Polonious Next consider a rise in r. y 2 =c 2 Agents are producing and consuming the same in each period y 1 =c 1

Polonious y 1 =c 1 What happens to Consumption as the interest rate rises? y 2 =c 2

Polonious y 1 =c 1 y 2 =c 2 Here c 1 falls while c 2 rises This is due solely to the pure substitution effect as there is no income effect

Polonious y 1 =c 1 y 2 =c 2 Here c 1 falls while c 2 rises So now c 1 < y 1 (saving) and c 2 < y 2 (using savings)

Overall effect Period 1 : c 1 Period 2 : c 2 Substitution Effect Income Effect Overall

Overall effect Period 1 : c 1 Period 2 : c 2 Substitution Effect DownUp Income Effect Overall

Overall effect Period 1 : c 1 Period 2 : c 2 Substitution Effect DownUp Income Effect None Overall

Overall effect Period 1 : c 1 Period 2 : c 2 Substitution Effect DownUp Income Effect None OverallDownUp

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 => C 2 ↑ and C 1 ↓ for the economy as a whole What about the economy as a whole?

So as r goes Up, c 1 goes Down. This is our first key demand relationship

So as r goes Up, c 1 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, c 1 goes Down. This is our first key demand relationship c1c1 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, c 1 goes Down. This is our first key demand relationship c1c1 r c d (r) Aggregate Consumption Function Slopes down

Note here we are implicitly solving the problem: Maximize U ( ( 1) ( 2 ) Subject to 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 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. C 1 v C 2 Consumption now versus consumption later U(c 1,l 1 )+ U(c 2,l 2 )

Problem 3: Work Now or Later What about the choice between work now versus work later? U(c 1,l 1 )+ U(c 2,l 2 )

Problem 3: Work Now or Later L 1 v L 2 What do the indifference curves look like? To see this lets look at something we like leisure now and leisure later.

I1I1 I2I2 I3I3 I4I4 I5I5 Leisure in period 2 O Leisure in period 1

I1I1 I2I2 I3I3 I4I4 I5I5 Leisure in period 2 O Leisure in period 1 24 Hours

I1I1 I2I2 I3I3 I4I4 I5I5 Leisure in period 2 O Leisure in period 1 24 Hours Work in 1 Work in 2

I1I1 I2I2 I3I3 I4I4 I5I5 Leisure in period 2 O Leisure in period 1 24 Hours Work in 1 Work in 2 Work Origin Work in 1 Work in 2 O

I1I1 I2I2 I3I3 I4I4 I5I5 Leisure in period 2 O Leisure in period 1 Work Origin Work in 1 Work in 2 Leisure in period 1 Leisure in period 2 O

I1I1 I2I2 I3I3 I4I4 I5I5 O Work Origin Work in 1 Work in 2 Leisure in period 1 Leisure in period 2 O

I1I1 I5I5 Work Origin Work in 1 Work in 2 Leisure in period 2 O Utility Increase as work falls

What is the budget constrain in this instant. Recall in the problem where we considered c 1 v c 2 we effectively held y 1 and y 2 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 (y 1, y 2 )

Choose y 1,y 2 with c 1,c 2 fixed Choosing L 1, L 2 Given C 1, C 2, w and r But to get y we must work (L) for wage w

I1I1 I5I5 Work in 1 Work in 2 O Budget Constraint Slope = – (1+r) L1L1 L2L2

I1I1 I5I5 Work in 1 Work in 2 O Suppose now that the interest rate rises L1L1 L2L2

I1I1 I5I5 Work in 1 Work in 2 O So L 1 goes up and L 2 falls L1L1 L2L2

Overall effect of rise in r on aggregate L Period 1 : l 1 Period 2 : l 2 Substitution Effect Income Effect Overall

Overall effect of rise in r on aggregate L Period 1 : l 1 Period 2 : l 2 Substitution Effect UpDown Income Effect Overall

Overall effect of rise in r on aggregate L Period 1 : l 1 Period 2 : l 2 Substitution Effect UpDown Income Effect None on Agg.None on Agg Overall

Overall effect of rise in r on aggregate L Period 1 : l 1 Period 2 : l 2 Substitution Effect UpDown Income Effect None on Agg.None on Agg OverallUpDown

So if the interest rises L 1 rises But increase in L 1 means an increase in output, y

So if the interest rises L 1 rises But increase in L 1 means an increase in output, y L1L1 L2L2 y1y1 y2y2

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 So now, have relationship between willingness to Supply and interest rate

y s =f (L(r)) r y So now, have relationship between willingness to Supply and interest rate

r ↑ => L s ↑ => y s ↑ or y s = f (L( r ))

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 y D =c D yeye rere ysys r Y

yeye rere ysys r Y Interested in how shocks to the production function effect the equilibrium level of output, y e, and rate of interest, r e.

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)

1 st Case: Permanent Shock to the production function Eg: 1 Economics Growth: y ↑ forever. y L Y 1 =f 1 (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 constant eg. 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) y 1 =f 1 (L)

Let us study the positive permanent shock first. Y=f(L) y c 0 = y 0 LoLo L Positive Shock: Production function moves up

y 1 =f 1 (L) c 0 =y 0 y=f(L) y LoLo L Positive Shock: Production function moves up Know:y ↑c ↑ Unsure:L:income effect ↓ Substitute effect ( MP L ↓?) Net effect = ?

Positive Shock: Production function moves up. Know:y ↑c ↑ Unsure:L:income effect ↓ Substitute effect = MP L ↓ Net effect =?

|So output definitely rises Thus, the aggregate supply curve moves out r ysys ysys y

THE END