidden":true,"merged":[[2,2,3,3],[2,6,3,7]]}
[]
[]
[null,null,"Table I: Initial solution",null,null,null,"Table II: Comparative Analysis"]
[]
[null,null,"Parameters",null,null,null,"Parameters"]
[null,2,"π",{"$f":"B6/10","v":0.2},null,2,"π",{"$f":"+F6/10","v":0.2}]
[null,null,null,0.3]
[null,3,"p",{"$f":"+B8/10","v":0.3},null,3,"p",{"$f":"F8/10","v":0.3}]
[]
[null,null,"w0",1000,null,null,"w0",1000]
[]
[null,null,"l",700,null,null,"l",700]
[]
[]
[null,null,"Variables",null,null,null,"Variables"]
[null,null,"w1",526.66667075755061,null,null,"w1",526.66666272520365]
[null,null,"w2",902.85714110376409,null,null,"w2",902.85714454564618]
[]
[null,null,"Constraints",null,null,null,"Constraints"]
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[null,null,"w0-l-w1≤0",{"$f":"+D10-D12-D16","v":-226.66667075755061},null,null,"w0-l-w1≤0",{"$f":"+H10-H12-H16","v":-226.66666272520365}]
[null,null,"wo-w1-p*l≥0",{"$f":"+D10-D16-D8*D12","v":263.33332924244939},null,null,"wo-w1-p*l≥0",{"$f":"+H10-H16-H8*H12","v":263.33333727479635}]
[null,null,"wo-pl-w2≤0",{"$f":"+D10-D8*D12-D17","v":-112.85714110376409},null,null,"wo-pl-w2≤0",{"$f":"+H10-H8*H12-H17","v":-112.85714454564618}]
[null,null,"w0-w2≥0",{"$f":"+D10-D17","v":97.142858896235907},null,null,"w0-w2≥0",{"$f":"+H10-H17","v":97.142855454353821}]
[]
[null,null,"Quantity of q",null,null,null,"Quantity of q"]
[null,null,"q=(w0-w2)/p",{"$f":"+(D10-D17)/D8","v":323.80952965411973},null,null,"q=(w0-w2)/p",{"$f":"+(H10-H17)/H8","v":323.80951818117944}]
[]
[null,null,"Expected utility function",null,null,null,"Expected utility function"]
[null,null,"π*ln(w1)+(1-π)*ln(w2)",{"$f":"D6*LN(D16)+(1-D6)*LN(D17)","v":6.6977650379389262},null,null,"π*ln(w1)+(1-π)*ln(w2)",{"$f":"H6*LN(H16)+(1-H6)*LN(H17)","v":6.6977650379384377}]
[]
[null,null,"Note: This option presents a logarithmic utility function u(w)=ln(w). Use the scroll bars to modify the parameters of the insurance problem. Then, call Solver and click Solve in the Solver Parameters window."]
[null,null,"For example, use the scroll bar below the probability of a robbery  π in cell H6, adjusting it from π=0.2 to  π=0.4. Then call Solver and, click Solve in the Solver Parameters window. "]
[null,null,"Change the letter H for D in all cells of the Solver Parameters window if you modify the parameters of Table I."]
[null,null,"If Solver shows a message \"Solver encountered an error value in the Objective Cell or a Constraint cell\" just change the initial values of the variables to, for example 100."]
[null,null,"π= probability of robbery"]
[null,null,"p=  insurance premium rate"]
[null,null,"w0= initial wealth "]
[null,null,"l= amount of wealth stolen if robbery"]
[null,null,"w1= agent’s wealth if robbery"]
[null,null,"w2= agent’s wealth if no robbery"]
[null,null,"q= amount of insurance"]
[]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Initial solution",null,null,null,"Final solution"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,20,"w1","w1prime","w2budget","w2prime","C2utility",null,"w1","w1prime","C2utility"]
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[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"β",1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"c1","c2",null,null,null,"c1","c2",null,"restriccion"]
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[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"c1","c2",null,null,null,"c1","c2"]
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[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"y1","y2"]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"y1","y2"]
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{"sheet":"log","index":4,"n_rows":14,"n_cols":2,"rows_kept":14,"cut":false,"hidden":true,"merged":[]}
[]
[null,"Repeteri figura 5 pero con la siguiente función de utilidad esperada"]
[]
[null,"π*ln(w1)+(1-π)*ln(w2)"]
[]
[]
[]
[]
[null,"Incluír el scroll bars"]
[null,"0.1≤π≤1"]
[null,"0.1≤p≤0.9"]
[]
[null,"500≤l≤750"]
[null,"850≤w ≤1150"]

{"sheet":"Figure D","index":5,"n_rows":167,"n_cols":27,"rows_kept":167,"cut":false,"hidden":true,"merged":[[2,2,3,3],[2,6,3,7]]}
[]
[]
[null,null,"Table I: Initial solution",null,null,null,"Table II: Comparative Analysis"]
[]
[null,null,"Parameters",null,null,null,"Parameters"]
[null,2,"π",{"$f":"B6/10","v":0.2},null,2,"π",{"$f":"F6/10","v":0.2}]
[]
[null,3,"p",{"$f":"B8/10","v":0.3},null,3,"p",{"$f":"F8/10","v":0.3}]
[]
[null,null,"w0",1000,null,null,"w0",1000]
[]
[null,3,"σ",{"$f":"B12/10","v":0.3},null,3,"σ",{"$f":"IF(F13=1, 1.05, F14)","v":0.3}]
[null,null,null,null,null,{"$f":"+F12/10","v":0.3}]
[null,null,"l",700,null,{"$f":"+F12/10","v":0.3},"l",700]
[]
[]
[null,null,"Variables",null,null,null,"Variables"]
[null,null,"w1",300,null,null,"w1",300.00000000000011]
[null,null,"w2",1000,null,null,"w2",1000]
[]
[null,null,"Constraints",null,null,null,"Constraints"]
[null,null,"p*w1+(1-p)*w2-w0+pl=0",{"$f":"+D8*D18+(1-D8)*D19-D10+D8*D14","v":0},null,null,"p*w1+(1-p)*w2-w0+pl=0",{"$f":"+H8*H18+(1-H8)*H19-H10+H8*H14","v":0}]
[null,null,"w0-l-w1≤0",{"$f":"+D10-D14-D18","v":0},null,null,"w0-l-w1≤0",{"$f":"+H10-H14-H18","v":0}]
[null,null,"wo-w1-p*l≥0",{"$f":"+D10-D18-D8*D14","v":490},null,null,"wo-w1-p*l≥0",{"$f":"+H10-H18-H8*H14","v":489.99999999999989}]
[null,null,"wo-pl-w2≤0",{"$f":"+D10-D8*D14-D19","v":-210},null,null,"wo-pl-w2≤0",{"$f":"+H10-H8*H14-H19","v":-210}]
[null,null,"w0-w2≥0",{"$f":"+D10-D19","v":0},null,null,"w0-w2≥0",{"$f":"+H10-H19","v":0}]
[]
[null,null,"Quantity of q",null,null,null,"Quantity of q"]
[null,null,"q=(w0-w2)/p",{"$f":"+(D10-D19)/D8","v":0},null,null,"q=(w0-w2)/p",{"$f":"+(H10-H19)/H8","v":0}]
[]
[null,null,"Expected utility function",null,null,null,"Expected utility function"]
[null,null,"π*(w1^(1-σ)/(1-σ))+(1-π)*(w2^(1-σ)/(1-σ))",{"$f":"D6*(D18^(1-D12)/(1-D12))+(1-D6)*(D19^(1-D12)/(1-D12))","v":159.36239045662825},null,null,"π*(w1^(1-σ)/(1-σ))+(1-π)*(w2^(1-σ)/(1-σ))",{"$f":"H6*(H18^(1-H12)/(1-H12))+(1-H6)*(H19^(1-H12)/(1-H12))","v":159.36239045662825}]
[]
[null,null,"This option considers an isoelastic utility function with σ≠1.  Use the scroll bars to modify the parameters of the insurance problem. Then, call Solver and click Solve in the Solver Parameters window."]
[null,null,"For example, use the scroll bar below the probability of a robbery  π in cell H6, adjusting it from π=0.2 to  π=0.4. Then call Solver and, click Solve in the Solver Parameters window. "]
[null,null,"Change the letter H for D in all cells of the Solver Parameters window if you modify the parameters of Table I."]
[null,null,"If Solver shows a message \"Solver encountered an error value in the Objective Cell or a Constraint cell\" just change the initial values of the variables to, for example 100."]
[null,null,"π=  probability of robbery"]
[null,null,"p= insurance premium rate"]
[null,null,"w0= initial wealth "]
[null,null,"σ= parameter of the expected utility function "]
[null,null,"l= amount of wealth stolen if robbery"]
[null,null,"w1= agent’s wealth if robbery"]
[null,null,"w2= agent’s wealth if no robbery"]
[null,null,"q= amount of insurance"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Initial solution",null,null,null,"Final solution"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,20,"w1","w1prime","w2budget","w2prime","C2utility",null,"w1","w1prime","C2utility"]
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[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"β",1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"c1","c2",null,null,null,"c1","c2",null,"restriccion"]
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[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"c1","c2",null,null,null,"c1","c2"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,{"$f":"'Figure D'!D19","v":1000},null,null,null,0,{"$f":"'Figure D'!$H$19","v":1000}]
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[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"y1","y2"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"'Figure D'!#REF!","v":{"$error":"#REF!"}},{"$f":"'Figure D'!D10","v":1000},null,null,null,"y1","y2"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"'Figure D'!D8","v":0.3},{"$f":"'Figure D'!D10","v":1000},null,null,null,0,{"$f":"'Figure D'!$H$10","v":1000}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"'Figure D'!$H$8","v":0.3},{"$f":"'Figure D'!$H$10","v":1000}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"y1","y2"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"'Figure D'!D8","v":0.3},0,null,null,null,"y1","y2"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"'Figure D'!D8","v":0.3},{"$f":"'Figure D'!D10","v":1000},null,null,null,{"$f":"'Figure D'!$H$8","v":0.3},0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"'Figure D'!$H$8","v":0.3},{"$f":"'Figure D'!$H$10","v":1000}]

{"sheet":"DARA","index":6,"n_rows":16,"n_cols":3,"rows_kept":16,"cut":false,"hidden":true,"merged":[]}
[]
[]
[]
[]
[null,null,"Repeteri figura 5 pero con la siguiente función de utilidad esperada"]
[]
[null,null,"π*(w1^(1-σ)/(1-σ))+(1-π)*(w2^(1-σ)/(1-σ))"]
[]
[]
[]
[null,null,"Incluír el scroll bars"]
[null,null,"0.1≤π≤1"]
[null,null,"0.1≤p≤0.9"]
[null,null,"1≤σ≤4"]
[null,null,"500≤l≤750"]
[null,null,"850≤w ≤1150"]

{"sheet":"Hoja1","index":7,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}