# 1 IS-LM Model LM Function. 2 Outline Introduction Assets Market Bond Market Money Market Money Demand Md = Mt + Ma Transaction Demand Mt = dY Asset Demand.

## Presentation on theme: "1 IS-LM Model LM Function. 2 Outline Introduction Assets Market Bond Market Money Market Money Demand Md = Mt + Ma Transaction Demand Mt = dY Asset Demand."— Presentation transcript:

1 IS-LM Model LM Function

2 Outline Introduction Assets Market Bond Market Money Market Money Demand Md = Mt + Ma Transaction Demand Mt = dY Asset Demand Ma = Ma - er Money Supply Ms = Ms Money Market Equilibrium Md = Ms

3 Outline Deriving the LM Function Graphical Approach 4-quadrant Horizontal Summation of Mt and Ma Simple Algebra Slope of the LM Curve d/e Income Elasticity of Money Demand d Interest Elasticity of Money Demand e

4 Outline Shift of the LM Curve Change in the Money Supply Ms Change in the Money Demand Change in the Asset Demand for Money Ma Change in the Transaction Demand for Money d Interest Rate and Income Determination Equilibrium in the Goods Market (IS) & Assets / Money Market (LM) Simple Algebra of the IS-LM Model

5 Outline Implications of the IS-LM Model Effects of a change in IS E or T Effects of a change in LM Ms or Md Disequilibrium in the goods market in the money market

6 Introduction In the goods market, the IS curve is the loci of different combinations of interest rate and income that satisfy the equilibrium condition (W = J) In the assets market, the LM curve is the loci of different combinations of interest rate and income that satisfy the equilibrium condition (Ms = Md)

7 Introduction Accordingly, we can determine the interest rate and income that satisfy the equilibrium conditions of both the goods market (W = J) and assets market (Ms = Md) Still, the labour market may not be in equilibrium. There may be labour shortage (Y > Yf) or unemployment (Y < Yf)

8 Assumption In this short-run IS-LM model, we still assume the price level is fixed. Hence, nominal income (Y) equals real income (Q) & nominal money balances (M) equals real money balances (m = M/P)

9 Assets Market An individual has to face the choice of allocating his financial wealth into different assets, like money, bonds, stocks and foreign currencies. Here, only two types of assets, money and bonds are considered. It is assumed that an individual will store his financial wealth in either money or bonds

10 Assets Market Money Market & Bond Market The equilibrium condition of the assets market is that the supply of financial assets equals the demand for financial assets Assets Supply=Money Supply+Bond Supply Assets Demand=Money Demand+Bond Demand In equilibrium, Assets Supply = Assets Demand Ms + Bs = Md + Bd

11 Assets Market Money Market & Bond Market Assets Market can be divided into money market and bond market If the money market is in equilibrium, i.e., Ms = Md The bond market will also be in equilibrium, i.e., Bs = Bd Thus, in the IS-LM model, only the money market is considered.

12 Money Market Money Supply Ms In the IS-LM model, money supply is postulated as an exogenous function, whose value is determined by the monetary authority. Ms = Ms Besides, there is no difference between nominal money supply and real money supply

13 Money Market Money Demand Md In the IS-LM model, money demand Md consists of transactions demand Mt and asset demand Ma Mt is assumed to be positively related to income Ma is assumed to be negatively related to interest rate. Thus, Md is hypothesised to be a function of both income and interest rate Md = f(Y, r)

14 Money Demand Transactions Demand Mt Money serves as the medium of exchange. The higher the level of real / nominal income, the higher will be the transactions demand for money (real balances) Mt = dYd > 0 The coefficient d is the income elasticity of money demand. Mt/ Y = d

15 Money Demand Transactions Demand Mt Y Mt Mt = dY Slope of ray = slope of tangent = d

16 Money Demand Transactions Demand Mt It is upward sloping as Mt is positively related to income Y. A change in income Y will lead to a movement along the Mt curve, an induced change Mt When there is a rise in transactions demand d for money, the slope of the Mt curve will be larger, Mt is steeper

17 Money Demand Transactions Demand Mt Factors affecting Mt Pay period shortened Mt flatter, d Method 1: \$100 daily Average money holding = Method 2: \$700 weekly Average money holding = The use of Credit Cards Mt flatter, d

18 Money Demand Asset Demand Ma Liquidity is a measure of an asset s capacity to be rapidly resold at a price close to its purchase price. An asset is liquid if it can easily and quickly be converted into cash at low cost. Money is the most liquid asset. Also, holding money involves lower risk compared with other assets

19 Money Demand Asset Demand Ma However, having a bank balance or a stock of cash involves cost as it yields no interest earnings. Conversely, bonds yield interest earnings. Moreover, there may be capital gain/loss

20 Money Demand Asset Demand Ma Suppose all bonds are perpetuities (i.e. pay interest forever and never repay the principal) P = I/r P: the price of bond I: Interest earnings r: Market interest rate When r is expected to fall, P is expected to rise, and vice versa. That means there ll be capital gain

21 Money Demand Asset Demand Ma Ma r When r is relatively high, holding bonds yield large interest returns And r is expected to fall, Price of bonds is expected to rise, holding bonds can reap capital gain More bonds will be held Hence, demand for money as an asset will be less *

22 Money Demand Asset Demand Ma Ma r When r is relatively low, holding bonds yield less interest returns And r is expected to rise, Price of bonds is expected to fall, holding bonds will suffer capital loss. Less bonds will be held Hence, demand for money as an asset will be greater *

23 Money Demand Asset Demand Ma When r rises, the cost of holding money will increase. Thus, people will hold less cash. That explains why the asset demand for money Ma is postulated as negatively related to r Ma = Ma - er e >0

24 Money Demand Asset Demand Ma The coefficient e is defined as the interest elasticity of money demand e = Ma/ r It measures the responsiveness of money demand to interest rate. The more interest elastic is the asset demand for money, the greater will be the fall in asset demand as a result of a rise in interest rate

25 Money Demand Asset Demand Ma r Ma Ma = Ma - er x-intercept = Ma1 Ma2 Ma1 is more interest elastic e is larger, i.e., Ma is larger given a certain r 1/e is smaller, i.e., Ma1 is flatter

26 Money Demand Asset Demand Ma It is downward sloping because r and Ma are negatively related. A change in interest rate r will cause a movement along the Ma curve, i.e., an induced change Ma A change in the autonomous asset demand for money Ma will shift the Ma curve

27 Money Demand Asset Demand Ma r Ma The more interest elastic is the asset demand, the flatter will be the Ma curve r e = e = 0

28 Digression Price elasticity of demand Ed = ( Qx d /Qx d )/( Px/Px) =slope of ray/slope of tangent Price elasticity of supply Es = ( Qx s /Qx s )/( Px/Px) Income elasticity of demand Ei= ( Qx d /Qx d )/( I/I) Cross elasticity of demand Exy= ( Qx d /Qx d )/( Py/Py) Goods x and y can be substitutes or complements

29 Digression Autonomous Consumption a Interest Elasticity of Investment b = I/ r Marginal Propensity to Consume c = C/ Y Income Elasticity of Money Demand d = Mt/ Y Interest Elasticity of Money Demand e = Ma/ r Marginal Propensity to Invest i = I/ Y Marginal Propensity to Import m = M/ Y Marginal Propensity to Save s = S/ Y Proportional Tax Rate t = T/ Y

30 Digression Expenditure Multiplier k E = Y/ E = Y/ C = Y/ I = Y/ G = Y/ X = Y/ M Tax Multiplier k T = Y/ T Balanced Budget Multiplier k B = k E + k T = Y/ G + Y/ T

31 Deriving the LM Function Money market equilibrium In money market equilibrium, Ms = Md Ms=Ms Ma=Ma - er Mt=dY Md=Ma + Mt=Ma - er + dY Ms =Ma + Mt

32 Deriving the LM Function Money market equilibrium Mt Ma If Ms = Ms = \$1bn, Ms = Mt + Ma If Ma = 0, Mt = It Mt = 0, Ma = 45 A \$1 increase in Mt implies a \$1 decrease in Ma given Ms = Ms A movement along the 45 line

33 Deriving the LM Function Money market equilibrium Mt Ma The 45 line is the loci of Mt and Ma which represents money market equilibrium, i.e., Ms = Md * Ms = Md = Ma + Mt * Ms < Md = Ma + Mt * Ms > Md = Ma + Mt * *

34 Deriving the LM Function Money market equilibrium Excess Money Demand Excess Money Supply Mt Ma Mt Excess Money Excess Money What happens if Ms = Ms increases?

35 Deriving the LM Function 4-Quadrant Method Mt MaY Refer slide 15 Mt = dY What happens if d ?

36 Deriving the LM Function 4-Quadrant Method Ma r Refer slide 25 Ma = Ma - er What happens if theres Ma or e ?

37 Deriving the LM Function 4-Quadrant Method r Ma Mt r1r1 Ma 1 Mt 1 Y1Y1 * r2r2 Ma 2 Mt 2 Y2Y2 * LM Curve Y

38 LM Function Suppose the money market is initially in equilibrium with Ms = Md. Holding Ms constant, a rise in Y will lead to a rise in Mt since Mt = dY there ll be an excess demand for money Ms < Md = Mt + Ma

39 LM Function r will increase to reduce Ma in order to keep the money market in equilibrium since Ma = Ma - er Ms = Ms = Md = Mt + Ma This positive relationship between interest rate r and national income Y in the money market is represented by the upward sloping LM curve in slide 37

40 Deriving the LM Function Horizontal Summation r Md Since Mt = dY, the transactions demand for money is independent of r Mt 1 = dY 1 Mt 2 = dY 2 When Y increases, Mt will rise at all levels of interest rate

41 Deriving the LM Function Horizontal Summation r Ma, Mt, Md Ma = Ma - er Mt 1 = dY 1 Md = Ma + Mt If Y increases, Mt increases Mt 2 = dY 2

42 Deriving the LM Function Horizontal Summation Md, Ms r Md 1 = Ma - er + d Y 1 Md 2 = Ma - er + d Y 2 Ms = Ms r1r1 r2r2 Y r

43 Deriving the LM Function Horizontal Summation r Y Y1Y2 r1 r2 LM

44 Simple Algebra of the LM Ms = Ms Mt = dYMa = Ma - er Md = Mt + Ma In equilibrium, Ms = Md

45 Simple Algebra of the LM Money Market Y = r = slope of the LM curve = r/ Y = Goods Market Y = r = slope of the IS curve = r/ Y =

46 Slope of the LM curve d/e The smaller d, the flatter LM If there is a decrease in d (= Mt/ Y), the increase in Mt will be smaller given any rise in income The excess demand will be smaller a smaller increase in r, which reduces Ma, is enough to restore equilibrium in the money market

47 Slope of the LM curve d/e The larger e, the flatter LM If there is an increase in e (= Ma/ r), the decrease in Ma will be larger, given any increase in interest The excess supply will be larger A larger increase in Y, which increases Mt, is required to restore equilibrium in the money market.

48 Revision Slope of the IS curve -s/b The smaller s, the flatter IS the increase in saving (s = S/ Y) is smaller given any increase in income excess supply is smaller a smaller decrease in interest rate, which increases investment, is required to restore equilibrium in the goods market The larger b, the flatter IS The increase in investment (b= I/ r) is larger, given any decrease in interest rate, excess demand is larger a larger increase in income, which increases saving, is required to restore equilibrium in the goods market

49 The smaller d, the flatter LM r Ma Mt r1r1 Ma 1 Mt 1 Y1Y1 * r2r2 Ma 2 Mt 2 Y2Y2 * Steeper LM Y Y * Flatter LM

50 The larger e, the flatter LM r Ma Mt r1r1 Ma 1 Mt 1 Y1Y1 * r2r2 Ma 2 Mt 2 Y2Y2 * Steeper LM Y Y * Flatter LM

51 Two extreme cases Smaller slope, flatter LM slope = d/e = 0 d = e = r Y Y r Larger slope, steeper LM slope = d/e = d = e =

52 Shift of the LM Curve Y = when r = 0, Y = which is the x-intercept of the LM curve If there is a change in money supply Ms or money demand Ma the LM curve will shift.

53 Shift of the LM Curve Increase in Ms r Ma Mt r1r1 Ma 1 Mt 1 Y1Y1 * r2r2 Ma 2 Mt 2 Y2Y2 * LM Curve Y

54 Shift of the LM Curve Increase in Ms LM equation, Y = If we differentiate the equation w.r.t. Ms Y/ Ms = 1/d OR Y= Ms /d

55 Shift of the LM Curve Decrease in Ma r Ma Mt r1r1 Ma 1 Mt 1 Y1Y1 * r2r2 Ma 2 Mt 2 Y2Y2 * LM Curve Y

56 Shift of the LM Curve Decrease in Ma LM equation, Y = If we differentiate the equation w.r.t. Ma Y/ Ma = - 1/d OR Y= - Ma /d

57 Interest Rate & Income Determination refer slide 6 r Y LM slope = x-intercept = IS slope = x-intercept = rere Ye

58 Simple Algebra of the IS-LM Model Refer slide 45 Do the following past paper questions.

59 1999 A#6 Refer to the following information about an economy C = 600 + 0.75YC = consumption expenditure I = 400 - 4000rY = national income Mt = 0.25YI = investment expenditure Ma = 190 - 600rr = interest rate Ms = 500Mt = transaction demand for money Ma = asset demand for money Ms = money supply The equilibrium levels of income and interest rate in this economy are ___ and ___ respectively. A. 1200..17.5%C. 1600..15% B. 1500..20%D. 1800..13.75%

60 Implications of the IS-LM Model Effect of a change in IS: E X - intercept = r Y If there is a +ve G, the IS curve will shift to the right by the amount of k E G With an upward-sloping LM, both r and Y will increase

61 Implications of the IS-LM Model Effect of a change in IS: T X - intercept = r Y If there is a -ve T, the IS curve will shift to the right by the amount of -c k E T With an upward-sloping LM, both r and Y will increase

62 Implications of the IS-LM Model Effect of a change in LM: Ms r Y X - intercept If there is a +ve Ms, the LM curve will shift to the right by the amount of Ms/d With a downward-sloping IS, r will decrease but Y will increase

63 Implications of the IS-LM Model Effect of a change in LM: Ma r Y X - intercept If there is a -ve Ma, the LM curve will shift to the right by the amount of - Ma/d With a downward-sloping IS, r will decrease but Y will increase

64 2000 A#5 Which of the following will lead to a leftward shift of an LM curve? A. A fall in interest rate B. more widespread use of credit cards C. an increase in the liquidity preference D. a decrease in national income

65 2000 A#12 If the amount of money held for transaction purposes is 40% of the national income, then a \$200 increase in the money supply will lead to a rightward shift in the LM curve by an amount of A. \$80 B. \$200 C. \$250 D. \$500

66 2000 A#13 An increase in the marginal propensity to consume would result in A. a parallel shift of the IS curve to the right B. a parallel shift of the IS curve to the left C. a flatter IS curve D. a steeper IS curve

67 2000 A#14 In the IS-LM model, if there is a simultaneous cut in government expenditure and money supply, then A. national income will decrease while interest rate will rise B. national income will decrease while interest rate will fall C. interest rate can either rise or fall D. national income can either increase or decrease

68 2000 A#15 Which of the following concerning the value of a bond is correct? A. The closer to maturity the bond is, the greater will be the change in its value for a change in interest rate. B. The further to maturity the bond is, the greater will be the change in its value for a change in interest rate. C. A change in interest rate will not affect the value of a bond. D. The impact of a change in interest rate on the value of the bond does not depend on its maturity date.

69 2000 A#21 In the IS-LM model, which of the following are correct if investment is independent of interest rate? (1) An increase in money supply will have no effect on national income (2) An increase in money supply will have no effect on interest rate. (3) An increase in government expenditure will lead to an increase in interest rate A. (1) and (2) onlyC. (2) and (3) only B. (1) and (3) onlyD. (1), (2) and (3)

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