1613 lines
54 KiB
Mathematica
1613 lines
54 KiB
Mathematica
|
(*CacheID: 234*)
|
||
|
|
(* Internal cache information:
|
||
|
|
NotebookFileLineBreakTest
|
||
|
|
NotebookFileLineBreakTest
|
||
|
|
NotebookDataPosition[ 0, 0]
|
||
|
|
NotebookDataLength[ 55640, 1611]
|
||
|
|
NotebookOptionsPosition[ 43711, 1422]
|
||
|
|
NotebookOutlinePosition[ 44120, 1439]
|
||
|
|
CellTagsIndexPosition[ 44077, 1436]
|
||
|
|
WindowFrame->Normal*)
|
||
|
|
|
||
|
|
(* Beginning of Notebook Content *)
|
||
|
|
Notebook[{
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"Profits", ":=",
|
||
|
|
RowBox[{"v", "-",
|
||
|
|
RowBox[{"(", " ",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"\[Alpha]", " ", "p"}], "-",
|
||
|
|
RowBox[{"e", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}], "p"}], "+", "cs"}],
|
||
|
|
")"}]}]}]], "Input",
|
||
|
|
CellChangeTimes->{{3.846015218306656*^9, 3.846015248503848*^9}, {
|
||
|
|
3.846015319367432*^9, 3.8460153524606247`*^9}},
|
||
|
|
CellLabel->"In[1]:=",ExpressionUUID->"3bb3da7d-bb03-45e8-97dd-2768c4a330b4"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"Profitv", ":=",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"\[Alpha]", " ", "p"}], "-",
|
||
|
|
RowBox[{"e", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}], "p"}], "-",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "e"}], ")"}], "\[Theta]"}], "-",
|
||
|
|
RowBox[{"k", "*",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"e", "*", "e"}], ")"}]}], "-", "cv"}]}],
|
||
|
|
"\[IndentingNewLine]"}]], "Input",
|
||
|
|
CellChangeTimes->{{3.846015366863325*^9, 3.846015430269812*^9}, {
|
||
|
|
3.846015534863706*^9, 3.846015610340621*^9}, {3.8460157829827137`*^9,
|
||
|
|
3.846015784821113*^9}, 3.846015818648089*^9},
|
||
|
|
CellLabel->"In[2]:=",ExpressionUUID->"a0a05b1c-092f-45d3-958b-6f6f6db87303"],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData["Profitv"], "Input",
|
||
|
|
CellChangeTimes->{{3.84601582542632*^9, 3.846015829832897*^9}},
|
||
|
|
CellLabel->"In[3]:=",ExpressionUUID->"71ee1270-ea36-4acc-94db-dc48ffe86013"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "cv"}], "-",
|
||
|
|
RowBox[{
|
||
|
|
SuperscriptBox["e", "2"], " ", "k"}], "-",
|
||
|
|
RowBox[{"e", " ", "p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}]}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "-",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "e"}], ")"}], " ", "\[Theta]"}]}]], "Output",
|
||
|
|
CellChangeTimes->{3.8460158307343616`*^9},
|
||
|
|
CellLabel->"Out[3]=",ExpressionUUID->"140e314c-6402-4e91-b92c-62c44f5ba43d"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData["Profitv"], "Input",
|
||
|
|
CellChangeTimes->{{3.846015837225103*^9, 3.846015841860371*^9}},
|
||
|
|
CellLabel->"In[4]:=",ExpressionUUID->"11d5dc5f-343c-4251-ab18-015232c9f2d1"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "cv"}], "-",
|
||
|
|
RowBox[{
|
||
|
|
SuperscriptBox["e", "2"], " ", "k"}], "-",
|
||
|
|
RowBox[{"e", " ", "p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}]}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "-",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "e"}], ")"}], " ", "\[Theta]"}]}]], "Output",
|
||
|
|
CellChangeTimes->{3.8460158432582283`*^9},
|
||
|
|
CellLabel->"Out[4]=",ExpressionUUID->"3227026d-e675-4995-b271-ddbd4ca89536"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{3.8460158716523542`*^9},
|
||
|
|
NumberMarks->False,ExpressionUUID->"3bf5d625-4d78-454e-9335-fbe4dbbc1cd8"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.846015874149228*^9,
|
||
|
|
3.8460158741500072`*^9}},ExpressionUUID->"2e6d6539-8fd8-49f3-a149-\
|
||
|
|
d4b553202033"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{3.8460158753977757`*^9},
|
||
|
|
NumberMarks->False,ExpressionUUID->"e672dd71-9de7-403a-b3cb-1f7ee65d291e"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.84601587745958*^9,
|
||
|
|
3.8460158774602327`*^9}},ExpressionUUID->"36da0a40-43e5-4609-aa01-\
|
||
|
|
e0614fe18963"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.8460156703920107`*^9, 3.84601567234361*^9},
|
||
|
|
3.846015774090412*^9,
|
||
|
|
3.846015817288226*^9},ExpressionUUID->"b8521a2a-4f73-40a5-81a7-\
|
||
|
|
c75332efc30b"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"D", "[",
|
||
|
|
RowBox[{"Profitv", ",", "e"}], "]"}]], "Input",
|
||
|
|
CellChangeTimes->{{3.846015456586561*^9, 3.846015484511428*^9}, {
|
||
|
|
3.846015521663026*^9, 3.846015522941908*^9}},
|
||
|
|
CellLabel->"In[7]:=",ExpressionUUID->"0a340e55-6c1b-4523-b674-8f04383e6aae"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"Factor", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "e", " ", "k"}], "-",
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}]}], "+", "\[Theta]"}], "]"}]], \
|
||
|
|
"Input",
|
||
|
|
CellChangeTimes->{{3.84601591898872*^9, 3.846015926778664*^9}},
|
||
|
|
CellLabel->"In[8]:=",ExpressionUUID->"4ab18add-3f2d-443d-a319-9babf3d24ef3"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.846015944313939*^9,
|
||
|
|
3.846015944314764*^9}},ExpressionUUID->"c94e3235-6b09-4229-9717-\
|
||
|
|
8d6799594eed"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.846015680445264*^9,
|
||
|
|
3.846015716042446*^9}},ExpressionUUID->"7e710fd3-19cb-4366-80ff-\
|
||
|
|
3b1a7a9941d7"],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"Solve", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "e", " ", "k"}], "-",
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}]}], "+", "\[Theta]"}], "\[Equal]",
|
||
|
|
"0"}], ",", "e"}], "]"}]], "Input",
|
||
|
|
CellChangeTimes->{{3.8460156920793333`*^9, 3.846015720951009*^9}, {
|
||
|
|
3.84601591497917*^9, 3.846015915908428*^9}},
|
||
|
|
CellLabel->"In[9]:=",ExpressionUUID->"8a567ca0-a1ac-4491-98e9-8ea667215fbf"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"e", "\[Rule]",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}], "}"}], "}"}]], "Output",
|
||
|
|
CellChangeTimes->{3.846015721841674*^9, 3.846015946247868*^9},
|
||
|
|
CellLabel->"Out[9]=",ExpressionUUID->"995a38b8-08bd-46d9-8dc2-16c1dcb273cb"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"e", ":=",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}]], "Input",
|
||
|
|
CellChangeTimes->{{3.846015984649746*^9, 3.846015993199431*^9}},
|
||
|
|
CellLabel->"In[10]:=",ExpressionUUID->"e7b62be6-5781-4261-b4a0-bf2eac2671f3"],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData["e"], "Input",
|
||
|
|
CellChangeTimes->{3.846015995653957*^9},
|
||
|
|
CellLabel->"In[11]:=",ExpressionUUID->"5953ef85-9e41-4461-bb16-1276935d4ebe"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}],
|
||
|
|
RowBox[{"2", " ", "k"}]]], "Output",
|
||
|
|
CellChangeTimes->{3.84601599606651*^9},
|
||
|
|
CellLabel->"Out[11]=",ExpressionUUID->"7e50d72b-f53b-4c48-9e55-6e2abc929de6"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData["Profitv"], "Input",
|
||
|
|
CellLabel->"In[12]:=",ExpressionUUID->"6ce9a3ec-f3de-4238-8734-7761b1796309"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "cv"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}], ")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]], "-",
|
||
|
|
FractionBox[
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}], ")"}], "2"],
|
||
|
|
RowBox[{"4", " ", "k"}]], "-",
|
||
|
|
RowBox[{"\[Theta]", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}], ")"}]}]}]], "Output",
|
||
|
|
CellChangeTimes->{3.8460160076386414`*^9},
|
||
|
|
CellLabel->"Out[12]=",ExpressionUUID->"9e4ac26f-3a2a-4254-aa46-7b5fb902817f"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"D", "[",
|
||
|
|
RowBox[{"Profitv", ",", "p"}], "]"}]], "Input",
|
||
|
|
CellChangeTimes->{{3.8460161193014793`*^9, 3.846016128984997*^9}},
|
||
|
|
CellLabel->"In[13]:=",ExpressionUUID->"b557bb6c-b890-45db-99bc-c8a4213e5fe5"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}], "+", "\[Alpha]", "+",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", "\[Theta]"}],
|
||
|
|
RowBox[{"2", " ", "k"}]], "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}], ")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]], "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}], ")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}]], "Output",
|
||
|
|
CellChangeTimes->{3.846016132835639*^9},
|
||
|
|
CellLabel->"Out[13]=",ExpressionUUID->"9fad0a65-2ba8-4522-a42f-675fc904a4de"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"Simplify", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}], "+", "\[Alpha]", "+",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", "\[Theta]"}],
|
||
|
|
RowBox[{"2", " ", "k"}]], "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}], ")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]], "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}], ")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}], "]"}]], "Input",
|
||
|
|
NumberMarks->False,
|
||
|
|
CellLabel->"In[14]:=",ExpressionUUID->"7ed7b0c2-9f2c-4795-811c-00950b85eb72"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}], "+",
|
||
|
|
RowBox[{"2", " ", "k", " ", "\[Alpha]"}], "+",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", "\[Theta]"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]], "Input",
|
||
|
|
CellChangeTimes->{3.846016607133621*^9},
|
||
|
|
CellLabel->"Out[14]=",ExpressionUUID->"dd5bab20-4fac-490e-9583-f373c25ab454"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"Solve", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}], "+",
|
||
|
|
RowBox[{"2", " ", "k", " ", "\[Alpha]"}], "+",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", "\[Theta]"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]], "\[Equal]", "0"}], ",", "p"}], "]"}]], "Input",\
|
||
|
|
|
||
|
|
CellChangeTimes->{{3.846016614064641*^9, 3.846016670988596*^9}},
|
||
|
|
CellLabel->"In[1]:=",ExpressionUUID->"62fa6239-3ca5-4af4-8681-8349b2c9d7e0"],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[{
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"p", "\[Rule]",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-",
|
||
|
|
|
||
|
|
RowBox[{"\[Alpha]", " ", "\[Theta]"}]}],
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]]}], "}"}],
|
||
|
|
"}"}], "\[IndentingNewLine]",
|
||
|
|
RowBox[{"p", ":=",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-",
|
||
|
|
RowBox[{"\[Alpha]", " ", "\[Theta]"}]}],
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]]}]}], "Input",
|
||
|
|
CellChangeTimes->{{3.846016716553187*^9, 3.846016724939755*^9}},
|
||
|
|
CellLabel->"In[3]:=",ExpressionUUID->"ceb83690-d99d-4b41-9f2f-70e3444dc20a"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"p", "\[Rule]",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-",
|
||
|
|
|
||
|
|
RowBox[{"\[Alpha]", " ", "\[Theta]"}]}],
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]]}], "}"}],
|
||
|
|
"}"}]], "Output",
|
||
|
|
CellChangeTimes->{3.846016726043373*^9},
|
||
|
|
CellLabel->"Out[3]=",ExpressionUUID->"2a15f4c7-7258-43ad-9747-f6c651a0e310"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"e", ":=",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}]], "Input",
|
||
|
|
CellChangeTimes->{{3.846016701374612*^9, 3.846016702324121*^9}, {
|
||
|
|
3.846016742409114*^9, 3.846016743259778*^9}},
|
||
|
|
CellLabel->"In[5]:=",ExpressionUUID->"1240cc78-595f-4e00-b456-7365abbe6c6b"],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData["e"], "Input",
|
||
|
|
CellChangeTimes->{3.846016746131781*^9},
|
||
|
|
CellLabel->"In[6]:=",ExpressionUUID->"4b85e34a-efda-419f-a449-927507b9e126"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"\[Theta]", "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-",
|
||
|
|
RowBox[{"\[Alpha]", " ", "\[Theta]"}]}],
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]], "+",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"\[Alpha]", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-",
|
||
|
|
RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}],
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]], "Output",
|
||
|
|
CellChangeTimes->{3.8460167465633593`*^9},
|
||
|
|
CellLabel->"Out[6]=",ExpressionUUID->"c5c5b7a4-8514-4877-9e67-960b372aa095"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[BoxData["p"], "Input",
|
||
|
|
CellChangeTimes->{3.846016750170773*^9},
|
||
|
|
CellLabel->"In[7]:=",ExpressionUUID->"89b40378-51dd-4601-a63d-25a1531797f0"],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[{
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-",
|
||
|
|
RowBox[{"\[Alpha]", " ", "\[Theta]"}]}],
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}],
|
||
|
|
"2"]], "\[IndentingNewLine]",
|
||
|
|
RowBox[{"Profits", ":=",
|
||
|
|
RowBox[{"v", "-",
|
||
|
|
RowBox[{"(", " ",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"\[Alpha]", " ", "p"}], "-",
|
||
|
|
RowBox[{"e", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}], "p"}], "+", "cs"}], ")"}]}]}]}],\
|
||
|
|
"Input",
|
||
|
|
CellChangeTimes->{{3.846016771223298*^9, 3.8460167720968657`*^9}},
|
||
|
|
CellLabel->"In[8]:=",ExpressionUUID->"2697ac19-67a0-437d-8078-fcd5c7b3f222"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-",
|
||
|
|
RowBox[{"\[Alpha]", " ", "\[Theta]"}]}],
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]]], "Output",
|
||
|
|
CellChangeTimes->{3.846016775678307*^9},
|
||
|
|
CellLabel->"Out[8]=",ExpressionUUID->"13707097-1b33-4903-bb54-c6850064615c"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData["Profits"], "Input",
|
||
|
|
CellChangeTimes->{{3.8460167799372587`*^9, 3.846016782740767*^9}},
|
||
|
|
CellLabel->"In[10]:=",ExpressionUUID->"e108d512-a08d-4cb1-8d27-397ce465c5ce"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "cs"}], "+", "v", "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"\[Alpha]", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-",
|
||
|
|
|
||
|
|
RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}],
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]], "+",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-",
|
||
|
|
|
||
|
|
RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"\[Theta]", "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]",
|
||
|
|
"-",
|
||
|
|
RowBox[{"\[Alpha]", " ", "\[Theta]"}]}],
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]], "+",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"\[Alpha]", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]",
|
||
|
|
"-",
|
||
|
|
RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}],
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]]}], ")"}]}],
|
||
|
|
RowBox[{"2", " ", "k", " ",
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]}]], "Output",
|
||
|
|
CellChangeTimes->{3.8460167837856703`*^9},
|
||
|
|
CellLabel->"Out[10]=",ExpressionUUID->"66e113e1-bf2f-43cb-a081-7fb1bdf207a3"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"Simplify", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "cs"}], "+", "v", "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"\[Alpha]", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-",
|
||
|
|
RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}],
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]], "+",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-",
|
||
|
|
RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"\[Theta]", "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]",
|
||
|
|
"-",
|
||
|
|
RowBox[{"\[Alpha]", " ", "\[Theta]"}]}],
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]], "+",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"\[Alpha]", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]",
|
||
|
|
"-",
|
||
|
|
RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}],
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]]}], ")"}]}],
|
||
|
|
RowBox[{"2", " ", "k", " ",
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]}],
|
||
|
|
"]"}]], "Input",
|
||
|
|
NumberMarks->False,
|
||
|
|
CellLabel->"In[11]:=",ExpressionUUID->"e13d292f-57c0-4450-80a7-83eaf3411d3c"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "cs"}], "+", "v"}]], "Output",
|
||
|
|
CellChangeTimes->{3.846016980163444*^9},
|
||
|
|
CellLabel->"Out[11]=",ExpressionUUID->"d3dac461-e24f-427c-acab-a49f1568e2a0"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.846016753048232*^9,
|
||
|
|
3.846016773857314*^9}},ExpressionUUID->"eaa61adc-d59f-43a9-a49e-\
|
||
|
|
178d00d07ac6"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.846016649690462*^9,
|
||
|
|
3.846016649691337*^9}},ExpressionUUID->"95c64216-5fe5-4455-b0b9-\
|
||
|
|
61777e2a04a8"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"Profits", ":=",
|
||
|
|
RowBox[{"v", "-",
|
||
|
|
RowBox[{"(", " ",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"\[Alpha]", " ", "p"}], "-",
|
||
|
|
RowBox[{"e", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}], "p"}], "+", "cs"}],
|
||
|
|
")"}]}]}]], "Input",
|
||
|
|
CellLabel->"In[1]:=",ExpressionUUID->"0654e6e3-41f3-4d1f-a8ea-c3f331d864e6"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"e", ":=",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}]], "Input",
|
||
|
|
CellChangeTimes->{{3.8460163684501543`*^9, 3.846016381951235*^9},
|
||
|
|
3.846016601662344*^9, 3.8460170768538103`*^9},
|
||
|
|
CellLabel->"In[2]:=",ExpressionUUID->"c7d307cd-897d-4245-85db-f3685b3eac2f"],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData["Profits"], "Input",
|
||
|
|
CellChangeTimes->{{3.8460170796540413`*^9, 3.84601708209195*^9}},
|
||
|
|
CellLabel->"In[3]:=",ExpressionUUID->"94cccf4c-a4e5-4e64-a45f-fc6dd50c5a95"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "cs"}], "+", "v", "-",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}], ")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}]], "Output",
|
||
|
|
CellChangeTimes->{3.846017083106876*^9},
|
||
|
|
CellLabel->"Out[3]=",ExpressionUUID->"a7265267-4142-49a9-9acd-c2524b95f0c8"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"Simplify", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "cs"}], "+", "v", "-",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}], ")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}], "]"}]], "Input",
|
||
|
|
NumberMarks->False,
|
||
|
|
CellLabel->"In[4]:=",ExpressionUUID->"816518cf-3a37-4e82-ab04-c68b0fdd85fd"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "cs"}], "+", "v", "-",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}], "+", "\[Theta]"}],
|
||
|
|
")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}]], "Output",
|
||
|
|
CellChangeTimes->{3.846017157499614*^9},
|
||
|
|
CellLabel->"Out[4]=",ExpressionUUID->"17f965f4-a3e8-4449-9997-c2d0cb375307"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.8460175031139507`*^9, 3.8460175177086678`*^9},
|
||
|
|
3.8460176636680183`*^9},ExpressionUUID->"9f7a8caf-e11c-4b41-8454-\
|
||
|
|
9ece08e1f784"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.846017661864953*^9,
|
||
|
|
3.846017661866694*^9}},ExpressionUUID->"43730951-7bc7-4d4e-b46a-\
|
||
|
|
03d0b62103b0"],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"D", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "cs"}], "+", "v", "-",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}], "+", "\[Theta]"}],
|
||
|
|
")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}], ",", "p"}], "]"}]], "Input",
|
||
|
|
CellChangeTimes->{{3.846017628486609*^9, 3.846017640007743*^9}, {
|
||
|
|
3.846017680078972*^9, 3.8460176808675423`*^9}, {3.846017714098559*^9,
|
||
|
|
3.8460177142911663`*^9}},
|
||
|
|
CellLabel->"In[3]:=",ExpressionUUID->"cd015583-d29f-40ef-a169-8ca777fdeb1c"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}], "-", "\[Alpha]", "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}], "+", "\[Theta]"}],
|
||
|
|
")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}]], "Output",
|
||
|
|
CellChangeTimes->{3.846017716912532*^9},
|
||
|
|
CellLabel->"Out[3]=",ExpressionUUID->"d6787726-298c-4a62-8023-a065641bae10"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"Simplify", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}], "-", "\[Alpha]", "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}], "+", "\[Theta]"}],
|
||
|
|
")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}], "]"}]], "Input",
|
||
|
|
NumberMarks->False,
|
||
|
|
CellLabel->"In[4]:=",ExpressionUUID->"c4e9f1bf-29f0-4346-921e-7e84a3f81318"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "p", " ",
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}], "-",
|
||
|
|
RowBox[{"2", " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-",
|
||
|
|
RowBox[{"\[Alpha]", " ", "\[Theta]"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]], "Output",
|
||
|
|
CellChangeTimes->{3.846017806724074*^9},
|
||
|
|
CellLabel->"Out[4]=",ExpressionUUID->"bc4934ef-ecf5-44a9-9bb5-e69f8dc7e26e"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"Solve", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "p", " ",
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}], "-",
|
||
|
|
RowBox[{"2", " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-",
|
||
|
|
RowBox[{"\[Alpha]", " ", "\[Theta]"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]], "\[Equal]", "0"}], ",", "p"}], "]"}]], "Input",\
|
||
|
|
|
||
|
|
CellChangeTimes->{{3.846017847291198*^9, 3.8460178568423977`*^9}},
|
||
|
|
CellLabel->"In[5]:=",ExpressionUUID->"318afe78-5b90-4666-824f-74ca2db08caa"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"p", "\[Rule]",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-",
|
||
|
|
|
||
|
|
RowBox[{"\[Alpha]", " ", "\[Theta]"}]}],
|
||
|
|
RowBox[{"2", " ",
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]}], "}"}],
|
||
|
|
"}"}]], "Output",
|
||
|
|
CellChangeTimes->{3.846017857901329*^9},
|
||
|
|
CellLabel->"Out[5]=",ExpressionUUID->"c3f0e0f5-3457-4184-aeec-c93670f8aeb8"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"D", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "cs"}], "+", "v", "-",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}], "+", "\[Theta]"}],
|
||
|
|
")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}], ",", "\[Alpha]"}], "]"}]], "Input",
|
||
|
|
CellChangeTimes->{{3.8460179504954967`*^9, 3.846017962132217*^9}},
|
||
|
|
CellLabel->"In[1]:=",ExpressionUUID->"1dec5ea9-2cf8-44bb-a449-6da977f93631"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
SuperscriptBox["p", "2"], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]], "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}], "+", "\[Theta]"}],
|
||
|
|
")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}]], "Output",
|
||
|
|
CellChangeTimes->{3.8460179651780863`*^9},
|
||
|
|
CellLabel->"Out[1]=",ExpressionUUID->"1a776a35-f34f-4253-b4fa-a49156c6bd66"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"Simplify", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
SuperscriptBox["p", "2"], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]], "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}], "+", "\[Theta]"}],
|
||
|
|
")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}], "]"}]], "Input",
|
||
|
|
NumberMarks->False,
|
||
|
|
CellLabel->"In[2]:=",ExpressionUUID->"ce5b930b-7ae7-40ae-84a1-2429cc3d9f3b"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"2", " ", "k"}], "+",
|
||
|
|
RowBox[{"2", " ", "p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}], "+", "\[Theta]"}],
|
||
|
|
")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}]], "Output",
|
||
|
|
CellChangeTimes->{3.8460180130845213`*^9},
|
||
|
|
CellLabel->"Out[2]=",ExpressionUUID->"a95a3ac8-3885-4d2c-a18f-11f3b093b701"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"Solve", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"2", " ", "k"}], "+",
|
||
|
|
RowBox[{"2", " ", "p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}], "+", "\[Theta]"}],
|
||
|
|
")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}], "\[Equal]", "0"}], ",", "\[Alpha]"}],
|
||
|
|
"]"}]], "Input",
|
||
|
|
CellChangeTimes->{{3.846018075925934*^9, 3.846018090842647*^9}},
|
||
|
|
CellLabel->"In[3]:=",ExpressionUUID->"dc797e01-6cbb-4c2c-882c-c068017833a7"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"\[Alpha]", "\[Rule]",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "k"}], "+",
|
||
|
|
RowBox[{"2", " ", "p"}], "-", "\[Theta]"}],
|
||
|
|
RowBox[{"2", " ", "p"}]]}], "}"}], "}"}]], "Output",
|
||
|
|
CellChangeTimes->{3.84601809188128*^9},
|
||
|
|
CellLabel->"Out[3]=",ExpressionUUID->"96faf296-700b-4726-8b0c-b492afc4e113"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"Solve", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"2", " ", "k"}], "+",
|
||
|
|
RowBox[{"2", " ", "p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}], "+",
|
||
|
|
"\[Theta]"}], ")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}], "\[Equal]", "0"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "p", " ",
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}], "-",
|
||
|
|
RowBox[{"2", " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-",
|
||
|
|
RowBox[{"\[Alpha]", " ", "\[Theta]"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]], "\[Equal]", "0"}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"p", ",", "\[Alpha]"}], "}"}]}], "]"}]], "Input",
|
||
|
|
CellChangeTimes->{{3.8460181343162413`*^9, 3.846018135711637*^9}, {
|
||
|
|
3.846018347453306*^9, 3.846018404960094*^9}, {3.8460185740634003`*^9,
|
||
|
|
3.846018575680637*^9}, 3.8460186157369947`*^9},
|
||
|
|
CellLabel->"In[3]:=",ExpressionUUID->"a412039f-ac24-4b34-910b-c3c7e3855a5b"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"p", "\[Rule]", "0"}], ",",
|
||
|
|
RowBox[{"\[Alpha]", "\[Rule]",
|
||
|
|
FractionBox["\[Theta]",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"2", " ", "k"}], "+", "\[Theta]"}]]}]}], "}"}],
|
||
|
|
"}"}]], "Output",
|
||
|
|
CellChangeTimes->{3.846018621737824*^9},
|
||
|
|
CellLabel->"Out[3]=",ExpressionUUID->"1a6e4494-23ca-498a-b995-a31a2504048b"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.846018519634491*^9, 3.846018520697936*^9},
|
||
|
|
3.846018619546912*^9},ExpressionUUID->"f2efcebd-c836-4bb1-8b6c-\
|
||
|
|
a743cee0145e"],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"Profitc", "=",
|
||
|
|
RowBox[{"v", "-", "cs", "-", "cv", "-",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "e"}], ")"}], "\[Theta]"}], "-",
|
||
|
|
RowBox[{"k", "*", "e", "*", "e"}]}]}]], "Input",
|
||
|
|
CellChangeTimes->{{3.846019198138075*^9, 3.846019235197626*^9}},
|
||
|
|
CellLabel->"In[1]:=",ExpressionUUID->"95e9d5b4-ae0d-439d-8609-f4212fb88b80"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "cs"}], "-", "cv", "-",
|
||
|
|
RowBox[{
|
||
|
|
SuperscriptBox["e", "2"], " ", "k"}], "+", "v", "-",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "e"}], ")"}], " ", "\[Theta]"}]}]], "Output",
|
||
|
|
CellChangeTimes->{3.846019238137308*^9},
|
||
|
|
CellLabel->"Out[1]=",ExpressionUUID->"9489ebab-7836-4f49-bd55-563296d4fc29"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData["Profitc"], "Input",
|
||
|
|
CellChangeTimes->{{3.8460192387446938`*^9, 3.846019240922443*^9}},
|
||
|
|
CellLabel->"In[2]:=",ExpressionUUID->"70bfa0a2-3c90-4c7e-be5e-dc473aa8d8dc"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "cs"}], "-", "cv", "-",
|
||
|
|
RowBox[{
|
||
|
|
SuperscriptBox["e", "2"], " ", "k"}], "+", "v", "-",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "e"}], ")"}], " ", "\[Theta]"}]}]], "Output",
|
||
|
|
CellChangeTimes->{3.8460192419407063`*^9},
|
||
|
|
CellLabel->"Out[2]=",ExpressionUUID->"bd9c95dc-13db-43ef-afd4-18b4addb8fb2"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"D", "[",
|
||
|
|
RowBox[{"Profitc", ",", "e"}], "]"}]], "Input",
|
||
|
|
CellChangeTimes->{{3.8460192454453077`*^9, 3.8460192523194733`*^9}},
|
||
|
|
CellLabel->"In[3]:=",ExpressionUUID->"26bdd9a8-5c03-4aae-b72e-ea8663edbf6a"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "e", " ", "k"}], "+", "\[Theta]"}]], "Output",
|
||
|
|
CellChangeTimes->{3.846019253089736*^9},
|
||
|
|
CellLabel->"Out[3]=",ExpressionUUID->"5dfd5456-45e3-4d11-a9e3-de81f3c21dee"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"Solve", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ", "e", " ", "k"}], "+", "\[Theta]"}], "\[Equal]",
|
||
|
|
"0"}], ",", "e"}], "]"}]], "Input",
|
||
|
|
CellChangeTimes->{{3.8460193690957193`*^9, 3.8460193788758173`*^9}, {
|
||
|
|
3.846019426509116*^9, 3.846019428297203*^9}},
|
||
|
|
CellLabel->"In[2]:=",ExpressionUUID->"3c000c14-eb6f-4fa5-a08e-90675a28c411"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"e", "\[Rule]",
|
||
|
|
FractionBox["\[Theta]",
|
||
|
|
RowBox[{"2", " ", "k"}]]}], "}"}], "}"}]], "Output",
|
||
|
|
CellChangeTimes->{3.846019429288889*^9},
|
||
|
|
CellLabel->"Out[2]=",ExpressionUUID->"77ecf3fd-838e-4be7-a0e1-f88f42ea9186"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"e", ":=",
|
||
|
|
FractionBox["\[Theta]",
|
||
|
|
RowBox[{"2", " ", "k"}]]}]], "Input",
|
||
|
|
CellChangeTimes->{{3.846019436954875*^9, 3.8460194433938704`*^9}},
|
||
|
|
CellLabel->"In[3]:=",ExpressionUUID->"e5d1c427-6e16-42be-86bc-bb15c6de4b50"],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"Profitc", "=",
|
||
|
|
RowBox[{"v", "-", "cs", "-", "cv", "-",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "e"}], ")"}], "\[Theta]"}], "-",
|
||
|
|
RowBox[{"k", "*", "e", "*", "e"}]}]}]], "Input",
|
||
|
|
CellChangeTimes->{{3.846019446217527*^9, 3.8460194741601467`*^9}},
|
||
|
|
CellLabel->"In[5]:=",ExpressionUUID->"2b1994aa-0118-4c78-94b1-c652c9324d89"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "cs"}], "-", "cv", "+", "v", "-",
|
||
|
|
FractionBox[
|
||
|
|
SuperscriptBox["\[Theta]", "2"],
|
||
|
|
RowBox[{"4", " ", "k"}]], "-",
|
||
|
|
RowBox[{"\[Theta]", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-",
|
||
|
|
FractionBox["\[Theta]",
|
||
|
|
RowBox[{"2", " ", "k"}]]}], ")"}]}]}]], "Output",
|
||
|
|
CellChangeTimes->{3.8460194749421453`*^9},
|
||
|
|
CellLabel->"Out[5]=",ExpressionUUID->"a0fa896f-397f-493d-bf3c-18973b690edd"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"Simplify", "[", "Profitc", "]"}]], "Input",
|
||
|
|
NumberMarks->False,
|
||
|
|
CellLabel->"In[6]:=",ExpressionUUID->"2ff39867-da3e-49e9-b5b1-4faeec8bb712"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "cs"}], "-", "cv", "+", "v", "-", "\[Theta]", "+",
|
||
|
|
FractionBox[
|
||
|
|
SuperscriptBox["\[Theta]", "2"],
|
||
|
|
RowBox[{"4", " ", "k"}]]}]], "Output",
|
||
|
|
CellChangeTimes->{3.846019499765358*^9},
|
||
|
|
CellLabel->"Out[6]=",ExpressionUUID->"918d0df8-f0ea-4482-b6c1-d0490b2e9e03"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"Solve", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "cs"}], "-", "cv", "+", "v", "-", "\[Theta]", "+",
|
||
|
|
FractionBox[
|
||
|
|
SuperscriptBox["\[Theta]", "2"],
|
||
|
|
RowBox[{"4", " ", "k"}]]}], "\[Equal]", "0"}], ",", "v"}],
|
||
|
|
"]"}]], "Input",
|
||
|
|
CellChangeTimes->{{3.846019583072732*^9, 3.846019592558894*^9}},
|
||
|
|
CellLabel->"In[7]:=",ExpressionUUID->"79150a3f-e969-4ea4-a555-11ed43cb27d5"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"v", "\[Rule]",
|
||
|
|
RowBox[{"cs", "+", "cv", "+", "\[Theta]", "-",
|
||
|
|
FractionBox[
|
||
|
|
SuperscriptBox["\[Theta]", "2"],
|
||
|
|
RowBox[{"4", " ", "k"}]]}]}], "}"}], "}"}]], "Output",
|
||
|
|
CellChangeTimes->{3.846019592960248*^9},
|
||
|
|
CellLabel->"Out[7]=",ExpressionUUID->"4cddf14c-3fd4-4479-877b-f33c6449133a"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.846019464545184*^9,
|
||
|
|
3.846019464545923*^9}},ExpressionUUID->"829dd63b-df37-41f2-818d-\
|
||
|
|
389dda287f24"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"e", ":=",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}]], "Input",
|
||
|
|
CellChangeTimes->{{3.846019424886437*^9, 3.846019424887388*^9},
|
||
|
|
3.846020155352811*^9},
|
||
|
|
CellLabel->"In[1]:=",ExpressionUUID->"474f25a2-693b-4cc3-a116-b1a928826120"],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData["e"], "Input",
|
||
|
|
CellChangeTimes->{3.8460201584093924`*^9},
|
||
|
|
CellLabel->"In[2]:=",ExpressionUUID->"9756bd99-6357-4bfd-aaf5-37127b6d5126"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}],
|
||
|
|
RowBox[{"2", " ", "k"}]]], "Output",
|
||
|
|
CellChangeTimes->{3.84602015978747*^9},
|
||
|
|
CellLabel->"Out[2]=",ExpressionUUID->"25c9b8f5-de55-4584-8dd9-3ee6961dd8e5"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"Profits", ":=",
|
||
|
|
RowBox[{"v", "-",
|
||
|
|
RowBox[{"(", " ",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"\[Alpha]", " ", "p"}], "-",
|
||
|
|
RowBox[{"e", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}], "p"}], "+", "cs"}],
|
||
|
|
")"}]}]}]], "Input",
|
||
|
|
CellChangeTimes->{3.846019420931046*^9, 3.846020170639949*^9},
|
||
|
|
CellLabel->"In[3]:=",ExpressionUUID->"f60fb38a-06fc-4449-9c21-f14e0c9f761c"],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData["Profits"], "Input",
|
||
|
|
CellChangeTimes->{{3.846020172812964*^9, 3.84602017560811*^9}},
|
||
|
|
CellLabel->"In[4]:=",ExpressionUUID->"892f139e-b128-4d75-9d0f-ca0298adebc2"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "cs"}], "+", "v", "-",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}], ")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}]], "Output",
|
||
|
|
CellChangeTimes->{3.846020176566676*^9},
|
||
|
|
CellLabel->"Out[4]=",ExpressionUUID->"c5a2c64e-5fba-4bee-90f3-c0e98b44df04"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"D", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "cs"}], "+", "v", "-",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}], ")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}], ",", "\[Alpha]"}], "]"}]], "Input",
|
||
|
|
CellChangeTimes->{{3.846020231205083*^9, 3.8460202821402073`*^9}},
|
||
|
|
CellLabel->"In[6]:=",ExpressionUUID->"3e4a8fe0-6819-4b87-a519-232ea3b51545"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{
|
||
|
|
SuperscriptBox["p", "2"], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"1", "-", "\[Alpha]"}], ")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]], "-",
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"p", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "p"}], "+",
|
||
|
|
RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}], ")"}]}],
|
||
|
|
RowBox[{"2", " ", "k"}]]}]], "Output",
|
||
|
|
CellChangeTimes->{{3.8460202741627083`*^9, 3.8460202830261908`*^9}},
|
||
|
|
CellLabel->"Out[6]=",ExpressionUUID->"6956331b-b249-4f9d-8471-45736fab4eac"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.846019421951312*^9,
|
||
|
|
3.846019421952146*^9}},ExpressionUUID->"6f6b949f-7c03-40f7-a8af-\
|
||
|
|
164288772a61"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.846017701382214*^9,
|
||
|
|
3.846017701383142*^9}},ExpressionUUID->"6f95b30f-8e7e-4c3c-9edb-\
|
||
|
|
c0c2b4a41f0f"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{3.8460176992469587`*^9},
|
||
|
|
NumberMarks->False,ExpressionUUID->"31f726ef-b11a-43fa-a0bd-78319243b995"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.846017704084765*^9,
|
||
|
|
3.846017704085779*^9}},ExpressionUUID->"075dda5e-1741-4fb6-841b-\
|
||
|
|
cd4f4c3f6c4c"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.846017591012312*^9, 3.846017594163546*^9}},
|
||
|
|
CellLabel->"In[7]:=",ExpressionUUID->"54f3896d-fc29-4562-b3bd-83138a9a95d3"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{3.846017583868177*^9},
|
||
|
|
NumberMarks->False,ExpressionUUID->"7b25b87a-bb5b-4552-b86e-a7fdf416fc78"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.8460175819528627`*^9,
|
||
|
|
3.846017581953753*^9}},ExpressionUUID->"f276d2f7-d824-4833-a146-\
|
||
|
|
6874e5837562"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.846016589841724*^9,
|
||
|
|
3.846016589842585*^9}},ExpressionUUID->"287e5101-50ac-46c8-b1ac-\
|
||
|
|
053f0b80193d"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{3.8460165922891817`*^9},
|
||
|
|
NumberMarks->False,ExpressionUUID->"d7c19fe8-d709-47fe-b14a-69639d1630e7"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.846016598823448*^9,
|
||
|
|
3.846016598824512*^9}},ExpressionUUID->"bceac606-4783-4ede-9655-\
|
||
|
|
7837c48724fc"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{3.846016595050538*^9},
|
||
|
|
NumberMarks->False,ExpressionUUID->"74cb7dc2-1f86-4d44-9ced-4e06db03bd46"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.846016596738965*^9,
|
||
|
|
3.846016596739897*^9}},ExpressionUUID->"29d503e3-1e16-40fb-8e7a-\
|
||
|
|
4d05553df717"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.8460165618546247`*^9,
|
||
|
|
3.846016561859408*^9}},ExpressionUUID->"4ae8f227-ec57-4460-81d9-\
|
||
|
|
552986166846"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{3.8460165592080507`*^9},
|
||
|
|
NumberMarks->False,ExpressionUUID->"e31755ea-4e51-4410-bac1-9b3c866c4aab"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.846016556085349*^9,
|
||
|
|
3.8460165560862303`*^9}},ExpressionUUID->"f1902e02-50fa-4a19-b8e7-\
|
||
|
|
a055bd2f71aa"],
|
||
|
|
|
||
|
|
Cell[BoxData["\[IndentingNewLine]"], "Input",
|
||
|
|
CellChangeTimes->{{3.846016496921628*^9, 3.846016539265564*^9},
|
||
|
|
3.84601660519853*^9},ExpressionUUID->"c730a72e-1dc2-4b47-9a0e-\
|
||
|
|
9174b6670a3b"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.8460165360237627`*^9,
|
||
|
|
3.846016536024789*^9}},ExpressionUUID->"e85e937c-bbb4-4755-ab82-\
|
||
|
|
b8f8a21ad73c"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.846016470336779*^9, 3.846016475798122*^9},
|
||
|
|
3.846016566006571*^9},ExpressionUUID->"af17a3a2-842e-4297-9dd8-\
|
||
|
|
04b760428994"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{3.84601652289954*^9,
|
||
|
|
3.846016567669478*^9},ExpressionUUID->"3c85075c-b71e-4b67-88e1-\
|
||
|
|
cf3c34c9a315"],
|
||
|
|
|
||
|
|
Cell[BoxData[""], "Input",
|
||
|
|
CellChangeTimes->{{3.846016569941721*^9,
|
||
|
|
3.846016569942333*^9}},ExpressionUUID->"65cbec44-ed62-4805-9ecd-\
|
||
|
|
6578b08381a0"]
|
||
|
|
},
|
||
|
|
WindowSize->{808, 730},
|
||
|
|
WindowMargins->{{226, Automatic}, {-25, Automatic}},
|
||
|
|
FrontEndVersion->"12.1 for Mac OS X x86 (64-bit) \
|
||
|
|
(2020\:5e743\:670813\:65e5)",
|
||
|
|
StyleDefinitions->"Default.nb",
|
||
|
|
ExpressionUUID->"3a92eaf2-f0c9-4e23-871a-62905c1fbb3b"
|
||
|
|
]
|
||
|
|
(* End of Notebook Content *)
|
||
|
|
|
||
|
|
(* Internal cache information *)
|
||
|
|
(*CellTagsOutline
|
||
|
|
CellTagsIndex->{}
|
||
|
|
*)
|
||
|
|
(*CellTagsIndex
|
||
|
|
CellTagsIndex->{}
|
||
|
|
*)
|
||
|
|
(*NotebookFileOutline
|
||
|
|
Notebook[{
|
||
|
|
Cell[400, 13, 470, 12, 30, "Input",ExpressionUUID->"3bb3da7d-bb03-45e8-97dd-2768c4a330b4"],
|
||
|
|
Cell[873, 27, 698, 18, 52, "Input",ExpressionUUID->"a0a05b1c-092f-45d3-958b-6f6f6db87303"],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[1596, 49, 176, 2, 30, "Input",ExpressionUUID->"71ee1270-ea36-4acc-94db-dc48ffe86013"],
|
||
|
|
Cell[1775, 53, 467, 13, 34, "Output",ExpressionUUID->"140e314c-6402-4e91-b92c-62c44f5ba43d"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[2279, 71, 177, 2, 30, "Input",ExpressionUUID->"11d5dc5f-343c-4251-ab18-015232c9f2d1"],
|
||
|
|
Cell[2459, 75, 467, 13, 34, "Output",ExpressionUUID->"3227026d-e675-4995-b271-ddbd4ca89536"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[2941, 91, 146, 2, 30, "Input",ExpressionUUID->"3bf5d625-4d78-454e-9335-fbe4dbbc1cd8"],
|
||
|
|
Cell[3090, 95, 154, 3, 30, InheritFromParent,ExpressionUUID->"2e6d6539-8fd8-49f3-a149-d4b553202033"],
|
||
|
|
Cell[3247, 100, 146, 2, 30, "Input",ExpressionUUID->"e672dd71-9de7-403a-b3cb-1f7ee65d291e"],
|
||
|
|
Cell[3396, 104, 153, 3, 30, InheritFromParent,ExpressionUUID->"36da0a40-43e5-4609-aa01-e0614fe18963"],
|
||
|
|
Cell[3552, 109, 202, 4, 30, "Input",ExpressionUUID->"b8521a2a-4f73-40a5-81a7-c75332efc30b"],
|
||
|
|
Cell[3757, 115, 276, 5, 44, "Input",ExpressionUUID->"0a340e55-6c1b-4523-b674-8f04383e6aae"],
|
||
|
|
Cell[4036, 122, 380, 10, 44, InheritFromParent,ExpressionUUID->"4ab18add-3f2d-443d-a319-9babf3d24ef3"],
|
||
|
|
Cell[4419, 134, 152, 3, 30, InheritFromParent,ExpressionUUID->"c94e3235-6b09-4229-9717-8d6799594eed"],
|
||
|
|
Cell[4574, 139, 152, 3, 30, "Input",ExpressionUUID->"7e710fd3-19cb-4366-80ff-3b1a7a9941d7"],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[4751, 146, 499, 13, 44, "Input",ExpressionUUID->"8a567ca0-a1ac-4491-98e9-8ea667215fbf"],
|
||
|
|
Cell[5253, 161, 393, 10, 49, "Output",ExpressionUUID->"995a38b8-08bd-46d9-8dc2-16c1dcb273cb"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[5661, 174, 333, 8, 46, "Input",ExpressionUUID->"e7b62be6-5781-4261-b4a0-bf2eac2671f3"],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[6019, 186, 148, 2, 30, "Input",ExpressionUUID->"5953ef85-9e41-4461-bb16-1276935d4ebe"],
|
||
|
|
Cell[6170, 190, 281, 7, 49, "Output",ExpressionUUID->"7e50d72b-f53b-4c48-9e55-6e2abc929de6"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[6488, 202, 112, 1, 30, "Input",ExpressionUUID->"6ce9a3ec-f3de-4238-8734-7761b1796309"],
|
||
|
|
Cell[6603, 205, 939, 29, 53, "Output",ExpressionUUID->"9e4ac26f-3a2a-4254-aa46-7b5fb902817f"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[7579, 239, 230, 4, 44, "Input",ExpressionUUID->"b557bb6c-b890-45db-99bc-c8a4213e5fe5"],
|
||
|
|
Cell[7812, 245, 1131, 37, 50, "Output",ExpressionUUID->"9fad0a65-2ba8-4522-a42f-675fc904a4de"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[8958, 285, 1178, 38, 60, "Input",ExpressionUUID->"7ed7b0c2-9f2c-4795-811c-00950b85eb72"],
|
||
|
|
Cell[10139, 325, 509, 15, 50, InheritFromParent,ExpressionUUID->"dd5bab20-4fac-490e-9583-f373c25ab454"],
|
||
|
|
Cell[10651, 342, 658, 19, 63, "Input",ExpressionUUID->"62fa6239-3ca5-4af4-8681-8349b2c9d7e0"],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[11334, 365, 865, 26, 98, InheritFromParent,ExpressionUUID->"ceb83690-d99d-4b41-9f2f-70e3444dc20a"],
|
||
|
|
Cell[12202, 393, 520, 16, 55, "Output",ExpressionUUID->"2a15f4c7-7258-43ad-9747-f6c651a0e310"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[12737, 412, 381, 9, 46, "Input",ExpressionUUID->"1240cc78-595f-4e00-b456-7365abbe6c6b"],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[13143, 425, 147, 2, 30, "Input",ExpressionUUID->"4b85e34a-efda-419f-a449-927507b9e126"],
|
||
|
|
Cell[13293, 429, 855, 25, 61, "Output",ExpressionUUID->"c5c5b7a4-8514-4877-9e67-960b372aa095"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[14163, 457, 147, 2, 30, "Input",ExpressionUUID->"89b40378-51dd-4601-a63d-25a1531797f0"],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[14335, 463, 712, 21, 76, InheritFromParent,ExpressionUUID->"2697ac19-67a0-437d-8078-fcd5c7b3f222"],
|
||
|
|
Cell[15050, 486, 408, 11, 55, "Output",ExpressionUUID->"13707097-1b33-4903-bb54-c6850064615c"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[15495, 502, 180, 2, 30, "Input",ExpressionUUID->"e108d512-a08d-4cb1-8d27-397ce465c5ce"],
|
||
|
|
Cell[15678, 506, 1761, 55, 66, "Output",ExpressionUUID->"66e113e1-bf2f-43cb-a081-7fb1bdf207a3"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[17476, 566, 1811, 55, 80, "Input",ExpressionUUID->"e13d292f-57c0-4450-80a7-83eaf3411d3c"],
|
||
|
|
Cell[19290, 623, 190, 4, 34, "Output",ExpressionUUID->"d3dac461-e24f-427c-acab-a49f1568e2a0"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[19495, 630, 152, 3, 30, "Input",ExpressionUUID->"eaa61adc-d59f-43a9-a49e-178d00d07ac6"],
|
||
|
|
Cell[19650, 635, 152, 3, 30, InheritFromParent,ExpressionUUID->"95c64216-5fe5-4455-b0b9-61777e2a04a8"],
|
||
|
|
Cell[19805, 640, 353, 10, 30, "Input",ExpressionUUID->"0654e6e3-41f3-4d1f-a8ea-c3f331d864e6"],
|
||
|
|
Cell[20161, 652, 384, 9, 46, "Input",ExpressionUUID->"c7d307cd-897d-4245-85db-f3685b3eac2f"],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[20570, 665, 178, 2, 30, "Input",ExpressionUUID->"94cccf4c-a4e5-4e64-a45f-fc6dd50c5a95"],
|
||
|
|
Cell[20751, 669, 500, 14, 50, "Output",ExpressionUUID->"a7265267-4142-49a9-9acd-c2524b95f0c8"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[21288, 688, 524, 15, 60, "Input",ExpressionUUID->"816518cf-3a37-4e82-ab04-c68b0fdd85fd"],
|
||
|
|
Cell[21815, 705, 578, 18, 50, "Output",ExpressionUUID->"17f965f4-a3e8-4449-9997-c2d0cb375307"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[22408, 726, 181, 3, 30, "Input",ExpressionUUID->"9f7a8caf-e11c-4b41-8454-9ece08e1f784"],
|
||
|
|
Cell[22592, 731, 152, 3, 30, InheritFromParent,ExpressionUUID->"43730951-7bc7-4d4e-b46a-03d0b62103b0"],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[22769, 738, 785, 22, 60, "Input",ExpressionUUID->"cd015583-d29f-40ef-a169-8ca777fdeb1c"],
|
||
|
|
Cell[23557, 762, 719, 24, 53, "Output",ExpressionUUID->"d6787726-298c-4a62-8023-a065641bae10"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[24313, 791, 753, 25, 63, "Input",ExpressionUUID->"c4e9f1bf-29f0-4346-921e-7e84a3f81318"],
|
||
|
|
Cell[25069, 818, 483, 13, 53, "Output",ExpressionUUID->"bc4934ef-ecf5-44a9-9bb5-e69f8dc7e26e"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[25589, 836, 628, 17, 63, "Input",ExpressionUUID->"318afe78-5b90-4666-824f-74ca2db08caa"],
|
||
|
|
Cell[26220, 855, 550, 17, 55, "Output",ExpressionUUID->"c3f0e0f5-3457-4184-aeec-c93670f8aeb8"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[26807, 877, 692, 20, 60, "Input",ExpressionUUID->"1dec5ea9-2cf8-44bb-a449-6da977f93631"],
|
||
|
|
Cell[27502, 899, 624, 21, 53, "Output",ExpressionUUID->"1a776a35-f34f-4253-b4fa-a49156c6bd66"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[28163, 925, 653, 22, 63, "Input",ExpressionUUID->"ce5b930b-7ae7-40ae-84a1-2429cc3d9f3b"],
|
||
|
|
Cell[28819, 949, 463, 14, 51, "Output",ExpressionUUID->"a95a3ac8-3885-4d2c-a18f-11f3b093b701"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[29319, 968, 615, 18, 61, "Input",ExpressionUUID->"dc797e01-6cbb-4c2c-882c-c068017833a7"],
|
||
|
|
Cell[29937, 988, 398, 11, 54, "Output",ExpressionUUID->"96faf296-700b-4726-8b0c-b492afc4e113"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[30372, 1004, 1288, 35, 63, "Input",ExpressionUUID->"a412039f-ac24-4b34-910b-c3c7e3855a5b"],
|
||
|
|
Cell[31663, 1041, 382, 11, 50, "Output",ExpressionUUID->"1a6e4494-23ca-498a-b995-a31a2504048b"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[32060, 1055, 175, 3, 30, InheritFromParent,ExpressionUUID->"f2efcebd-c836-4bb1-8b6c-a743cee0145e"],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[32260, 1062, 365, 8, 30, InheritFromParent,ExpressionUUID->"95e9d5b4-ae0d-439d-8609-f4212fb88b80"],
|
||
|
|
Cell[32628, 1072, 347, 9, 34, "Output",ExpressionUUID->"9489ebab-7836-4f49-bd55-563296d4fc29"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[33012, 1086, 179, 2, 30, "Input",ExpressionUUID->"70bfa0a2-3c90-4c7e-be5e-dc473aa8d8dc"],
|
||
|
|
Cell[33194, 1090, 349, 9, 34, "Output",ExpressionUUID->"bd9c95dc-13db-43ef-afd4-18b4addb8fb2"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[33580, 1104, 231, 4, 44, "Input",ExpressionUUID->"26bdd9a8-5c03-4aae-b72e-ea8663edbf6a"],
|
||
|
|
Cell[33814, 1110, 229, 5, 34, "Output",ExpressionUUID->"5dfd5456-45e3-4d11-a9e3-de81f3c21dee"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[34080, 1120, 404, 10, 44, "Input",ExpressionUUID->"3c000c14-eb6f-4fa5-a08e-90675a28c411"],
|
||
|
|
Cell[34487, 1132, 279, 7, 49, "Output",ExpressionUUID->"77ecf3fd-838e-4be7-a0e1-f88f42ea9186"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[34781, 1142, 248, 5, 46, "Input",ExpressionUUID->"e5d1c427-6e16-42be-86bc-bb15c6de4b50"],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[35054, 1151, 367, 8, 30, "Input",ExpressionUUID->"2b1994aa-0118-4c78-94b1-c652c9324d89"],
|
||
|
|
Cell[35424, 1161, 436, 12, 53, "Output",ExpressionUUID->"a0fa896f-397f-493d-bf3c-18973b690edd"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[35897, 1178, 166, 3, 44, "Input",ExpressionUUID->"2ff39867-da3e-49e9-b5b1-4faeec8bb712"],
|
||
|
|
Cell[36066, 1183, 304, 7, 53, "Output",ExpressionUUID->"918d0df8-f0ea-4482-b6c1-d0490b2e9e03"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[36407, 1195, 430, 11, 63, "Input",ExpressionUUID->"79150a3f-e969-4ea4-a555-11ed43cb27d5"],
|
||
|
|
Cell[36840, 1208, 363, 9, 53, "Output",ExpressionUUID->"4cddf14c-3fd4-4479-877b-f33c6449133a"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[37218, 1220, 152, 3, 30, InheritFromParent,ExpressionUUID->"829dd63b-df37-41f2-818d-389dda287f24"],
|
||
|
|
Cell[37373, 1225, 358, 9, 46, InheritFromParent,ExpressionUUID->"474f25a2-693b-4cc3-a116-b1a928826120"],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[37756, 1238, 149, 2, 30, "Input",ExpressionUUID->"9756bd99-6357-4bfd-aaf5-37127b6d5126"],
|
||
|
|
Cell[37908, 1242, 280, 7, 49, "Output",ExpressionUUID->"25c9b8f5-de55-4584-8dd9-3ee6961dd8e5"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[38203, 1252, 417, 11, 30, "Input",ExpressionUUID->"f60fb38a-06fc-4449-9c21-f14e0c9f761c"],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[38645, 1267, 176, 2, 30, "Input",ExpressionUUID->"892f139e-b128-4d75-9d0f-ca0298adebc2"],
|
||
|
|
Cell[38824, 1271, 500, 14, 50, "Output",ExpressionUUID->"c5a2c64e-5fba-4bee-90f3-c0e98b44df04"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[39361, 1290, 606, 16, 60, "Input",ExpressionUUID->"3e4a8fe0-6819-4b87-a519-232ea3b51545"],
|
||
|
|
Cell[39970, 1308, 572, 17, 76, "Output",ExpressionUUID->"6956331b-b249-4f9d-8471-45736fab4eac"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[40557, 1328, 152, 3, 30, InheritFromParent,ExpressionUUID->"6f6b949f-7c03-40f7-a8af-164288772a61"],
|
||
|
|
Cell[40712, 1333, 152, 3, 30, InheritFromParent,ExpressionUUID->"6f95b30f-8e7e-4c3c-9edb-c0c2b4a41f0f"],
|
||
|
|
Cell[40867, 1338, 146, 2, 30, "Input",ExpressionUUID->"31f726ef-b11a-43fa-a0bd-78319243b995"],
|
||
|
|
Cell[41016, 1342, 152, 3, 30, InheritFromParent,ExpressionUUID->"075dda5e-1741-4fb6-841b-cd4f4c3f6c4c"],
|
||
|
|
Cell[41171, 1347, 170, 2, 30, InheritFromParent,ExpressionUUID->"54f3896d-fc29-4562-b3bd-83138a9a95d3"],
|
||
|
|
Cell[41344, 1351, 144, 2, 30, "Input",ExpressionUUID->"7b25b87a-bb5b-4552-b86e-a7fdf416fc78"],
|
||
|
|
Cell[41491, 1355, 154, 3, 30, InheritFromParent,ExpressionUUID->"f276d2f7-d824-4833-a146-6874e5837562"],
|
||
|
|
Cell[41648, 1360, 152, 3, 30, InheritFromParent,ExpressionUUID->"287e5101-50ac-46c8-b1ac-053f0b80193d"],
|
||
|
|
Cell[41803, 1365, 146, 2, 30, "Input",ExpressionUUID->"d7c19fe8-d709-47fe-b14a-69639d1630e7"],
|
||
|
|
Cell[41952, 1369, 152, 3, 30, InheritFromParent,ExpressionUUID->"bceac606-4783-4ede-9655-7837c48724fc"],
|
||
|
|
Cell[42107, 1374, 144, 2, 30, "Input",ExpressionUUID->"74cb7dc2-1f86-4d44-9ced-4e06db03bd46"],
|
||
|
|
Cell[42254, 1378, 152, 3, 30, InheritFromParent,ExpressionUUID->"29d503e3-1e16-40fb-8e7a-4d05553df717"],
|
||
|
|
Cell[42409, 1383, 154, 3, 30, InheritFromParent,ExpressionUUID->"4ae8f227-ec57-4460-81d9-552986166846"],
|
||
|
|
Cell[42566, 1388, 146, 2, 30, "Input",ExpressionUUID->"e31755ea-4e51-4410-bac1-9b3c866c4aab"],
|
||
|
|
Cell[42715, 1392, 154, 3, 30, InheritFromParent,ExpressionUUID->"f1902e02-50fa-4a19-b8e7-a055bd2f71aa"],
|
||
|
|
Cell[42872, 1397, 193, 3, 52, InheritFromParent,ExpressionUUID->"c730a72e-1dc2-4b47-9a0e-9174b6670a3b"],
|
||
|
|
Cell[43068, 1402, 154, 3, 30, InheritFromParent,ExpressionUUID->"e85e937c-bbb4-4755-ab82-b8f8a21ad73c"],
|
||
|
|
Cell[43225, 1407, 175, 3, 30, "Input",ExpressionUUID->"af17a3a2-842e-4297-9dd8-04b760428994"],
|
||
|
|
Cell[43403, 1412, 149, 3, 30, InheritFromParent,ExpressionUUID->"3c85075c-b71e-4b67-88e1-cf3c34c9a315"],
|
||
|
|
Cell[43555, 1417, 152, 3, 30, InheritFromParent,ExpressionUUID->"65cbec44-ed62-4805-9ecd-6578b08381a0"]
|
||
|
|
}
|
||
|
|
]
|
||
|
|
*)
|
||
|
|
|