Chapter 6 Income Determination II --- The IS-LM Model

1. Chapter 6 Income Determination II --- The IS-LM Model

2. Contents: • 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

3. Contents: • Shift of the LM curve • Equilibrium in both the goods market and money market • Change in equilibrium caused by an autonomous change in injection or withdrawal • Change in equilibrium caused by an autonomous change in money demandor money supply

4. Assumptions of the IS-LM Model

5. Assumptions of the IS-LM model: 1. Yf 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.

6. Keynesian models

7. What is the IS Curve?

8. What is the IS Curve? • 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).

9. Graphical Derivation of the IS Curve

10. Four-quadrant diagram r Quadrant II (NW quadrant) Quadrant I (NE quadrant) 0 Y J Quadrant III (SW quadrant) Quadrant IV (SE quadrant) W

11.   Quadrant II (NW quadrant) r Injection function:J = I + G + X J G and X are autonomous. r Iis negatively related to r. Thus,Jisnegatively relatedtor. J=I+G+X J 0

12. Y  W  Quadrant IV (SE quadrant) 0 Y Withdrawal function W = S + T + M S, Tand Mare positively related to Y Thus, W is positively related to Y W=S+T+M W

13. 45o J=W Quadrant III (SW quadrant) J1 0 J J and W of points on the 45° line are equal. Hence they represent equilibrium in the goods market, whereJ = W. W1(= J1) W

14. r Equilibrium in goods market 0 IS J Y W A When interest rate = r0 injection = J0 r0 B J0 Y0 45o W0 To achieve equilibrium:J0 = W0 Corresponding national income = Y0

15. Slope of the IS Curve

16. r r0 Z Y 0 Y0 Initial goods market equil.: (Y0, r0) Downward sloping 1. If r ( r0 to r1) J ( J0 to J1) • So at point Z, J > W 2.To restore equil., Y should (Y0 to Y1) to raise W until W = J again. • r & Y are negatively related. r1 IS Y1

17. Shift of the IS Curve

18. r B (Y1,r0)   A (Y0,r0) IS1 IS0 Y 0 Assumption: An autonomous  in J or  inW (not caused by changes in r or Y) • J > W  If r remains constant, Y has to  to Y1 until W  & equates with J again.  IS curveshifts rightward to restore equilibrium.

19. r C (Y0,r1)  IS1 IS0 Y 0 Assumption: An autonomous  in J or  in W (not caused by changes in r or Y) • J > W  If Y remains constant, r has to  to r1 until J  & equates with W again.   IS curve shifts upward to restore equilibrium. A (Y0,r0)

20.  D (Y2, r0) E (Y0, r2)  IS2 Assumption: An autonomousin J or in W (not caused by changes in r or Y) r • J < W  IS curve shiftsleftward or downwardto restore equilibrium. A (Y0,r0)  IS0 Y 0

21. 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.

22. Q6.3: Fill in the following table. J autonomously W autonomously J autonomously W autonomously

23. What is the LM Curve?

24. What is the LM Curve? • LM curveis 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 (Md) or real liquidity preference (L) = real money supply (Ms)].

25. Graphical derivation of the LM Curve

26. Income elasticity of transactions demand for money Transactions demand for money: Mt = dY • dis the change in Mt resulting from a unit change in income. • Income & Mt arepositively related& sod > 0.

27. Interest elasticity of asset demand for money Autonomous asset demand for money Asset demand for money: Ma = e r + Ma* • e is the change in Maresulting from a unit change in r • e < 0 • Ma* is the autonomous asset demand for money • Ma* > 0

28. Money supply function M1is the sum of legal tender in public circulation and demand deposits General price level

29. Four-quadrant diagram r Quadrant II (NW quadrant) Quadrant I (NE quadrant) 0 Y Ma Quadrant III (SW quadrant) Quadrant IV (SE quadrant) Mt

30. Ma  r  Ma = er + Ma* Quadrant II (NW quadrant) r Asset demand for money Mais negatively related to r Ma 0

31. Y  Mt  Mt = dY Quadrant IV (SE quadrant) Y Transactions demand for money Mtis positively related to Y Mt

32. Mt = M1/P - Ma Mt 45o Quadrant III (SW quadrant) Ma M1/P Ma  Equil. Condition: (Md=Ms ) If Mt = M1/P - Ma, then Mt + Ma = Md = M1/P= Ms M1/P = Ms = Ma+Mt M1/P Mt

33. r LM Equilibrium in money market 0 Y Ma Mt When interest rate = r0 assets demand = Ma0 B A r0 Ma0 Y0 Mt0 • In Equilibrium: • Mt0 = Ms – Ma0 • Ma0 + Mt0 = Ms Corresponding national income = Y0 45o

34. Slope of the LM Curve

35. Z Assume initial money market equil.: (Y0, r0) r If Y(Y0 to Y1) Mt ( Mt0 to Mt1) • At point Z, Md > Ms Upward sloping LM To restore equilibrium, r should ( r0 to r1 ) such that Ma & Mt + Ma equates with Ms again. r1 r0 • r & Y are positively related Y 0 Y1 Y0

36. Shift of the LM Curve

37. r LM1 LM0  A (Y0,r0) 0 Y Assumption:An autonomous  in Md or in Ms (not caused by changes in r or Y) • Md > Ms If r remains constant, Y has to  to Y1such that Mt and Md = Ms again. B (Y1,r0)  • LM curveshifts leftward to restore equilibrium.

38. r LM1 LM0  A (Y0,r0) Y 0 Assumption:An autonomous  in Md or  in Ms (not caused by changes in r or Y) • Md > Ms If Y remains constant, r has to to r1 such that Ma and Md = Ms again. C (Y0,r1)  • LM curveshifts upward to restore equilibrium

39. r LM2  D (Y2,r0)  E (Y0,r2) Y 0 Assumption:An autonomous  in Md or in Ms (not caused by changes in r or Y) LM0 • Md < Ms A(Y0,r0)  LM curveshifts rightwardordownward 

40. Q6.4: Derive from four-quadrant diagrams, the change in the LM curve (a) when there is an autonomous rise in Ma. (b) when there is an autonomous fall in Ma. (c) when there is an autonomous rise in Mt. (d) when there is an autonomous fall in Mt. (e) when there is an autonomous rise in Ms. (f) when there is an autonomous fall in Ms.

41. Q6.5: Fill in the following table. Mdautonomously Msautonomously Mdautonomously Msautonomously

42. Equilibrium in Both the Goods Market and Money Market

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

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

45. r Y 0 Money market equilibrium and the LM curve Pt. B lies above pt. A. At pt. B, r  Ma At pt. B, Md < Ms With excess money balance, people buy bonds to earn interest. B (Md < Ms)  A (Md=Ms)  Bond price r  LM

46. r C( Md > Ms)  Y 0 Money market equilibrium and the LM curve With excess money demand, people sell bonds for liquidity. LM Bond price r  A (Md=Ms) Pt. C lies below pt. A. At pt. C, r  Ma At pt. C, Md > Ms 

47. Adjustment towards twin equilibrium • 1. Whenever a point isnot on the IS curve, • Y will changeuntil it reaches the IS curve. 2. Whenever a point is not on the LM curve, r will change until it reaches the LM curve.

48. r LM IS Y 0 Adjustment towards twin equilibrium J<W  Y Md<Ms r  J>W  Y J<W  Y Md<Ms r Md>Ms r    J>W  Y Md>Ms r

49. Change in Equilibrium Caused by an Autonomous Change in Injection or Withdrawal

50. r Y 0 Transmission mechanism: Autonomous J or W  LM0 IS curve shifts rightward r1 As J > W YW & Mt r0  Md > MsrMa & J  Until both markets restore equil. IS1 IS0 } Y0 Y1 Y’ Crowding-out effect