The IS Curve October 24 2016 1 25 Accounting in the Goods Market I Recall national income accounting I Equilibrium on the goods market closed economy Y C I G T otal supply T otal demand I I Recall savings is S Y C G I I I We assume N X 0 no international trade a closed economy So the equilibrium condition is I S Both are functions of real interest rates Goal Derive the Investment Savings IS curve I Relationship between output Y and real interest rate r 2 25 Savings Curve I Analyze S and r from the consumption model I S curve from our consumption model I Euler equation and budget constraint u0 c 1 r u0 cf I Effect of change in r is theoretically ambiguous on C and S I I Depends on whether consumer saves or borrows income substitution effect Need to go to the data I I and cf 1 r S y f Assume S is increasing in r Curve shifters Y Y f G taxes and wealth 3 25 Investment Curve I Analyze I and r from investment model I From optimality M P K f ucf I I will always be decreasing in r I I and ucf r Because ucf is increasing in r Curve shifters expected MPK 4 25 IS curve I Equilibrium I S and r is the intersection of I and S I The goods market clears when desired investment equals desired national saving I Adjustments in the real interest rate bring about equilibrium I For any level of output Y the IS curve shows the real interest rate r for which the goods market is in equilibrium 5 25 IS curve I At higher levels of output the saving curve is shifted to the right compared to the situation at the lower level of output I Since the investment curve is downward sloping equilibrium at the higher level of output has a lower real interest rate I Thus a higher level of output must lead to a lower real interest rate so the IS curve slopes downward I The IS curve shows the relationship between the real interest rate and output for which investment equals saving 6 25 IS curve and Goods Market I I Find equilibrium for different Y shifting S Why doesn t I shift with Y 7 25 IS curve Alternative interpretation I Beginning at a point of equilibrium suppose the real interest rate rises I The increased real interest rate causes people to increase saving and thus reduce consumption and causes firms to reduce investment I So the quantity of goods demanded declines I To restore equilibrium the quantity of goods supplied would have to decline I So higher real interest rates are associated with lower output that is the IS curve slopes downward 8 25 Factors that shift the IS curve I Any change that reduces desired national saving relative to desired investment shifts the IS curve up and to the right I Intuitively imagine constant output so a reduction in saving means more investment relative to saving the interest rate must rise to reduce investment and increase saving 9 25 Example of Change in G I I I What if G temporary increases but Y remains the same Savings curve shifts changing r Temporarily shifts the IS curve since at same Y 10 25 Example of Increase in Future TFP I Assume Af suddenly increases I I What happens to S curve I I I I Note timing future TFP Higher future Y f Income effect dominates so more consumption less savings So S curve shifts to left What happens to I curve I I I Increase in Af increases the M P K f Firms increase investment I curve shifts to the right 11 25 TFP Example Consumption Smoothing I The equilibrium real interest rate goes up unambiguously I I I Less people are saving yet firms would really like to invest Funds are scarce so lenders can charge a higher interest rate The amount of saving and investment is ambiguous I Two opposite forces saving decreases investment increases 12 25 The Full Employment FE Curve I FE line captures the labor markets I I Important equations I I I Output Y AF N K Labor Supply Demand w MPN P UN 1 N w UC 1 C P The amount produced given N K independent of r I I With the IS curve determines equilibrium Y and r We are going to assume that given current capital and productivity FE is vertical Curve Shifters I TFP labor supply increase capital stock increase 13 25 Example 1 Temporary increase in Today s TFP To determine the way the curves shift consider the effect market by market I Labor market I Labor demand shifts to the right I Labor supply is unaffected Temporary shock A new short run equilibrium in the labor market with higher N and higher Pw Given the level of K we know that output must increase Recall the production function Y AF K N Therefore the FE line shifts to the right I I I All workers are more productive 14 25 Example 1 Temporary increase in Today s TFP To determine the way the curves shift consider the effect market by market I Goods market I I Output changes so real income change and therefore saving increase However recall that this is exactly the example we used to construct the IS curve this is a movement along the existing IS curve not a shift of the IS curve 15 25 Example 1 Temporary increase in Today s TFP 0 16 25 Example 1 Temporary increase in Today s TFP To summarize what are the predictions when TFP increases temporarily I I I I Labor and the real wage increase Output increases the real interest rate decreases Firms invest more r declines moving along the I curve in the goods market Consumers consume more and save more the role of r in the Euler equation and smoothing 17 25 Example 2 Temporary increase in Today s Gov t Expenditure I Labor market I I I I I PVLR declines NS shifts to the right No direct effect on labor demand In equilibrium Pw and N With unchanged A and K Y increases and the FE line shifts to the right Goods Market I I I Consumption declines but by less than G consumption smoothing S and the S curve shifts to the left No effect on the I curve In the goods market equilibrium r IS curve shifts up 18 25 Example 2 Temporary increase in Today s Gov t Expenditure Case 1 The shift of IS is smaller than the shift of FE 0 0 0 Equilibrium interest rates stays the same or even drops 19 25 Example 2 Temporary increase in Today s Gov t Expenditure Case 2 The shift of IS is larger than the shift of FE 0 0 0 0 Equilibrium interest rates increase 20 25 Example 3 A Temporary Preference Shock I I I The purpose of this example is to show an example for a wide variety …