# Aggregate Demand I: Building the IS-LM Model Chapter 11 Aggregate Demand I: Building the IS-LM Model Part 3 A MORE COMPLEX THEORY OF SHORT-RUN EQUILIBRIUM IN THE GOODS MARKET THE IS CURVE Planned Investment The Keynesian Cross model assumed that planned investment expenditure (I) is exogenous Recall that, in chapter 3, we had assumed that investment spending is inversely related to the real interest rate The IS Curve theory of the goods market brings back the investment function I = I(r) Investment and the real interest rate Assumption: investment spending is inversely related to the real interest rate I = I(r), such that r I

r I (r ) I Investment and the real interest rate Specifically, I = Io Irr Here Ir is the effect of r on I and Io represents all other factors that also affect business investment spending such as business optimism, technological progress, etc. I1 > Io , increased business optimism increase in investment (I) r I1 Irr Io Irr

I Investment: example Suppose I = 12 2r is the investment function Then, if r = 5 percent, we get I = 12 2(5) = 2. Need to be careful with units: is 5 percent, 5 or .05? Hopefully, I remember to tell you. The IS Curve The goods market is in equilibrium when Y=C+I+G The IS curve is a graph that shows all combinations of r and Y for which the goods market is in equilibrium Therefore, the basic equation underlying the IS curve is Y = C(Y T) + I(r) + G Oops, we now have one equation and 2 unknowns! Deriving the IS Curve: algebra Y C (Y T ) I (r ) G

Y Co C y (Y T ) I o I r r G Y Co C y Y C y T I o I r r G Y C y Y Co C y T I o I r r G (1 C y ) Y Co C y T I o I r r G Cy 1 Ir Y (Co I o G ) T r 1 Cy 1 Cy 1 Cy Spending multiplier Tax multiplier Interest rate effect

Deriving the IS Curve: algebra The basic equation underlying the IS curve is Y C (Y T ) I (r ) G for specific consumption and investment functions, the equation underlying the IS curve can also be expressed as: Cy 1 Ir Y (Co I o G ) T r 1 Cy 1 Cy 1 Cy The two equations are equivalent forms of the IS curve. Comparing the Equations of the Keynesian Cross and the IS Curve Keynesian Cross Model

Cy 1 Y (Co I o G ) T 1 Cy 1 Cy Spending multiplier Tax multiplier This is the only difference IS Curve Model Cy 1 Ir Y (Co I o G )

T r 1 Cy 1 Cy 1 Cy Spending multiplier Tax-cut multiplier Interest rate effect The IS Curve Cy 1 Ir Y (Co I o G ) T r 1 Cy

1 Cy 1 Cy Spending multiplier Tax multiplier r Interest rate effect Any change in the real interest rate will cause an opposite change in real total GDP by a multiple determined by the size of the interest rate effect. r1 r r2

This is why the IS curve is negatively sloped. IS Y1 Y2 Y Y The IS Curve: effect of fiscal policy Cy 1 Ir Y (Co I o G ) T r 1 Cy 1 Cy 1 Cy Spending

multiplier Any increase in Co + Io + G causes the IS curve to shift right by the amount of the increase magnified by the spending multiplier That is, if the real interest rate is unchanged, the Keynesian Cross model is the same as the IS curve model. Tax multiplier IS Interest rate effect r r1 Y IS1 Y1 Y2

IS2 Y The IS Curve: effect of fiscal policy Cy 1 Ir Y (Co I o G ) T r 1 Cy 1 Cy 1 Cy Spending multiplier Any decrease in taxes (T) causes the IS curve to shift right by the amount of the tax cut magnified by the tax-cut multiplier Tax multiplier

IS Interest rate effect r r1 Y IS1 Y1 Y2 IS2 Y What Shifts the IS Curve? The IS curve shifts right if there is: an increase in Co + Io + G, or a decrease in T. Also goes the other way!

Deriving the IS curve: graphs PE =Y P E r I PE I Y Any change in the real interest rate will cause an opposite change in real total GDP by a multiple determined by the size of the interest rate effect. r

Y1 PE =C +I (r2 ) +G PE =C +I (r1 ) +G Y Y2 r1 r2 IS Y1 Y2 Y The natural rate of interest

Recall, the chapter 3 loanable funds model gave us a long-run theory of the real interest rate At the long-run interest rate, both Y = C + I + G (or, equivalently, S = I) and Y= Note: r* in the diagram satisfies the requirement of long-run equilibrium. r* is the natural rate of interest. The interest rate consistent with full employment.

PE = Y PE PE = C + I() + G PE = C + I(r1) + G r Y1 Y r1 r* IS Y1

Y The theory of short-run equilibrium in the money market THE MONEY MARKET IN THE SHORT RUN: THE LM CURVE The Theory of Liquidity Preference Due to John Maynard Keynes. A simple theory in which the interest rate is determined by money supply and money demand. Two financial assets Money and bonds. Money supply i=r The supply of real money balances

is fixed: M interest rate M P s s P M P M and P are exogenous. M P M/P real money balances

Money demand i=r interest rate Demand for real money balances: M P s d (M P ) L(i , Y ) L (r ) ( Assume E =0, => i = r M P

M/P real money balances Equilibrium i=r The interest rate interest adjusts to equate the rate supply and demand for money: M P s r1 L (r )

M P L(r ) M P M/P real money balances Equilibrium The interest rate adjusts to equate the supply and demand for money. Excess supply of money creates an excess demand for other assets bonds in the Keynesian model. Excess demand for money creates an excess supply of other assets bonds in the Keynesian model. M P L(r ) i= r

interest rate M P s Excess supply of money r2 r1 r3 Excess demand for money M P L (r ) M/P real money balances How the Fed increases and decreases the interest rate

i=r To decrease r, Fed interest increases M, creating an rate excess supply of money. The demand for bonds increase and interest rates decrease. r1 r2 L (r ) M1 P M/P M2 real money P balances

Prices are sticky (fixed?) in the short run Assumption: the money supply (M), which is controlled by the central bank, is exogenous Assumption: the overall price level (P) is fixed. Assumption: expected inflation (E) zero ) zero Prices are sticky in the short run The long-run analysis of Chapter 5 assumed that P is endogenous. in the long run P changes proportionately with M. The short-run analysis in the IS-LM model assumes that P is exogenous: it is what it is, it is historically determined That is, the overall price level is sticky: what it was last week, it will be this week too Prices are sticky in the short run This sticky-prices assumption is the crucial distinction between long-run and short-run macroeconomic analysis

With the exception of this assumption, all assumptions made in short-run analysis are also assumed in long-run analysis So, the differences between long-run and shortrun theories are caused by this sticky-prices assumption CASE STUDY: Monetary Tightening & Interest Rates Late 1970s: > 10% Oct 1979: Fed Chairman Paul Volcker announces that monetary policy would aim to reduce inflation From Aug 1979 to April 1980, Fed reduced M/ P 8.0% Jan 1983: = 3.7% How How do do you you think think this this policy policy change

change would would affect affect nominal nominal interest interest rates? rates? Monetary Tightening & Interest Rates, cont. The effects of a monetary tightening on nominal interest rates model short run long run Liquidity preference Quantity theory, Fisher effect

(Keynesian) (Classical) prices sticky flexible prediction i > 0 Why? i < 0 Why? actual outcome 8/1979: i = 10.4% 4/1980: i = 15.8% 8/1979: i = 10.4%

1/1983: i = 8.2% The LM curve Put Y back into the money demand function: M P d L(r ,Y ) The LM curve is a graph of all combinations of r and Y that equate the supply and demand for real money balances. Equating money supply to money demand (M/P to Md), the equation for the LM curve is: M P L(r ,Y ) Deriving the LM curve (a) The market for

r real money balances (b) The LM curve r LM r2 r 2 r1 M1 P L (r , Y2 ) L (r , Y1 )

M/P r 1 Y1 Y2 Y Understanding the LM curves slope The LM curve is positively sloped. Intuition: An increase in income raises money demand. Since the money supply (supply of real balances) is fixed, there is now excess demand in the money market at the initial interest rate. Sell bonds, the interest rate increases to restore equilibrium in the money market. How M shifts the LM curve (a) The market for

r real money balances (b) The LM curve r LM 2 LM1 r2 r2 r1 r1 L (r , Y1 )

M2 M1 P P M/P Y1 Y NOW YOU TRY: Shifting the LM curve Suppose a wave of credit card fraud causes consumers to use cash more frequently in transactions. Use the liquidity preference model to show how these events shift the LM curve.

Both the goods market and the money market need to be in equilibrium SHORT-RUN EQUILIBRIUM IN THE IS-LM MODEL The short-run equilibrium The short-run equilibrium is the i= combination of r and Y that r simultaneously satisfies the equilibrium conditions in the goods & money markets: Y C (Y T ) I (r ) G IS M P L(r ,Y ) Remember: E = 0: (i - E) M/ = L(i,Y), LM

Y Equilibrium interest rate Equilibrium level of income Short-run equilibrium Note that the short-run equilibrium GDP does not have to be equal to the long-run equilibrium GDP (, also called potential GDP and natural GDP) Thus, like the Keynesian Cross model, the IS-LM model can explain recessions and booms. But, the Keynesian Cross model could determine only equilibrium GDP. The IS-LM

model determines the equilibrium interest rate as well. Equilibrium interest rate r LM IS Equilibrium level of income Y The IS-LM Model: summary Short-run equilibrium in the goods market is represented by a downward-sloping IS curve linking Y and r. Short-run equilibrium in the money market is represented by an

upward-sloping LM curve linking Y and r. The intersection of the IS and LM curves determine the shortrun equilibrium values of Y and r. The IS curve shifts right if there is: r an increase in Co + Io + G, or LM a decrease in T. The LM curve shifts right if: M/P increases (M or P ) If constant term in money demand equation increases IS Later we show the impact of a change in E Y The Big Picture Keynesian Keynesian Cross Cross Theory Theory of of

Liquidity Liquidity Preference Preference IS IS curve curve LM LM curve curve IS-LM IS-LM model model Agg. Agg. demand demand

curve curve Agg. Agg. supply supply curve curve Explanation Explanation of of short-run short-run fluctuations fluctuations Model Model of of Agg. Agg. Demand

Demand and and Agg. Agg. Supply Supply Preview of Chapter 12 In Chapter 12, we will use the IS-LM model to analyze the impact of policies and shocks. learn how the aggregate demand curve comes from IS-LM. use the IS-LM and AD-AS models together to analyze the short-run and long-run effects of shocks. use our models to learn about the Great Depression.