Title PageThe IS CurveOctober 24, 20161 / 25Accounting in the Goods MarketIRecall national income accountingIEquilibrium on the goods market (closed economy):Y = C + I + GT otal supply = T otal demandIWe assume N X = 0 (no international trade), a closedeconomyIRecall savings is: S ≡ Y − C − GISo, the equilibrium condition is: I = SIBoth are functions of real interest ratesIGoal: Derive the Investment-Savings (IS) curveIRelationship between output, Y , and real interest rate, r2 / 25Savings CurveIAnalyze S and r from the consumption modelI“S” curve from our consumption modelIEuler equation and budget constraintu0(c) = β(1 + r)u0(cf), and cf= (1 + r)S + yfIEffect of change in r is theoretically ambiguous on C and SIDepends on whether consumer saves or borrows,income/substitution effectINeed to go to the data:IAssume S is increasing in rICurve shifters: Y, Yf, G, taxes, and wealth3 / 25Investment CurveIAnalyze I and r from investment modelIFrom optimality:MP Kf= ucf, and ucf= r + δII will always be decreasing in rIBecause ucfis increasing in rICurve shifters: expected MPK, δ4 / 25IS curveIEquilibrium I = S and r is the intersection of I and SIThe goods market clears when desired investment equalsdesired national savingIAdjustments in the real interest rate bring aboutequilibriumIFor any level of output Y, the IS curve shows the realinterest rate r for which the goods market is in equilibrium5 / 25IS curveIAt higher levels of output, the saving curve is shifted to theright compared to the situation at the lower level of outputISince the investment curve is downward sloping,equilibrium at the higher level of output has a lower realinterest rateIThus a higher level of output must lead to a lower realinterest rate, so the IS curve slopes downwardIThe IS curve shows the relationship between the realinterest rate and output for which investment equals saving6 / 25IS curve and Goods MarketIFind equilibrium for different Y , shifting SIWhy doesn’t I shift with Y ?7 / 25IS curve: Alternative interpretationIBeginning at a point of equilibrium, suppose the realinterest rate risesIThe increased real interest rate causes people to increasesaving and thus reduce consumption, and causes firms toreduce investmentISo the quantity of goods demanded declinesITo restore equilibrium, the quantity of goods suppliedwould have to declineISo higher real interest rates are associated with loweroutput, that is, the IS curve slopes downward8 / 25Factors that shift the IS curveIAny change that reduces desired national saving relative todesired investment shifts the IS curve up and to the rightIIntuitively, imagine constant output, so a reduction insaving means more investment relative to saving; theinterest rate must rise to reduce investment and increasesaving9 / 25Example of Change in GIWhat if G temporary increases, but Y remains the same?ISavings curve shifts, changing rITemporarily shifts the IS curve (since at same Y )10 / 25Example of Increase in Future TFPIAssume Afsuddenly increasesINote timing: future TFPIWhat happens to S curve?IHigher future YfIIncome effect dominates, so more consumption, less savingsISo S curve shifts to leftIWhat happens to I curve?IIncrease in Afincreases the M P KfIFirms increase investmentII curve shifts to the right11 / 25TFP Example: Consumption SmoothingIThe equilibrium real interest rate goes up unambiguouslyILess people are saving, yet firms would really like to investIFunds are scarce so lenders can charge a higher interest rateIThe amount of saving and investment is ambiguousITwo opposite forces: saving decreases, investment increases12 / 25The Full Employment (FE) CurveI“FE” line captures the labor marketsIWith the IS curve, determines equilibrium Y and rIImportant equations:IOutput: Y = AF (N, K)ILabor Supply/Demand:MP N =wP, −UN=1 − τN1 + τCwPUCIThe amount produced given N, K independent of rIWe are going to assume that given current capital andproductivity: FE is verticalICurve ShiftersITFP, labor supply increase, capital stock increase13 / 25Example 1: Temporary increase inToday’s TFPTo determine the way the curves shift, consider the effect“market-by-market”:ILabor market:ILabor demand shifts to the right. (All workers are more productive)ILabor supply is unaffected. (Temporary shock)IA new short run equilibrium in the labor market withhigher N and higherwP.IGiven the level of K, we know that output mustincrease (Recall the production functionY = AF (K, N)).ITherefore, the FE line shifts to the right.14 / 25Example 1: Temporary increase inToday’s TFPTo determine the way the curves shift, consider the effect“market-by-market”:IGoods market:IOutput changes, so real income change, and thereforesaving increase.IHowever... recall that this is exactly the example we used toconstruct the IS curve ⇒ this is a movement along theexisting IS curve; not a shift of the IS curve.15 / 25Example 1: Temporary increase inToday’s TFP!!"!#$%!&'()*+!#,$%!-,!(!"!&#!./!./0!16 / 25Example 1: Temporary increase inToday’s TFPTo summarize... what are the predictions when TFP increasestemporarily?ILabor and the real wage increase.IOutput increases, the real interest rate decreases.IFirms invest more (r declines, moving along the I curve inthe goods market).IConsumers consume more and save more (the role of r inthe Euler equation, and smoothing).17 / 25Example 2: Temporary increase inToday’s Gov’t ExpenditureILabor market:IPVLR declines → NS shifts to the rightINo direct effect on labor demandIIn equilibrium:wP↓ and N ↑IWith unchanged A and K, Y increases and the FE lineshifts to the right.IGoods Market:IConsumption declines but by less than ∆G (consumptionsmoothing) ⇒ S ↓ and the S curve shifts to the leftINo effect on the I curveIIn the goods market equilibrium, r ↑ ⇒ IS curve shifts up18 / 25Example 2: Temporary increase inToday’s Gov’t ExpenditureCase 1: The shift of IS is “smaller” than the shift of FE!!!!"!#$%!&'()*+!#,$%!-,!(!"!&#!./!./0!-,0!(!"!&#!./!./0!-,!-,0!(!"!&#!./!./0!-,!Equilibrium interest rates stays the same or even drops19 / 25Example 2: Temporary increase inToday’s Gov’t ExpenditureCase 2: The shift of IS is “larger” than the shift of FE!!!!"!#$%!&'()*+!#,$%!-,!(!"!&#!./!./0!-,0!(!"!&#!./!./0!-,!-,0!(!"!&#!./!./0!-,!Equilibrium interest rates increase20 / 25Example 3: A Temporary PreferenceShockIThe purpose of this example is to show an example for awide variety of shocks that we can