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PS 2 – Tools: Data and Maths (60 raw points)
ECON 402, Prof. Bachmann
Due: January 27
Explain all your answers. “Results only” means partial credit only. Staple and write legibly. No spiral stuff.
The numbers in brackets are the subdivision of raw points for each question.
I)
Loci (20 raw points)
In this problem you will encounter loci again. It will result in a useful mnemonic for drawing graphs
in an exam, when you are under time pressure. Here you will derive that mnemonic.
In class, we looked at the following expression:
F(x, y)=0
(you can ignore z for this exercise). The
partial derivative of
F
with respect to
x
was positive and with respect to
y
it was negative. This led to
an upward sloping graph in
(x,y)
space (
x
being on the
x
axis and
y
being on the
y
axis) for all
(x,y)
combinations such that
F(x, y)=0.
Now, what happens to this graph, if the signs of the partial
derivatives change? This is the task ahead:
1)
Assume now that the partial derivatives of
F
with respect to both
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