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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? Is it a borrower? Is it a lender? Or a Polonius? What about the economy as a whole? 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 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 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. 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 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 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 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 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 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 s r y ys y THE END