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Econ 102: Fall 2007
Discussion Section Handout #9 Answer Key
1.
Consumption Functions
We are given the following equations from the Keynesian Model, find the autonomous consumption
level, marginal propensity to consume (MPC) and marginal propensity to save (MPS).
Find the savings
function with respect to disposable income, and then use the given information about net taxes to find the
consumption and savings function with respect to real output.
If the consumption function with respect to
disposable income is not given, find that first!
Note
: Remember when we have the consumption function in the form C =
a
+
b
(Y – T) that autonomous
consumption is
a
and the marginal propensity to consume is
b
.
To solve for the consumption and savings functions with respect to real output rather than disposable
income we need to enter the value of net taxes.
The savings function with respect to disposable income is S = -
a
+ (1 –
b
) (Y – T)
(a)
C = 125 + 0.75(Y-T)
Net Taxes = 100
Autonomous Consumption Level
:
a
= 125
M
P
C
:
b
= 0.75
M
P
S
:
MPS = 1-MPC = 0.25
Savings Function w/ respect to DI
:
S = -
a
+ MPS(Y – T) = -125 + 0.25(Y – T)
Consumption Function w/ respect to Y
:
C = 125 + 0.75(Y – 100) = 50 + 0.75Y
Savings Function w/ respect to Y
:
S = -125 + 0.25(Y – 100) = -150 + 0.25Y
(b)
C = 0.80(300-T+Y)
Net Taxes = 50
=
240 – 0.8(T – Y) = 240 + 0.8(Y – T)
Autonomous Consumption Level
:
a
= 240
M
P
C
:
b
= 0.8
M
P
S
:
MPS = 1-MPC = 0.2
Savings Function w/ respect to DI

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