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Notebook[{
Cell["\<\
Mathematica Problem Set 2
\
\>", "Title",
CellFrame->True,
TextAlignment->Center,
ImageRegion->{{0, 1}, {0, 1}}],
Cell["\<\
Use Mathematica to solve the following problems:
\
\>", "Text",
ImageRegion->{{0, 1}, {0, 1}}],
Cell["\<\
\
\>", "Input",
PageWidth->Infinity,
ImageRegion->{{0, 1}, {0, 1}}],
Cell["\<\
A firm produces output Q using labor, L, and capital, K. Its production \
function is:
Q = 10 L^.6 K^.4
\
\>", "Text",
ImageRegion->{{0, 1}, {0, 1}},
Background->GrayLevel[1]],
Cell["\<\
1. Plot the production function in 3 dimensions with Q on the vertical axis. \
Set the range on L from 0 to 15 and the range on K from 0 to 1000.
\
\>", "Text",
ImageRegion->{{0, 1}, {0, 1}}],
Cell[CellGroupData[{Cell["\<\
Clear[f,L,K]
f[L_,K_] = 10 L^(.6) K^(.4)
Plot3D[f[L,K], {L, 0, 15}, {K, 0, 1000},
AxesLabel->{\"Labor\",\" Capital\",\"\"},
PlotLabel->\"Total Product\"];
\
\>", "Input",
PageWidth->Infinity,
ImageRegion->{{0, 1}, {0, 1}}],
Cell[OutputFormData["\<\
10*K^0.4*L^0.6
\
\>", "\<\
0.4 0.6
10 K L
\
\>"], "Output",
PageWidth->Infinity,
ImageRegion->{{0, 1}, {0, 1}}],
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9) Suppose this is a monopoly firm facing the demand curve:
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10) Add the marginal cost and average cost curves to your diagram in question \
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The profit maximizing output is 411.056 and the monopoly profits are 157.139.
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11.) Determine the price and output if this were a competitive industry.
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12.) Determine the deadweight loss of this monopoly.
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