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