Simplified Consumption And Investment Functions

For the following problems, SHOW YOUR WORK and round to one decimal point. If you struggle with the math, still try to intuitively and graphically answer
C
and
D
. Consider an economy with the following data:
C(Y−T)=125+0.75(Y−T)
I=2
O0−10r
G is the level of government purchases, T=100
M
s
=800 and the price level is P
M
D
=P(0.8Y−16(r+π
r
)) Simplified Consumption And Investment Functions

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Please note the simplified consumption and investment functions (ignoring wealth and
r
effect on
C
, and
Y
effect on I). Note also that the initial price level and government purchases are some constant
P
and
G
, respectively and assume expected inflation
=NX=0
. Let the full employment level of output
=1,600
. A) Construct the IS curve, simplifying the expression as much as possible, solving for
Y
. B) The LM curve can be represented as
Y=20r+1000/P
. Let
G=250
and
P=1
. Solve for the short run equilibrium level of
r Simplified Consumption And Investment Functions

and
Y

. C) Use the space below to illustrate your short run equilibrium in B), including your numerical answers where possible on your diagram, including an accurate label for
Y
10T

. Calculate the
r
that will adjust over time to the long run equilibrium in this economy. D) Explain briefly how the LR adjustment result in changes to the IS and/or LM curves, and how
P
and
Y
and its components,
C
and
I
, are expected to change over time. Simplified Consumption And Investment Functions