Polonious Next consider a rise in r. y 2 =c 2 Agents are producing and consuming the same in each...
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Transcript of Polonious Next consider a rise in r. y 2 =c 2 Agents are producing and consuming the same in each...
Polonious
Next consider a rise in r.
y2=c2
Agents are producing and consuming the same in each period
y1=c1
Polonious
y1=c1
What happens to Consumption as the interest rate rises?y2=c2
Polonious
y1=c1
y2=c2
Here c1 falls while c2 rises
This is due solely to the pure substitution effect as there is no income effect
Polonious
y1=c1
y2=c2
Here c1 falls while c2 rises
So now c1 < y1 (saving) and c2 < y2 (using savings)
Overall effect
Period 1 : c1 Period 2 : c2
Substitution Effect
Income Effect
Overall
Overall effect
Period 1 : c1 Period 2 : c2
Substitution Effect
Down Up
Income Effect
Overall
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?
Is it a borrower? Is it a lender? Or a Polonius?
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
What about the economy as a whole?
So as r goes Up, c1 goes Down.
This is our first key demand relationship
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
c1
r …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
c1
r
cd(r)
Aggregate Consumption Function Slopes down
Note here we are implicitly solving the problem: Maximize U ( (1) (2)
Subject to
r
YY
r
CC
112
12
1
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
r
YY
r
CC
112
12
1
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.
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
What about the choice between work now versus work later?
U(c1,l1)+ U(c2,l2)
Problem 3: Work Now or Later
L1 v L2
What do the indifference curves look like?
To see this lets look at something we like
leisure now and leisure later.
fig
I1I2I3I4
I5
Leis
ure
in p
erio
d 2
O
Leisure in period 1
fig
I1I2I3
I4
I5
Lei
sure
in p
erio
d 2
O
Leisure in period 1 24 Hours
24 Hours
fig
I1I2I3
I4
I5
Lei
sure
in p
erio
d 2
O Leisure in period 124 Hours
24 Hours
Work in 1
Work in 2
fig
I1I2I3
I4
I5
Leisure
in p
eriod 2
OLeisure in period 124 Hours
24 Hours
Work in 1
Work in 2
Work Origin Work in 1
Work in 2
O
fig
I1I2I3
I4
I5
Leisure
in p
eriod 2
OLeisure in period 1
Work Origin Work in 1
Work in 2
Leisure in period 1
Lei
sure
in p
eri o
d 2
O
fig
I1I2I3
I4
I5
OWork Origin Work in 1
Work in 2
Leisure in period 1
Lei
sure
in p
eri o
d 2
O
fig
I1
I5
Work Origin Work in 1
Work in 2
Le i
s ure
in p
eri o
d 2
OUtility Increase as work falls
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
Choosing L1, L2
Given C1, C2, w and r
r1
cc
r1
yy 2
12
1
r
CC
r
wLwL
112
12
11
But to get y we must work (L) for wage w
fig
I1
I5
Work in 1
Work in 2
OBudget Constraint
Slope = – (1+r)
L1
L2
fig
I1
I5
Work in 1
Work in 2
OSuppose now that the interest rate rises
L1
L2
fig
I1
I5
Work in 1
Work in 2
OSo L1 goes up and L2 falls
L1
L2
Overall effect of rise in r on aggregate L
Period 1 : l1 Period 2 : l2
Substitution Effect
Income Effect
Overall
Overall effect of rise in r on aggregate L
Period 1 : l1 Period 2 : l2
Substitution Effect
Up Down
Income Effect
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
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
Overall Up Down
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
L1 L2
y1
y2
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
r
y
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
ys=f (L(r))r
y
So now, have relationship between willingness to Supply and interest rate
r ↑ => Ls ↑ => ys ↑
• or ys = f (L( r ))
0dr
dysand
Macroeconomic Equilibrium
We now combine the demand and supply curve we have derived from our microeconomics analysis to find the equilibrium in the economy
r
Y
Macroeconomic Equilibrium
yD=cD
ye
re
ysr
Y
yD=cD
ye
re
ysr
Y
Interested in how shocks to the production function effect the equilibrium level of output, ye, and rate of interest, re.
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.
y
L
Y1=f1(L)
Y=F(L)
So the production function shifts UP permanently
y=f(L)Y
L
E.g. 2: Permanent Change in Exogenous Input Price
Note when we write y = f(L) we are holding all other things constanteg. K stock, other inputs
Y
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,..)
So the production function shifts down permanently
And price of oil rises permanently (1973)
y=f(L)
y1=f1(L)
Let us study the positive permanent shock first.
Y=f(L)
y
c0= y0
Lo
L
Positive Shock: Production function moves up
y1=f1(L)
c0=y0y=f(L)
y
Lo
L
Positive Shock: Production function moves up Know: y ↑ c ↑ Unsure: L: income effect ↓ Substitute effect ( MPL ↓?) Net effect = ?
Positive Shock: Production function moves up.
Know: y ↑ c ↑ Unsure: L: income effect ↓ Substitute effect = MPL ↓
Net effect = ?
|So output definitely rises Thus, the aggregate supply curve moves
out
rys
ys
y
THE END