Transcript Aggregate Supply and Demand

Polonious
Agents are
producing and
consuming the
same in each
period
y2=c2
y1=c1
Next consider a rise in r.
Polonious
What happens to
Consumption as
the interest rate
rises?
y2=c2
y1=c1
Polonious
This is due solely to
the pure substitution
effect as there is no
income effect
y2=c2
y1=c1
Here c1 falls while c2 rises
Polonious
So now c1 < y1 (saving)
and
c2 < y2 (using savings)
y2=c2
y1=c1
Here c1 falls while c2 rises
Overall effect
Period 1 : c1
Substitution
Effect
Income Effect
Overall
Period 2 : c2
Overall effect
Substitution
Effect
Income Effect
Overall
Period 1 : c1
Period 2 : c2
Down
Up
Overall effect
Period 1 : c1
Period 2 : c2
Substitution
Effect
Down
Up
Income Effect
None
None
Overall
Overall effect
Period 1 : c1
Period 2 : c2
Substitution
Effect
Down
Up
Income Effect
None
None
Overall
Down
Up
What about the economy as a
whole?
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Is it a borrower?
Is it a lender?
Or a Polonius?
What about the economy as a
whole?
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On aggregate there must be a lender for
every borrower and visa versa.

=> No borrowing or lending in the
aggregate
so if interests rate rise on aggregate
=> C2 ↑ and C1 ↓ for the economy as a
whole
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So as r goes Up, c1 goes Down.
This is our first key demand relationship
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So as r goes Up, c1 goes Down.
This is our first key demand relationship
…and we can represent
it in the usual way with
price (r) on one axis and
demand on other


So as r goes Up, c1 goes Down.
This is our first key demand relationship
r
…and we can represent
it in the usual way with
price (r) on one axis and
demand on other
c1


So as r goes Up, c1 goes Down.
This is our first key demand relationship
r
Aggregate Consumption
Function Slopes down
cd(r)
c1


Note here we are implicitly solving the
problem:
Maximize U ( (1) (2)

Subject to
C2
Y2
C1 
  Y1 
1 r
1 r
So in this problem we have one constraint
covering consumption and earnings in the 2
periods
That is, this is a 2-period budget constraint.
EXERCISE

Write
C2
Y2
C1 
 Y1 
1 r
1 r
As two one-period budget constraints
that is,
Show how period 1’s consumption,
borrowing & lending and money holdings
depend on income in period 1, past
borrowing & lending and last period’s money
holdings.
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Ref: P67 – 70 Barro & Grilli
(for classes next week)
That ends Problem 2.
C1 v C2
Consumption now versus consumption
later
U(c1,l1)+ U(c2,l2)
Problem 3: Work Now or Later
U(c1,l1)+

U(c2,l2)
What about the choice between
work now versus work later?
Problem 3: Work Now or Later

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L1 v L2
What do the indifference curves look
like?
To see this lets look at something we
like
leisure now and leisure later.
Leisure in period 2
I5
I4
I1
O
Leisure in period 1
I2
I3
Leisure in period 2
24 Hours
I5
I4
I3
I2
I1
O
Leisure in period 1
24 Hours
24 Hours
Leisure in period 2
Work
in 2
I5
I4
I3
I2
I1
O
Leisure in period 1
Work in 1
24 Hours
24 Hours
Work in 1
O
Work
in 2
Leisure in period 2
O
Leisure in period 1
Work
Origin
Work
in 2
I5
I4
I3
I
I21
Work in 1
24 Hours
Leisure in period 1
I5
I4
I3
I
I21
O
Work
Origin
O
Leisure in period 2
Work
in 2
Work in 1
Leisure in period 1
O
I5
I4
I3
I
I21
Work
in 2
O
Work
Origin
Work in 1
Leisure in period 1
Utility
Increase as
work falls
Work
in 2
O
Work
Origin
Work in 1
What is the budget constrain in
this instant.
Recall in the problem where we
considered c1 v c2 we effectively held
y1and y2 constant and agents picked
their optimal consumption.
In this problem we assume we have
some consumption target we wish to
meet and we select when to work to
achieve it (y1, y2)
Choose y1,y2 with c1,c2 fixed
y2
c2
y1 
 c1 
1 r
1 r
But to get y we must work (L) for wage w
wL2
C2
wL11 
 C1 
1 r
1 r
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Choosing L1, L2
Given C1, C2, w and r
Work
in 2
Budget
Constraint
Slope = – (1+r)
L2
O
L
Work in 1
Work
in 2
Suppose now
that the interest
rate rises
L2
O
L
Work in 1
Work
in 2
So L1 goes up
and L2 falls
L2
O
L
Work in 1
Overall effect of rise in r on
aggregate L
Period 1 : l1
Substitution
Effect
Income Effect
Overall
Period 2 : l2
Overall effect of rise in r on
aggregate L
Substitution
Effect
Income Effect
Overall
Period 1 : l1
Period 2 : l2
Up
Down
Overall effect of rise in r on
aggregate L
Period 1 : l1
Period 2 : l2
Substitution
Effect
Up
Down
Income Effect
None on Agg.
None on Agg
Overall
Overall effect of rise in r on
aggregate L
Period 1 : l1
Period 2 : l2
Substitution
Effect
Up
Down
Income Effect
None on Agg.
None on Agg
Up
Down
Overall
So if the interest rises L1 rises
But increase in L1
means an increase
in output, y
So if the interest rises L1 rises
But increase in L1
means an increase
in output, y
y2
y1
L1
L2

So now, have relationship between
willingness to Supply and interest rate
We can graph this
supply relationship
in the usual way
with price (r) on one
axis and quantity on
the other

So now, have relationship between
willingness to Supply and interest rate
r
We can graph this
supply relationship
in the usual way
with price (r) on one
axis and quantity on
the other
y

So now, have relationship between
willingness to Supply and interest rate
r
ys=f (L(r))
y

r ↑ => Ls ↑ => ys ↑
• or ys = f (L( r ))
dys
and
0
dr
Macroeconomic Equilibrium
r
We now combine the demand and
supply curve we have derived
from our microeconomics
analysis to find the
equilibrium in the economy
Y
Macroeconomic Equilibrium
ys
r
re
yD=cD
ye
Y
Interested
in how shocks to the production
function effect the equilibrium level of output, ye,
and rate of interest, re.
ys
r
re
yD=cD
ye
Y
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But as with the stylised facts we are also
interested in
change in consumption
change in hours worked
And in more complex model change in
investment etc etc ( but we do not have
investment in the model as yet)
1st Case: Permanent Shock to the
production function

Eg: 1 Economics Growth: y ↑ forever.
So the production function shifts UP permanently
y
Y1=f1(L)
Y=F(L)
L
E.g. 2: Permanent Change in Exogenous
Input Price
y=f(L)
Y
Note when we write y = f(L)
we are holding all other
things constant
eg. K stock, other inputs
L
E.g. 2: Permanent Change in Exogenous
Input Price
So y = f(L,.. …. )
Y
L
E.g. 2: Permanent Change in Exogenous
Input Price
Suppose y = f(L, k,oil,..)
y=f(L)
Y
y1=f1(L)
And price of oil
rises permanently
(1973)
So the production
function shifts down
permanently
L
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Let us study the positive permanent shock
first.
Positive Shock: Production function moves up
y
Y=f(L)
c0= y0
Lo
L
Positive Shock: Production function moves up
 Know: y ↑ c ↑
 Unsure: L:
income effect ↓
 Substitute effect ( MPL ↓?) Net effect = ?
y1=f1(L)
y
y=f(L)
c0=y0
Lo
L
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Positive Shock: Production function moves
up.
Know: y ↑ c ↑
Unsure: L: income effect ↓
Substitute effect = MPL ↓
Net effect = ?
|So output definitely rises
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Thus, the aggregate supply curve moves
out
s
r
y
ys
y

THE END