© Pilot Publishing Company Ltd Chapter 6 Income Determination II --- The IS-LM Model

© Pilot Publishing Company Ltd Assumptions of the IS-LM Model What is the IS curve? Graphical derivation of the IS curve Slope of the IS curve Shift of the IS curve What is the LM curve? Graphical derivation of the LM curve Slope of the LM curve Contents:

© Pilot Publishing Company Ltd Shift of the LM curve Equilibrium in both the goods market and money marketEquilibrium in both the goods market and money market Change in equilibrium caused by an autonomous change in injection or withdrawalChange in equilibrium caused by an autonomous change in injection or withdrawal Change in equilibrium caused by an autonomous change in money demandor money supplyChange in equilibrium caused by an autonomous change in money demandor money supply Contents:

© Pilot Publishing Company Ltd Assumptions of the IS-LM Model

© Pilot Publishing Company Ltd Assumptions of the IS-LM model: 1. Y f is a constant. 2. An unemployment of resources. -- The model is to find out determinants of the equilibrium GNP and ways to eliminate unemployment. 3. GNP = GDP = Y. 4. Price level is kept constant. -- Nominal variables = real variables and nominal r = real r.

© Pilot Publishing Company Ltd Keynesian models Keynesian model Markets involvedEndogenous variables Y-E model (elementary Keynesian model) Goods marketY IS-LM model Goods market Money market Y and r AD-AS model Goods market Money market Factor market Y, r and P

© Pilot Publishing Company Ltd What is the IS Curve?

© Pilot Publishing Company Ltd  IS Curve is a line relating real national income (Y) to real interest rate (r) at which the goods market is in equilibrium (i.e., with Y = E or J = W). What is the IS Curve?

© Pilot Publishing Company Ltd Graphical Derivation of the IS Curve

© Pilot Publishing Company Ltd r Y W J 0 Quadrant II (NW quadrant) Quadrant III (SW quadrant) Quadrant IV (SE quadrant) Four-quadrant diagram Quadrant I (NE quadrant)

© Pilot Publishing Company Ltd r J J=I+G+X r J Injection function: J = I + G + X Quadrant II (NW quadrant) G and X are autonomous. Thus, J is negatively related to r. 0 I is negatively related to r.

© Pilot Publishing Company Ltd W W=S+T+M Y W Withdrawal function W = S + T + M S, T and M are positively related to Y Thus, W is positively related to Y Quadrant IV (SE quadrant) Y 0

© Pilot Publishing Company Ltd J1J1 J=W 45 o W J W 1 (= J 1 ) Quadrant III (SW quadrant) 0 J and W of points on the 45° line are equal. Hence they represent equilibrium in the goods market, where J = W.

© Pilot Publishing Company Ltd o r Y W J 0 A r0r0 J0J0 W0W0 Y0Y0 B IS When interest rate = r 0 injection = J 0 Corresponding national income = Y 0 Equilibrium in goods market To achieve equilibrium: J 0 = W 0

© Pilot Publishing Company Ltd Slope of the IS Curve

© Pilot Publishing Company Ltd IS Y1Y1 r1r1 r Y Y0Y0 r0r0 0 Initial goods market equil.: (Y 0, r 0 ) Downwar d sloping 1. If r  ( r 0 to r 1 )  J  ( J 0 to J 1 )  So at point Z, J > W 2. To restore equil., Y should  (Y 0 to Y 1 ) to raise W until W = J again. Z  r & Y are negatively related.

© Pilot Publishing Company Ltd Shift of the IS Curve

© Pilot Publishing Company Ltd r Y 0 IS 0 A (Y 0,r 0 ) B (Y 1,r 0 ) Assumption: An autonomous  in J or  in W (not caused by changes in r or Y) IS 1  J > W  Y has to  to Y 1 If r remains constant, Y has to  to Y 1 until W  & equates with J again.  IS curve shifts rightward to restore equilibrium.

© Pilot Publishing Company Ltd Assumption: An autonomous  in J or  in W (not caused by changes in r or Y)  J > W  r has to  to r 1 If Y remains constant, r has to  to r 1 until J  & equates with W again.  IS curve shifts upward to restore equilibrium. r Y 0 IS 0 IS 1 C (Y 0,r 1 ) A (Y 0,r 0 )

© Pilot Publishing Company Ltd IS 2 r Y 0 IS 0 A (Y 0,r 0 ) E (Y 0, r 2 ) D (Y 2, r 0 )  J < W  IS curve shifts leftward or downward to restore equilibrium. Assumption: An autonomous  in J or  in W (not caused by changes in r or Y)

© Pilot Publishing Company Ltd Q6.2: Derive from four-quadrant diagrams the change in the IS curve, (a) when there is an autonomous rise in J. (b) when there is an autonomous fall in J. (c) when there is an autonomous rise in W. (d) when there is an autonomous fall in W.

© Pilot Publishing Company Ltd ResultPossible causes Rightward (upward) shift of the IS curve Leftward (downward) shift of the IS curve Q6.3: Fill in the following table. W  autonomously J  autonomously W  autonomously J  autonomously

© Pilot Publishing Company Ltd What is the LM Curve?

© Pilot Publishing Company Ltd What is the LM Curve?  LM curve is a line relating real national income (Y) to real interest rate (r) at which the money market is in equilibrium [i.e.,with real money demand (M d ) or real liquidity preference (L) = real money supply (M s )].

© Pilot Publishing Company Ltd Graphical derivation of the LM Curve

© Pilot Publishing Company Ltd Transactions demand for money:  d is the change in M t resulting from a unit change in income.  Income & M t are positively related & so d > 0. M t = dY Income elasticity of transactions demand for money

© Pilot Publishing Company Ltd Asset demand for money:  e is the change in M a resulting from a unit change in r  e < 0 M a = e r + M a * Interest elasticity of asset demand for money Autonomous asset demand for money  M a * is the autonomous asset demand for money  M a * > 0

© Pilot Publishing Company Ltd Money supply function M1 is the sum of legal tender in public circulation and demand deposits General price level

© Pilot Publishing Company Ltd r Y MtMt MaMa 0 Quadrant II (NW quadrant) Quadrant III (SW quadrant) Quadrant IV (SE quadrant) Four-quadrant diagram Quadrant I (NE quadrant)

© Pilot Publishing Company Ltd r MaMa r MaMa M a = er + M a * 0 Asset demand for money M a is negatively related to r Quadrant II (NW quadrant)

© Pilot Publishing Company Ltd Y MtMt Y MtMt M t = dY Transactions demand for money M t is positively related to Y Quadrant IV (SE quadrant)

© Pilot Publishing Company Ltd M1/P = M s = M a +M t MaMa MtMt 45 o M1/P Equil. Condition: (M d =M s ) MaMa M t = M1/P - M a MtMt Quadrant III (SW quadrant) If M t = M1/P - M a, then M t + M a = M d = M1/P = M s

© Pilot Publishing Company Ltd r Y MtMt MaMa 0 45 o LM M a0 M t0 Y0Y0 r0r0 When interest rate = r 0 assets demand = M a0 In Equilibrium: M t0 = M s – M a0  M a0 + M t0 = M s Corresponding national income = Y 0 A B Equilibrium in money market

© Pilot Publishing Company Ltd Slope of the LM Curve

© Pilot Publishing Company Ltd Assume initial money market equil.: (Y 0, r 0 ) If Y  (Y 0 to Y 1 )  M t  ( M t0 to M t1 )  At point Z, M d > M s To restore equilibrium, r should  ( r 0 to r 1 ) such that M a  & M t + M a equates with M s again.  r & Y are positively related r0r0 Y0Y0 r Y Y1Y1 r1r1 0 Upward sloping LM Z

© Pilot Publishing Company Ltd Shift of the LM Curve

© Pilot Publishing Company Ltd B (Y 1,r 0 ) r Y 0 A (Y 0,r 0 ) LM 0 LM 1 Assumption: An autonomous  in M d or  in M s (not caused by changes in r or Y)  M d > M s If r remains constant, Y has to  to Y 1 such that M t  and M d = M s again.  LM curve shifts leftward to restore equilibrium.

© Pilot Publishing Company Ltd Assumption: An autonomous  in M d or  in M s (not caused by changes in r or Y)  M d > M s If Y remains constant, r has to  to r 1 such that M a  and M d = M s again.  LM curve shifts upward to restore equilibrium C (Y 0,r 1 ) r Y 0 A (Y 0,r 0 ) LM 0 LM 1

© Pilot Publishing Company Ltd r Y 0 A(Y 0,r 0 ) LM 0 LM 2 E (Y 0,r 2 ) D (Y 2,r 0 )  M d < M s  LM curve shifts rightward or downward Assumption: An autonomous  in M d or  in M s (not caused by changes in r or Y)

© Pilot Publishing Company Ltd Q6.4: Derive from four-quadrant diagrams, the change in the LM curve (a) when there is an autonomous rise in M a. (b) when there is an autonomous fall in M a. (c) when there is an autonomous rise in M t. (d) when there is an autonomous fall in M t. (e) when there is an autonomous rise in M s. (f) when there is an autonomous fall in M s.

© Pilot Publishing Company Ltd ResultPossible causes Rightward (downward) shift of the LM curve Leftward (upward) shift of the LM curve Q6.5: Fill in the following table. M d  autonomously M s  autonomously M d  autonomously M s  autonomously

© Pilot Publishing Company Ltd Equilibrium in Both the Goods Market and Money Market

© Pilot Publishing Company Ltd r Y 0 IS A(J = W) B(J < W) Goods market equilibrium and the IS curve There is an unintended inventory investment. Firms cut production & Y . Pt. B lies above pt. A. At pt. B, r   J   At pt. B, J < W

© Pilot Publishing Company Ltd r Y 0 IS A(J = W) C(J > W) There is an unintended inventory disinvestment. Firms raise production & Y . Goods market equilibrium and the IS curve Pt. C lies below pt. A. At pt. C, r   J   At pt. C, J > W

© Pilot Publishing Company Ltd r Y 0 Money market equilibrium and the LM curve LM B (M d < M s ) A (M d =M s ) Pt. B lies above pt. A. At pt. B, r   M a   At pt. B, M d < M s With excess money balance, people buy bonds to earn interest. Bond price   r 

© Pilot Publishing Company Ltd C( M d > M s ) Pt. C lies below pt. A. At pt. C, r   M a   At pt. C, M d > M s With excess money demand, people sell bonds for liquidity. r Y 0 LM A (M d =M s ) Money market equilibrium and the LM curve Bond price   r 

© Pilot Publishing Company Ltd Adjustment towards twin equilibrium 1. Whenever a point is not on the IS curve, Y will change until it reaches the IS curve. 2. Whenever a point is not on the LM curve, r will change until it reaches the LM curve.

© Pilot Publishing Company Ltd r Y 0 LM IS J<W  Y  M d <M s  r  J>W  Y  M d >M s  r  J>W  Y  M d <M s  r  J<W  Y  M d >M s  r  Adjustment towards twin equilibrium

© Pilot Publishing Company Ltd Change in Equilibrium Caused by an Autonomous Change in Injection or Withdrawal

© Pilot Publishing Company Ltd Crowding-out effect r Y 0 LM 0 IS 1 IS 0 r1r1 r0r0 Y1Y1 Y0Y0 Y’ } Transmission mechanism: Autonomous J  or W   As J > W  Y   W  & M t   M d > M s  r   M a  & J   Until both markets restore equil. IS curve shifts rightward

© Pilot Publishing Company Ltd Q6.6: When J < W, both income and interest rate fall. Describe the transmission mechanism.

© Pilot Publishing Company Ltd Change in Equilibrium Caused by an Autonomous Change in Money Demand or Money Supply

© Pilot Publishing Company Ltd Transmission Mechanism: Y1Y1 r1r1 LM 1 r Y 0 IS 0 LM 0 r0r0 Y0Y0 As M d > M s  r   M a  & J  Autonomous M d  or M s   LM curve shifts leftward  J < W  Y   W  & M t   Until both markets restore equil.

© Pilot Publishing Company Ltd Q6.7: When M d < M s, income rises and interest rate falls. Describe the transmission mechanism.

© Pilot Publishing Company Ltd Q6.8: (a) Suppose there exist an autonomous increase in J and an autonomous increase in M s. Predict the change in Y and r with the aid of an IS-LM diagram. (b) Suppose there exist an autonomous increase in W and an autonomous increase in M s. Predict the change in Y and r with the aid of an IS-LM diagram.

© Pilot Publishing Company Ltd Mathematical derivation of the IS-LM equilibrium In a four sector economy, E = C + I + G + X – M 1. Mathematical derivation of the IS curve where C = cY d +C*; Y d = Y-tY-T*+qY+Q*; I = br+I*+iY; G= G*; X = X*; M = mY+M*

© Pilot Publishing Company Ltd Mathematical derivation of equil. income & multiplier  Y = cY d +C* +br+I*+iY + G* +X*-mY-M*  Y = c(Y-tY-T*+qY+Q*)+C* +br+I*+iY +G*+X*-mY-M*  (1–c-i+ct-cq+m)Y = C*+ I*+ G*+ X*-M*-cT*+cQ* +br 1. Mathematical derivation of the IS curve Equation of IS curve: Y = E = C+I+G+X-M  r = (1)

© Pilot Publishing Company Ltd Given M d = M t + M a ; M s = M1/P where M t = dY & M a = er + M a *  dY + er +M a * = M1/P  er = -dY + (M1/P – M a *) 2. Mathematical derivation of the LM curve Equation of a LM curve: M d = M t + M a = M s  r = (2)

© Pilot Publishing Company Ltd Sub. equation (1) into (2), the equil. income can be found. =A*

© Pilot Publishing Company Ltd IS-LM multiplier Note: As b 0 and e 0  IS-LM multiplier is smaller than Y-E multiplier, because  When there is a rise in autonomous E, Y  With money market, Y   M t  & disturb money market  As M d > M s, r  and crowds out private investment  Overall  in equilibrium income is smaller.

© Pilot Publishing Company Ltd Correcting Misconceptions: 1. The IS curve represents situations with I = S. 2. Whenever J  or W , the IS curve shifts rightward or upward. 3. Whenever M d  or M s , the LM curve shifts leftward or upward.