Finding Y*
and Constructing Multipliers
Lecture 12
Dr. Jennifer P. Wissink
©2015 Jennifer P. Wissink, all rights reserved.
October 1, 2015
More Interesting Reads/Listens

Salon interviews the late Adam Smith
– The 18th century's patron saint of free markets
shares his surprising views about Barack Obama
and the U.S. economy
– http://www.salon.com/2009/10/06/adam_smith/singl
eton/
– THANKS MANU R!

Fear the Boom and Bust
– A Hayek vs. Keynes Rap Anthem
– http://www.youtube.com/watch?v=d0nERTFo-Sk
i>clicker question
HeavenLand is a country that is so nice that nearly all of its working citizenry stay in the
country and work in HeavenLand’s economy. In addition, since HeavenLand is so nice there
are a huge number of foreign citizens working in HeavenLand. Which one of the following
statements is most likely to be TRUE?
A.
B.
C.
D.
E.
Heavenland's G.N.P. will be greater than its G.D.P.
Heavenland's G.D.P. will be greater than its G.N.P.
Heavenland's G.N.P. and G.D.P. will be equal.
Heavenland's G.D.P. will tend to be equal to its disposal national income.
Heavenland's trade balance will be equal to zero.
Which one of the following individuals is considered unemployed according to the way the U.S.
calculates their official unemployment statistics?
A. John, who works without pay for 30 hours per week in the family owned tax accounting business.
B. Jill, who works 2 hours a week at Walmart as a greeter.
C. Rose, who is currently a full time student at Cornell and working 60 hours a week on her studies
to please her mom.
D. Leyton, a former NFL football player just released from his contract who is now actively searching
for some other job while taking a night class at TC3 (the local community college). His resume
states, “Put me in coach, I’m ready to play!”
E. A female with a Ph.D. in physics who decides to stay home and take care of her children after
graduation.
HHs: Consumption Function Concepts

the subsistence level of
consumption

the breakeven point
– dis-saving and saving

the marginal propensity to
consume (MPC)

the average propensity to
consume (APC)
HHs: Saving Function

From consumption to saving
Recall: C+S=Y, so… S = Y-C
Like a see-saw

Marginal Propensity to save

Average propensity to save

Note it will always be the
case that:


– MPC + MPS=1
– APC + APS=1
A LINEAR Aggregate Consumption Function
Derived from the Equation C = 100 + .75Y
AGGREGATE
INCOME, Y
(BILLIONS OF
DOLLARS)
AGGREGATE
CONSUMPTION, C
(BILLIONS OF
DOLLARS)
0
100
80
160
100
175
200
250
400
400
600
550
800
700
1,000
850
Deriving a Saving Function
C  100 .75Y
from a Consumption Function S  Y  C
S  100.25Y
Y
-
C
=
AGGREGATE AGGREGATE
INCOME
CONSUMPTION
(Billions of
(Billions of
Dollars)
Dollars)
S
AGGREGATE
SAVING
(Billions of
Dollars)
0
100
-100
80
160
-80
100
175
-75
200
250
-50
400
400
0
600
550
50
800
700
100
1,000
850
150
Firms: The Desired Investment Function

Desired Investment might depend on:
–
–
–
–
–
–
–
Aggregate Output(Income): Y
expected rate of return
interest rates
technological state of world
business expectations
animal spirits?
attitudes?

We will make this part of our model very simplistic for a
while...

Note: Keynes’ understanding/modeling of investment was so-so
The Desired/Planned Investment Function




For now, we assume that
desired/planned
investment does not
change when income (Y)
changes.
It is said to be an
autonomous variable.
a.k.a. exogenous
NOTE:
– Define MPI
– So..., marginal propensity
to invest = 0
Actual versus Planned Investment

Desired or planned investment refers to the
additions to capital stock and inventory that
are desired or planned by firms.
 Actual
investment is the actual amount of
investment that takes place; it includes items
such as unplanned changes in inventories.
Aggregate Desired Expenditure (AEd) for our
Simple Linear Frugal Economy
AE  C (Y )  I
d
d
Equilibrium Y*

Aggregate output/income ≡ Y
Aggregate desired expenditure =AEd(Y) = C(Y) + Id
Equilibrium Y* where: Y = AEd(Y), or Y* = C (Y*) + Id

SUPPOSE: Y > [C(Y) + Id]


–
–
–
–

Actual aggregate output/income > aggregate desired expenditure
So inventory investment is greater than planned
So actual investment is greater than planned investment
So something will change!
SUPPOSE [C(Y) + Id] > Y
–
–
–
–
Aggregate desired expenditure > actual aggregate output/income
So inventory investment is smaller than planned
So actual investment is less than planned investment
So something will change!
Equilibrium Y* - Graphically
Equilibrium Y* - Algebraically
AE d  C  I d
C  100 .75Y
I  25
d
By substituting (C) and
(Id) into (AEd) we get:
AE
d
 100.75Y  25
Now impose the
equilibrium condition that
Y* = AEd(Y*).
Y *  100 .75Y *  25
There is only one value of Y*
for which this statement is
true. We can find it by
rearranging terms:
Y *  .75Y *  100  25
Y *  .75Y *  125
.25Y *  125
125
Y* 
 500
.25
Equilibrium Y*- Using A Chart
C  100 .75Y I d  25
(1)
(2)
(3)
(4)
(5)
(6)
UNPLANNED
INVENTORY
CHANGE
Y  (C + I)
EQUILIBRIUM?
(Y = AE?)
AGGREGATE
OUTPUT
(INCOME) (Y)
AGGREGATE
CONSUMPTION (C)
PLANNED
INVESTMENT (I)
PLANNED
AGGREGATE
EXPENDITURE (AE)
C+I
100
175
25
200
 100
No
200
250
25
275
 75
No
400
400
25
425
 25
No
500
475
25
500
0
Yes
600
550
25
575
+ 25
No
800
700
25
725
+ 75
No
1,000
850
25
875
+ 125
No
The Saving & Investment
Approach to Equilibrium Y*


An alternative approach that some like better.
In a frugal economy we have:
– HH saving going out as a leakage
– Firm investment coming in as an injection

Recall:
– In the frugal economy, AEd = C + Id
– In equilibrium, Y = AEd
– We also know that HHs allocate aggregate output/income to
either saving or consumption: Y = C + S
– So… by substitution, at Y*, C + S = C + Id  at Y*, S = Id
So...
if Saving = Planned/Desired Investment
 we are at an equilibrium Y*
Equilibrium Y*- Using A Chart
C  100 .75Y I d  25
(1)
AGGREGATE
OUTPUT
(INCOME) (Y)
(2)
(3)
AGGREGATE
PLANNED
CONSUMPTION (C) INVESTMENT (Id)
(4)
(5)
PLANNED
UNPLANNED
AGGREGATE
INVENTORY
d
EXPENDITURE (AE )
CHANGE
C + Id
Y  (C + Id)
(6)
EQUILIBRIUM?
(Y = AEd?)
100
175 (S= -75)
25
200
 100
No
200
250 (S= -50)
25
275
 75
No
400
400 (S=0)
25
425
 25
No
500
475 (S=25)
25
500
0
Yes
600
550 (S=50)
25
575
+ 25
No
800
700 (S=100)
25
725
+ 75
No
1,000
850 (S=150)
25
875
+ 125
No
The S = Id Approach to Equilibrium Y*
i>clicker question
Suppose we are in equilibrium at Y*.
Suppose we have an exogenous increase in Id.
Suppose Id increases from $25 to $30.
Y* will...
A.
B.
C.
D.
E.
stay the same.
increase by $5.
decrease by $5.
increase by more than $5.
decrease by less than $5.