Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Business Conditions Analysis ECON 736 Professor Yamin Ahmad Lecture 4: The Building Blocks of Aggregate Demand Goods Market Equilibrium (IS Curve) Money Market Equilibrium (LM Curve) Big Concepts in this lecture the IS curve, and its relation to the Keynesian cross the loanable funds model the LM curve, and its relation to the theory of <a href="/keyword/liquidity-preference/" >liquidity preference</a> how the IS-LM model determines income and the interest rate in the short run when P is fixed Note: These lecture notes are incomplete without having attended lectures slide 1 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 The Big Picture Keynesian Keynesian Cross Cross Theory of Theory of Liquidity <a href="/keyword/liquidity-preference/" >liquidity preference</a> Preference IS IS curve curve LM LM curve curve IS-LM IS-LM model model Context Lecture 3 introduced the basic model of aggregate demand and aggregate supply. Explanation Explanation of short-run of short-run fluctuations fluctuations Long run prices flexible output determined by factors of production &amp; technology unemployment equals its natural rate Agg. Agg. demand demand curve curve Agg. Agg. supply supply curve curve Note: These lecture notes are incomplete without having attended lectures Model of Model of Agg. Agg. Demand Demand and Agg. and Agg. Supply Supply slide 2 Short run prices fixed output determined by aggregate demand unemployment negatively related to output Note: These lecture notes are incomplete without having attended lectures slide 3 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Recall: The Keynesian Cross A simple closed economy model in which income is determined by expenditure. (due to J.M. Keynes) Notation: Elements of the Keynesian Cross Consumption function: Govt policy variables: for now, planned Investment is exogenous: planned expenditure: equilibrium condition: C = C ( T ) Y G = G , T =T I = planned investment AE = C + I + G = planned expenditure Y = real GDP = actual expenditure Difference between actual &amp; planned expenditure = unplanned inventory investment Note: These lecture notes are incomplete without having attended lectures AE = C ( T ) + I + G Y Y = AE I =I actual expenditure = planned expenditure slide 5 slide 4 Note: These lecture notes are incomplete without having attended lectures Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Graphing planned expenditure AE planned expenditure Graphing the equilibrium condition AE planned expenditure AE =Y AE =C +I +G MPC 1 45 income, output, Y income, output, Y Note: These lecture notes are incomplete without having attended lectures slide 6 Note: These lecture notes are incomplete without having attended lectures slide 7 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 The equilibrium value of income AE planned expenditure An increase in government purchases AE At Y1, there is now an unplanned drop in inventory AE =Y AE =C +I +G AE YAE =C +I +G 2 = AE =C +I +G1 G income, output, Y Equilibrium income Note: These lecture notes are incomplete without having attended lectures so firms increase output, and income rises toward a new equilibrium. slide 8 Y AE1 = Y1 Y AE2 = Y2 slide 9 Note: These lecture notes are incomplete without having attended lectures Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Solving for Y Y = C + I + G Y = C + I + G = C + G = MPC Y + G Collect terms with Y on the left side of the equals sign: equilibrium condition in changes because I exogenous because C = MPC Y Solve for Y : The government purchases multiplier Definition: the increase in income resulting from a $1 increase in G. In this model, the govt purchases multiplier equals Example: If MPC = 0.8, then Y 1 = G 1 MPC (1 MPC) Y = G Note: These lecture notes are incomplete without having attended lectures 1 Y = G 1 MPC slide 10 Y 1 = = 5 G 1 0.8 An increase in G An increase in G causes income to causes income to increase 5 times increase 5 times as much! as much! slide 11 Note: These lecture notes are incomplete without having attended lectures Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Why the multiplier is greater than 1 Initially, the increase in G causes an equal increase in Y: Y = G. But Y C further Y further C further Y So the final impact on income is much bigger than the initial G. Note: These lecture notes are incomplete without having attended lectures An increase in taxes AE Initially, the tax increase reduces consumption, and therefore E: AE YAE =C +I +G 1 = AE =C2 +I +G At Y1, there is now an unplanned inventory buildup C = MPC T so firms reduce output, and income falls toward a new equilibrium slide 12 Y AE2 = Y2 Y AE1 = Y1 slide 13 Note: These lecture notes are incomplete without having attended lectures Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Solving for Y Y = C + I + G eq m condition in changes The tax multiplier Def: the change in income resulting from a $1 increase in T : = C = MPC ( Y T Solving for Y : I and G exogenous ) Y T Y T = MPC 1 MPC (1 MPC) Y = MPC T If MPC = 0.8, then the tax multiplier equals Final result: MPC Y = T 1 MPC slide 14 = 0.8 0.8 = = 4 1 0.8 0.2 Note: These lecture notes are incomplete without having attended lectures Note: These lecture notes are incomplete without having attended lectures slide 15 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 The tax multiplier is negative: A tax increase reduces C, which reduces income. is greater than one (in absolute value): A change in taxes has a multiplier effect on income. is smaller than the govt spending multiplier: Consumers save the fraction (1 MPC) of a tax cut, so the initial boost in spending from a tax cut is smaller than from an equal increase in G. Note: These lecture notes are incomplete without having attended lectures Walkthrough Example I: Economic Scenario: In the Keynesian Cross, assume that the consumption function is given by: C = 475 + 0.75(Y-T) Planned Investment, I = 150, G = 250, T = 100. a. Graph planned expenditure as a function of income b. What is the equilibrium level of income c. If government purchases increase by 125, what is the new equilibrium income? d. What level of government purchases is needed to achieve an income of 2600? slide 16 Note: These lecture notes are incomplete without having attended lectures slide 17 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 A Balanced Budget Approach Problem: Suppose that we face our canonical problem where C=475 + 0.75(Y-T), T = 100 I = 150, G = 250 Suppose that the government wishes to increase its spending by 100, but uses a balanced budget approach, thereby raising taxes by the same amount to finance its expenditures. Question: Is there any impact on GDP? Does it change? If so, by how much? slide 18 The IS curve Def: a graph of all combinations of r and Y that result in goods market equilibrium i.e. actual expenditure (output) = planned expenditure The equation for the IS curve is: Y = C ( T ) + I (r ) + G Y Note: These lecture notes are incomplete without having attended lectures Note: These lecture notes are incomplete without having attended lectures slide 19 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Deriving the IS curve AE AE =Y AE =C +I (r )+G 2 Why the IS curve is negatively sloped A fall in the interest rate motivates firms to increase investment spending, which drives up total planned spending (AE ). r I AE Y I r r1 r2 AE =C +I (r1 )+G Y1 Y2 Y To restore equilibrium in the goods market, output (a.k.a. actual expenditure, Y ) must increase. IS Y1 Y2 Y slide 20 Note: These lecture notes are incomplete without having attended lectures Note: These lecture notes are incomplete without having attended lectures slide 21 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Market For Loanable Funds Closed Economy Define Sp Y-T-C(Y-T) (+) The IS curve and the loanable funds model (a) The L.F. model (b) The IS curve and Sg T-G r S2 S1 r S Sp + Sg = Y C(Y-T) G = S(Y; G, T) (+) (-) (+) r2 r1 I (r ) S, I r2 r1 IS Y2 Y1 Y Capital Markets Equilibrium: S(Y;G,T) = I(r) (-) (Loanable Funds) Or Equivalently: Y = Yd C(Y-T) + I(r) + G slide 22 Note: These lecture notes are incomplete without having attended lectures Note: These lecture notes are incomplete without having attended lectures slide 23 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Algebra Of The IS Curve Suppose C = c0 + c1(Y-T) and I = I0 br (Note: Blanchard also considers the effect of sales on Investment by incorporating Y, i.e. I=b0+b1Y-b2r) Then Y= C + I + G = c0 + I0 + G + c1(Y-T) br If we collect like terms: Slope of the IS curve Y= c0 + I 0 + G c1T b r 1 c1 1 c1 Hold everything except Y and r fixed: Y = b r 1 c1 r c1 1 = &lt;0 Y b Thus IS is relatively flat if either: Y= c0 + I 0 + G c1T b r 1 c1 1 c1 slide 24 (i) b is very large; or (ii) (ii) c close to unity. Note: These lecture notes are incomplete without having attended lectures Note: These lecture notes are incomplete without having attended lectures slide 25 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Fiscal Policy and the IS curve We can use the IS-LM model to see how fiscal policy (G and T ) affects aggregate demand and output. Shifting the IS curve: G At any value of r, AE AE =Y AE =C +I (r )+G 1 2 G AE Y so the IS curve shifts to the right. The horizontal distance of the IS shift equals AE =C +I (r1 )+G1 Let s start by using the Keynesian cross to see how fiscal policy shifts the IS curve r r1 Y1 Y2 Y Y = 1 G 1 MPC Y1 Y IS1 Y2 IS2 Y slide 27 Note: These lecture notes are incomplete without having attended lectures slide 26 Note: These lecture notes are incomplete without having attended lectures Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Walkthrough Example II: Proportional Taxation Economic Scenario: Let us return to our previous example. Suppose we assume that the consumption function is given by: C = 475 + 0.75(Y-T) Planned Investment, I = 150, G = 250 However, suppose now, T = T0 + t1Y = 100 + (1/3)Y T0 and t1 are parameters of the tax code. The Theory of <a href="/keyword/liquidity-preference/" >liquidity preference</a> Due to John Maynard Keynes. A simple theory in which the interest rate is determined by money supply and money demand. Money supply is exogenous determined by Fed! a. How does this tax system change the way consumption responds to GDP? b. In the Keynesian Cross, how does this tax system alter the government purchases multiplier? c. Suppose now that I=150-500r. In the IS-LM model, how does this tax system alter the slope of the IS Curve? Note: These lecture notes are incomplete without having attended lectures People hold wealth in the form of either: Money Demand for money and demand for bonds! Bonds Note: These lecture notes are incomplete without having attended lectures slide 28 slide 29 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Money supply r Money demand P) s The supply of real money balances is fixed: interest rate (M r People either hold: Money Bonds interest rate (M P) s (M P) =M P s Demand for real money balances: M P L (r ) M P M/P real money balances slide 30 (M P) d = L (r ) M/P real money balances slide 31 Note: These lecture notes are incomplete without having attended lectures Note: These lecture notes are incomplete without having attended lectures Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Equilibrium The interest rate adjusts to equate the supply and demand for money: r interest rate How the Fed raises the interest rate (M P) s r To increase r, Fed reduces M interest rate r2 r1 r1 M P = L (r ) M P L (r ) M/P real money balances slide 32 Note: These lecture notes are incomplete without having attended lectures L (r ) M2 P M1 P M/P real money balances slide 33 Note: These lecture notes are incomplete without having attended lectures Professor Yamin Ahmad, Business Conditions Analysis ECON 736 CASE STUDY: Monetary Tightening &amp; Rates, cont. The effects of a monetary tightening on nominal interest rates short run model prices prediction actual outcome slide 34 Monetary Tightening &amp; Interest Rates Late 1970s: &gt; 10% Oct 1979: Fed Chairman Paul Volcker announces that monetary policy would aim to reduce inflation Aug 1979-April 1980: Fed reduces M/P 8.0% Jan 1983: = 3.7% long run Quantity theory, Fisher effect (Classical) <a href="/keyword/liquidity-preference/" >liquidity preference</a> (Keynesian) sticky i &gt; 0 8/1979: i = 10.4% 4/1980: i = 15.8% flexible i &lt; 0 8/1979: i = 10.4% 1/1983: i = 8.2% How do you think this policy change How do you think this policy change would affect nominal interest rates? would affect nominal interest rates? Note: These lecture notes are incomplete without having attended lectures Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 The LM curve Now let s put Y back into the money demand function: Nominal or Real Rates in Money Demand? d Money Market Equilibrium: M = M = L(i,Y ) (-)(+) P P What is real return to saving $1? (M P) d d = L (r ,Y ) Note: In Blanchard: M = YL(i ) = d Y d i 1 2 1+ r = P 1+ i 1+ r + i The LM curve is a graph of all combinations of r and Y that equate the supply and demand for real money balances. The equation for the LM curve is: This is known as the Fisher Equation. So: M P = L (r ,Y ) slide 36 M = L(r + , Y ) P Treat Ms as exogenous; for present set = 0. Note: These lecture notes are incomplete without having attended lectures Note: These lecture notes are incomplete without having attended lectures slide 37 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Deriving the LM curve (a) The market for Why the LM curve is upward sloping An increase in income raises money demand. r real money balances (b) The LM curve r LM r2 r1 M1 P r2 L (r , Y2 ) L (r , Y1 ) M/P Since the supply of real balances is fixed, there is now excess demand in the money market at the initial interest rate. r1 Y1 Y2 Y The interest rate must rise to restore equilibrium in the money market. Note: These lecture notes are incomplete without having attended lectures slide 38 Note: These lecture notes are incomplete without having attended lectures slide 39 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Equilibrium in the Bond Market? There are two assets (money and bonds), but only one equilibrium condition. Do we need to worry about bond market equilibrium as well? Answer: No! d Ms + Bs = A = M + Bd P P with A = real wealth. So : d Ms = M Bs = Bd P P Write: Algebra of the LM Curve d M = m + kY hr 0 P With M and P fixed: 0 = k Y - h r Slope of LM Curve : r k = &gt;0 Y h LM curve relatively flat if either: This is an example of Walras Law. Note: These lecture notes are incomplete without having attended lectures (i) k small; or (ii) (ii) h large ( Liquidity Trap ) slide 40 Note: These lecture notes are incomplete without having attended lectures slide 41 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 How M shifts the LM curve (a) The market for Shifts in LM curve (r fixed) LM2 LM1 M = k Y Y = 1 P M Pk What happens if k = 0? Hold Y fixed: M = h r r = 1 P M Ph r real money balances (b) The LM curve r r2 r1 M2 P M1 P r2 L (r , Y1 ) M/P r1 Y1 Y So vertical shift is independent of k Note: These lecture notes are incomplete without having attended lectures slide 42 Note: These lecture notes are incomplete without having attended lectures slide 43 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Walkthrough Example III: Economic Scenario: Suppose that the money demand function is: (M/P)d = 1000 100r where r is the interest rate (in percent). The money supply M is 1000, and the price level is 2. The short-run equilibrium The short-run equilibrium is the combination of r and Y that simultaneously satisfies the equilibrium conditions in the goods &amp; money markets: r LM a. Graph the supply and demand for real money balances. b. What is the equilibrium interest rate? c. Assume that the price level is fixed. What happens to the equilibrium interest rate if the supply of money is raised from 1000 to 1200? Y = C ( T ) + I (r ) + G Y IS Y M P = L (r ,Y ) Equilibrium interest rate Note: These lecture notes are incomplete without having attended lectures d. If the Fed wishes to raise the interest rate to 7 percent, what money supply should it set? Note: These lecture notes are incomplete without having attended lectures Equilibrium level of income slide 45 slide 44 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Equilibrium With Fixed Prices r Equilibrium in the IS-LM Model LM IS Curve c + I + G c T br 1 S (Y ;G,T ) = I (r) or Y = 0 0 (+)(-)(+) 1 c 1 c 1 1 LM Curve M = L(r,Y ) P (-)(+) (or M = m + kY hr) 0 P Interest Rate Equilibrium interest rate IS Equilibrium level of income Solve for Y and r in terms of G,T, M and P. Y Income and Output Note: These lecture notes are incomplete without having attended lectures slide 46 Note: These lecture notes are incomplete without having attended lectures slide 47 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Is there any reason to expect it to converge to this equilibrium from arbitrary r and Y? If there is an excess demand for money (excess supply of bonds) this should drive the return on bonds up, and vice versa. If savings exceeds planned investment, then consumers must be spending less and producers will be accumulating unwanted inventories. So they will cut back production, and vice versa. Hence the system should converge. Note: These lecture notes are incomplete without having attended lectures c + I +G c T m + kY M / P 1 b ( 0 ) Y= 0 0 1 c 1 c h 1 1 c + I + G c T bm / h + bM / hP 1 0 = 0 0 1 c + bk / h 1 Hence: 1 Y = &gt; 0 and 0 as h 0 G 1 c + bk / h 1 b Y = &gt; 0 and 0 as b 0 or h M hP(1 c + bk / h) 1 Note: These lecture notes are incomplete without having attended lectures slide 48 slide 49 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Fiscal Expansion r G 1 c + bk / h } Monetary Expansion r LM LM2 LM1 Interest Rate r2 Interest Rate B r1 A r1 A { r2 B G 1 c IS2 IS IS1 Y1 Y2 Y Y1 Y2 Y Income and Output Note: These lecture notes are incomplete without having attended lectures Income and Output slide 50 Note: These lecture notes are incomplete without having attended lectures slide 51 Professor Yamin Ahmad, Business Conditions Analysis ECON 736 Back to The Big Picture Keynesian Keynesian Cross Cross Theory of Theory of Liquidity <a href="/keyword/liquidity-preference/" >liquidity preference</a> Preference IS IS curve curve LM LM curve curve Summary 1. Keynesian cross IS-LM IS-LM model model Explanation Explanation of short-run of short-run fluctuations fluctuations basic model of income determination takes fiscal policy &amp; investment as exogenous fiscal policy has a multiplier effect on income. 2. IS curve Agg. Agg. demand demand curve curve Agg. Agg. supply supply curve curve Note: These lecture notes are incomplete without having attended lectures Model of Model of Agg. Agg. Demand Demand and Agg. and Agg. Supply Supply slide 52 comes from Keynesian cross when planned investment depends negatively on interest rate shows all combinations of r and Y that equate planned expenditure with actual expenditure on goods &amp; services slide 53 Summary 3. Theory of <a href="/keyword/liquidity-preference/" >liquidity preference</a> Summary 5. IS-LM model Intersection of IS and LM curves shows the unique point (Y, r ) that satisfies equilibrium in both the goods and money markets. basic model of interest rate determination takes money supply &amp; price level as exogenous an increase in the money supply lowers the interest rate 4. LM curve comes from <a href="/keyword/liquidity-preference/" >liquidity preference</a> theory when money demand depends positively on income shows all combinations of r and Y that equate demand for real money balances with supply slide 54 slide 55