(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 13.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 137000, 2985] NotebookOptionsPosition[ 130217, 2875] NotebookOutlinePosition[ 130662, 2892] CellTagsIndexPosition[ 130619, 2889] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell["\<\ This Mathematica notebook shows examples of how I make (most) graphs for the \ Intermediate Microeconomics class. If you have never used Mathematica, read at least these first: https://www.wolfram.com/language/fast-introduction-for-math-students/en/\ entering-input https://www.wolfram.com/language/fast-introduction-for-math-students/en/\ notebook-documents \ \>", "Text", CellChangeTimes->{{3.872825236719105*^9, 3.8728252665586176`*^9}, { 3.8728253037959547`*^9, 3.8728254884510593`*^9}, {3.8728263888662004`*^9, 3.87282639696239*^9}},ExpressionUUID->"179aed23-25f8-4e2d-809f-\ c8f5110a10cd"], Cell["\<\ Aalto students can install Mathematica by following the instructions here https://download.aalto.fi A free version is also available for everyone with a Raspberry Pi \ https://en.wikipedia.org/wiki/Raspberry_Pi \ \>", "Text", CellChangeTimes->{{3.87282607340895*^9, 3.8728261142597017`*^9}, { 3.87282614947171*^9, 3.8728261505170746`*^9}, {3.872826238507683*^9, 3.872826270908047*^9}, {3.872826333958333*^9, 3.8728263367396927`*^9}, { 3.872826380700965*^9, 3.8728264032710247`*^9}, {3.8728279323512373`*^9, 3.8728279420578127`*^9}},ExpressionUUID->"d79adcc4-0951-47b6-8c0e-\ d3a85d4c5129"], Cell["Marko Tervi\[ODoubleDot] 2022-09-23", "Text", CellChangeTimes->{{3.8728290287598944`*^9, 3.8728290752804756`*^9}},ExpressionUUID->"db39fc0d-2a85-4224-899a-\ ea6c9d8f5754"], Cell[CellGroupData[{ Cell["Example: Making graphs for PS 2.3", "Subsection", CellChangeTimes->{{3.872762060811226*^9, 3.872762072550612*^9}, 3.87276226639566*^9, {3.872823674972947*^9, 3.8728236864919987`*^9}, { 3.8728254453553815`*^9, 3.8728254455113544`*^9}, {3.8728255569672537`*^9, 3.872825561425738*^9}, {3.872827158039962*^9, 3.8728271692732573`*^9}},ExpressionUUID->"78bf84e0-f34e-40f1-bf9b-\ f26c46566698"], Cell["\<\ Recall problem 2.3 (Northland Transport). Let\[CloseCurlyQuote]s turn the assumptions of that problem into definitions.\ \>", "Text", CellChangeTimes->{{3.8727621434979424`*^9, 3.872762197390807*^9}, 3.8728235455993395`*^9, 3.872823621779043*^9, {3.872825567976515*^9, 3.872825573240431*^9}, {3.872827963968339*^9, 3.8728279896921887`*^9}},ExpressionUUID->"382246be-8fcb-4a44-bee2-\ 64bb5b5737e8"], Cell[BoxData[{ RowBox[{ RowBox[{"fc", "=", "7200"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"mc", "=", "20"}], ";", " ", RowBox[{"(*", " ", RowBox[{ RowBox[{"semicolon", " ", "suppresses", " ", "output"}], ",", " ", RowBox[{"but", " ", "is", " ", "not", " ", "required"}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"TC", "[", "q_", "]"}], ":=", RowBox[{"fc", "+", RowBox[{"mc", " ", "q"}]}]}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Pd", "[", "q_", "]"}], ":=", RowBox[{"200", "-", "q"}]}]}], "Input", CellChangeTimes->{{3.872762199737031*^9, 3.8727622291046705`*^9}, { 3.872823112095394*^9, 3.872823125418682*^9}, {3.872828801440894*^9, 3.872828869166326*^9}, {3.8728297763144817`*^9, 3.8728297884550533`*^9}}, CellLabel->"In[6]:=",ExpressionUUID->"f2decf6e-125d-46e2-84dd-a24e3a207efe"], Cell["Take a derivative of revenue to get marginal revenue ", "Text", CellChangeTimes->{{3.872762327813348*^9, 3.8727623593755093`*^9}, 3.872823780335037*^9, {3.8728242535736876`*^9, 3.8728242660248747`*^9}},ExpressionUUID->"23857732-8f78-4842-b0b4-\ 34e3e95dbac0"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"MR", "[", "q_", "]"}], "=", RowBox[{"D", "[", RowBox[{ RowBox[{ RowBox[{"Pd", "[", "q", "]"}], "q"}], ",", "q"}], "]"}]}]], "Input", CellChangeTimes->{{3.8727622855814853`*^9, 3.872762319889802*^9}, { 3.8727623617171807`*^9, 3.872762374122941*^9}, 3.8728237763416963`*^9}, CellLabel->"In[9]:=",ExpressionUUID->"b252bdb9-db47-47ed-b15a-e8f173cedf9e"], Cell[BoxData[ RowBox[{"200", "-", RowBox[{"2", " ", "q"}]}]], "Output", CellChangeTimes->{3.8728335696396284`*^9, 3.872833606308199*^9}, CellLabel->"Out[9]=",ExpressionUUID->"9c8098d1-d6d1-43a5-9bd9-f6fb5ebbd8f1"] }, Open ]], Cell["Profit-maximization must satisfy MR=MC", "Text", CellChangeTimes->{{3.8728236585457582`*^9, 3.8728236616244783`*^9}, { 3.872823790057185*^9, 3.8728237906196985`*^9}, {3.872824272093216*^9, 3.872824277177844*^9}, {3.8728280156381564`*^9, 3.872828020207486*^9}, { 3.8728302701848717`*^9, 3.872830326074075*^9}},ExpressionUUID->"0c0372f9-e134-4656-9284-\ 997e3074475b"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{"MR", "[", "q", "]"}], "==", "mc"}], ",", "q"}], "]"}], "\[IndentingNewLine]", RowBox[{"qM", "=", RowBox[{"q", "/.", RowBox[{"%", "[", RowBox[{"[", "1", "]"}], "]"}]}]}], "\[IndentingNewLine]", RowBox[{"pM", "=", RowBox[{"Pd", "[", "qM", "]"}]}]}], "Input", CellChangeTimes->{{3.8727623791345067`*^9, 3.8727623894451666`*^9}, { 3.8727625149266706`*^9, 3.8727625353764815`*^9}, 3.8727633018952847`*^9, { 3.8728237851039505`*^9, 3.8728237854786673`*^9}, {3.872828026116166*^9, 3.872828026502448*^9}}, CellLabel->"In[10]:=",ExpressionUUID->"ae319014-052d-4366-8b43-3af49fce56f6"], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{"q", "\[Rule]", "90"}], "}"}], "}"}]], "Output", CellChangeTimes->{ 3.872762389726464*^9, {3.872762517613849*^9, 3.8727625361261597`*^9}, 3.8727633024105425`*^9, {3.872823121525695*^9, 3.8728231283817863`*^9}, 3.872823792663166*^9, 3.8728242790054193`*^9, {3.8728249813758373`*^9, 3.8728250085438614`*^9}, 3.8728277525694633`*^9, 3.8728280535088444`*^9, 3.872833607432008*^9}, CellLabel->"Out[10]=",ExpressionUUID->"08410ac8-a8ff-49f4-8de5-6ab91b552211"], Cell[BoxData["90"], "Output", CellChangeTimes->{ 3.872762389726464*^9, {3.872762517613849*^9, 3.8727625361261597`*^9}, 3.8727633024105425`*^9, {3.872823121525695*^9, 3.8728231283817863`*^9}, 3.872823792663166*^9, 3.8728242790054193`*^9, {3.8728249813758373`*^9, 3.8728250085438614`*^9}, 3.8728277525694633`*^9, 3.8728280535088444`*^9, 3.872833607437989*^9}, CellLabel->"Out[11]=",ExpressionUUID->"f72cd77d-cdcf-4c68-83ca-96c1db250b38"], Cell[BoxData["110"], "Output", CellChangeTimes->{ 3.872762389726464*^9, {3.872762517613849*^9, 3.8727625361261597`*^9}, 3.8727633024105425`*^9, {3.872823121525695*^9, 3.8728231283817863`*^9}, 3.872823792663166*^9, 3.8728242790054193`*^9, {3.8728249813758373`*^9, 3.8728250085438614`*^9}, 3.8728277525694633`*^9, 3.8728280535088444`*^9, 3.872833607441988*^9}, CellLabel->"Out[12]=",ExpressionUUID->"e124fa35-578b-4fc4-ad1b-c45042f60568"] }, Open ]], Cell[TextData[{ StyleBox["Solve", FontSlant->"Italic"], " gives a list of solutions, even when there is just one. Solutions are \ \[OpenCurlyDoubleQuote]rules\[CloseCurlyDoubleQuote] like q\[Rule]90. Notice \ that double equality == defines an equation that may be solved, whereas a \ single equality = would define a value for the left hand side (as I did \ earlier with mc=20)" }], "Text", CellChangeTimes->{{3.87276243636187*^9, 3.872762479987544*^9}, { 3.872826640193591*^9, 3.8728266605851955`*^9}, {3.872828644063322*^9, 3.872828761115117*^9}, {3.8728291675535817`*^9, 3.8728291681160955`*^9}},ExpressionUUID->"59c29036-3105-4ed2-82ec-\ c12e68ef3d72"], Cell[TextData[{ "% refers to previous output\n[[1]] refers to first element of a list\n", StyleBox["q", FontSlant->"Italic"], "/.(rule) extracts the value of ", StyleBox["q", FontSlant->"Italic"], " as defined by the (rule)" }], "Text", CellChangeTimes->{{3.8727624162428246`*^9, 3.8727624271850443`*^9}, { 3.8727624820313363`*^9, 3.8727625078048124`*^9}, {3.872762606760173*^9, 3.872762692281274*^9}, {3.872826711957924*^9, 3.8728267396228485`*^9}},ExpressionUUID->"dff51707-2792-4290-8927-\ 44c0aa18ad5c"], Cell["Calculate maximized profits and resulting CS", "Text", CellChangeTimes->{{3.8728244513547134`*^9, 3.8728244629919877`*^9}},ExpressionUUID->"2296675f-f6bb-4126-b540-\ 5b390eb14fef"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"pM", " ", "qM"}], " ", "-", RowBox[{"TC", "[", "qM", "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"Pd", "[", "0", "]"}], "-", "pM"}], ")"}], RowBox[{"qM", "/", "2"}]}]}], "Input", CellChangeTimes->{{3.872762684901849*^9, 3.8727627505838127`*^9}, { 3.872763306145141*^9, 3.872763324066676*^9}, {3.872828023189509*^9, 3.8728280237895317`*^9}, 3.8728294668155994`*^9}, CellLabel->"In[13]:=",ExpressionUUID->"cc694f68-fdf5-4561-8b57-e9a868f142f2"], Cell[BoxData["900"], "Output", CellChangeTimes->{{3.8727626898921556`*^9, 3.8727627146321917`*^9}, 3.8727627508337774`*^9, 3.872763324566352*^9, 3.872823129621919*^9, 3.872823795007007*^9, 3.8728242805610614`*^9, 3.872825009785103*^9, 3.872827754609816*^9, 3.8728280561662397`*^9, 3.8728336089798317`*^9}, CellLabel->"Out[13]=",ExpressionUUID->"98f77839-0101-4788-b776-0df46c187adc"], Cell[BoxData["4050"], "Output", CellChangeTimes->{{3.8727626898921556`*^9, 3.8727627146321917`*^9}, 3.8727627508337774`*^9, 3.872763324566352*^9, 3.872823129621919*^9, 3.872823795007007*^9, 3.8728242805610614`*^9, 3.872825009785103*^9, 3.872827754609816*^9, 3.8728280561662397`*^9, 3.8728336089848275`*^9}, CellLabel->"Out[14]=",ExpressionUUID->"63e5f85a-76f1-496a-ad2b-ade42d230694"] }, Open ]], Cell["More generally, CS is defined as", "Text", CellChangeTimes->{{3.8728268228872995`*^9, 3.872826858786087*^9}, 3.872827880231986*^9},ExpressionUUID->"651558b8-c0d1-4d58-a780-\ 1b412191e6f9"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"Pd", "[", "q", "]"}], "-", "pM"}], ",", RowBox[{"{", RowBox[{"q", ",", "0", ",", "qM"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.872826787654708*^9, 3.8728268078272147`*^9}, { 3.872826841872566*^9, 3.872826843458438*^9}}, CellLabel->"In[15]:=",ExpressionUUID->"21be6403-5634-4589-9907-b2a712e1bbba"], Cell[BoxData["4050"], "Output", CellChangeTimes->{3.872826809168764*^9, 3.8728268619571424`*^9, 3.87282775600177*^9, 3.872828058221467*^9, 3.8728336103727307`*^9}, CellLabel->"Out[15]=",ExpressionUUID->"fc49bbc1-8446-46c8-a125-0349e1f45080"] }, Open ]], Cell["Let' s graph Marginal Cost, Demand, and Marginal Revenue", "Text", CellChangeTimes->{{3.872763064141282*^9, 3.872763085220072*^9}, { 3.8728271181256785`*^9, 3.872827125116975*^9}},ExpressionUUID->"479f29a9-45ae-4da6-91f2-\ 15edce2945f9"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{"mc", ",", RowBox[{"Pd", "[", "q", "]"}], ",", RowBox[{"MR", "[", "q", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"q", ",", "0", ",", "200"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{ 3.87276305662582*^9, {3.8728237989773293`*^9, 3.8728237992806945`*^9}}, 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\"TR\"]}], \"]\"}]\) plots \!\(\*SubscriptBox[StyleBox[\"f\", \ \"TI\"], StyleBox[\"i\", \"TI\"]]\) with features defined by the symbolic \ wrapper \!\(\*StyleBox[\"w\", \"TI\"]\).\n\!\(\*RowBox[{\"Plot\", \"[\", \ RowBox[{StyleBox[\"\[Ellipsis]\", \"TR\"], \",\", RowBox[{RowBox[{\"{\", \ StyleBox[\"x\", \"TI\"], \"}\"}], \"\[Element]\", StyleBox[\"reg\", \ \"TI\"]}]}], \"]\"}]\) takes the variable \!\(\*StyleBox[\"x\", \"TI\"]\) to \ be in the geometric region \!\(\*StyleBox[\"reg\", \"TI\"]\).", "Documentation" -> <| "Web" -> "http://reference.wolfram.com/language/ref/Plot.html"|>, "OwnValues" -> None, "UpValues" -> None, "DownValues" -> None, "SubValues" -> None, "DefaultValues" -> None, "NValues" -> None, "FormatValues" -> None, "Options" -> { AlignmentPoint -> Center, AspectRatio -> GoldenRatio^(-1), Axes -> True, AxesLabel -> None, AxesOrigin -> Automatic, AxesStyle -> {}, Background -> None, BaselinePosition -> Automatic, BaseStyle -> Directive[FontFamily -> "Palatino Linotype", 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PlotLegends -> None, PlotPoints -> Automatic, PlotRange -> {Full, Automatic}, PlotRangeClipping -> True, PlotRangePadding -> Automatic, PlotRegion -> Automatic, PlotStyle -> Automatic, PlotTheme :> $PlotTheme, PreserveImageOptions -> Automatic, Prolog -> {}, RegionFunction -> (True& ), RotateLabel -> True, ScalingFunctions -> None, TargetUnits -> Automatic, Ticks -> Automatic, TicksStyle -> {}, WorkingPrecision -> MachinePrecision}, "Attributes" -> {HoldAll, Protected, ReadProtected}, "FullName" -> "System`Plot"|>, False]]], "Output", CellChangeTimes->{3.872762939503683*^9, 3.8728243500376806`*^9, 3.8728277641176124`*^9, 3.8728280629309597`*^9, 3.8728336203080654`*^9}, CellLabel->"Out[18]=",ExpressionUUID->"a211dd91-f442-4364-8001-66444ce427f0"] }, Open ]], Cell["Let' s define some regions to highlight in the graph", "Text", CellChangeTimes->{{3.8728243579684544`*^9, 3.8728243748177114`*^9}, { 3.8728269157537313`*^9, 3.872826916644658*^9}},ExpressionUUID->"186071c0-e21f-4cba-b5ef-\ 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