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IS - LM Model By Wong Chuen-Ping

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**2 markets Goods Market Equilibrium: E = Y C + I = C + S I = S**

Money Market Equilibrium: Md = Ms

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**The Goods Market S = 0.2Y - 40 I = 260 - 2000r 0.2Y - 40 = 260 - 2000r**

In equilibrium: S = I 0.2Y - 40 = r Y = r IS equation Y S I r 60 0.10 700 100 0.08 900 140 1100 180 0.04 1300 220 0.02 260 500 0.06 1500

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The Goods Market Y = r

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IS curve IS curve shows all the combinations of real national income (Y) and real interest rate (r) at which the goods market is in equilibrium.

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How to derive IS curve? r r1 r2 I IS I2 I1 Y1 Y2 I 450 Y S1 S2 S S

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**ED & ES in product market**

I=S E=Y ES S>I Y>E ED C A B (Y , S ) (Y . S ) S<I IS Y<E Y

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**Disequilibrium in product market**

E=Y ES I<S E<Y ED I>S E>Y IS Y

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r r The IS Curve IS r1 r2 I Y I1 I2 Y1 Y2 I S S 45 S2 S S1 Y I

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**IS Curve IS r S, I S I2 I1 Y Y at r1, investment = I1**

Lower r, higher I r IS S, I r1 S r2 I2 I1 Y Y Y1 Y2 Y1 Y2

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**The Money Market Ms =400 Mt = 0.25Y Ma = 250 – 2000r**

In equilibrium: Ms = Mt + Ma 400 = 0.25Y r Y = r LM equation Y Ms Mt Ma r 400 150 250 1000 1600 600 0.05 0.125

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The Money Market Y = r Y R 600 1000 05 1400 0.1

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LM curve LM curve shows all the combinations of real national income (Y) and real interest rate (r) at which the money market is in equilibrium.

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**How to derive LM curve? LM r r2 r1 Ma Y Mt Ma A1 A2 Y1 Y2 H O T1**

Ms=OH=OK T2 Mt K Mt

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**ED & ES in Money market ES ED LM Md<Ms Md>Ms Md=Ms r (Y . Mt ) C**

B (Y , Mt ) Md>Ms ED Y

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**Disequilibrium in Money market**

LM Md<Ms Md=Ms ES Md>Ms ED Y

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**r r The LM Curve LM Mt r2 r1 Y Ma Mt T2 T1 Y Ma Ma A2 A1 Y1 Y2 H Mt**

Ms=OH=OK Y Ma O K

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**LM Curve LM r r M Y at Y1, Md = Md1 at Y2, Md = Md2**

Higher Y, higher Md LM r r Ms r2 r2 r1 r1 Md2 Md1 M Y Y1 Y2

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**Equilibrium in Product & Money Market**

LM A r1 IS Y1 Y

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**Disquilibrium in Product & Money Market**

< I S r Ms Md > LM F > I S > < Ms Md I S J G < Ms Md H > < IS I S Ms Md Y

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**IS-LM Equations Goods Market Money Market C = 100 + 0.8Y**

I = r In equilibrium: Y = E = C + I IS equation: Y = r Money Market Ms = 300 Mt = 0.2Y Ma = r In equilibrium: Ms = Md =Mt + Ma LM equation: Y = r R = 0.1 i.e. 10% Y = 1300

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**IS-LM Equations r = 0.05 i.e. 5% Y = 1475 Goods Market Money Market**

C = Yd I = r G = 525 T = 20%(Y-100) IS equation ? Money Market Ms = 800 Mt = Y Ma = r LM equation ? Y = r Y = r r = i.e. 5% Y = 1475

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**Shifts in the IS curve I r1 r2 I2 I1 Y1 Y2 S1 S2 r IS2 I2 I1 IS1 I 450**

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**Increase in Investment ( or↑G)**

↑I, at same r, Y↑, IS shifts to the right r △Y =△I x A B r1 IS2 IS1 Y1 Y2 Y

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Shifts in the IS curve S r r1 IS2 I1 I1 Y1 Y2 IS1 I 450 Y S1 S2 S S1

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**Decrease in Saving ( or↓T)**

↓S, at same r, E↑, Y↑, IS shifts to the right r A B r1 IS2 IS1 Y1 Y2 Y

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Shifts in the LM curve LM1 r Ms LM2 r1 Ma A1 Y1 Ma Y T1 Mt Mt

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**Increase in Money Supply**

at same Y, ↑Ms, Ms > Md, r↓ LM1 r LM2 A r1 B Y1 Y LM shifts to the right

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**Increase in Money Supply**

↑Ms, at same r, Y↑, LM shifts to the right r LM1 △Y =△Ms x LM2 A r1 B Y1 Y2 Y

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Shifts in the LM curve LM1 r Mt LM2 r1 Ma A1 Y1 Ma Y O T1 Mt2 Mt1 Mt

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**Decrease in Mt LM shifts to the right at same Y, Mt↓, Ms > Md, r↓**

B Y1 Y LM shifts to the right

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Shifts in the LM curve LM2 r Ma LM1 r1 Ma2 Ma1 A1 Y1 Ma Y O T1 Mt1 Mt

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**Increase in Ma LM shifts to the left at same Y, Ma↑, Ms < Md, r↑**

B A r1 Y1 Y LM shifts to the left

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**Increase in Investment (↑G, ↑C)**

LM B r2 A r1 IS2 IS1 Y1 Y2 Y

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**Increase in Saving (↑Tax)**

LM A r1 B r2 IS1 IS2 Y2 Y1 Y

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**Increase in Money Supply (↓Md)**

LM1 LM2 A r1 B r2 IS Y1 Y2 Y

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**Increase in demand for Money (↓Ms)**

LM2 r LM1 B r2 A r1 IS Y2 Y1 Y

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**Slope of the IS curve & MPS**

r↓, I↑→↑Y (ΔY = ΔI x ) r larger MPS, steeper IS r1 Smaller MPS, flatter IS r2 IS2 IS1 Y Y1 Y2 Y3 Smaller MPS, greater multiplier, flatter IS

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**Slope of IS & Interest elasticity of I**

r↓, I↑, more interest elastic, larger ΔI, largerΔY Less interest elastic I, steeper IS r r1 More interest elastic I, r2 flatter IS IS2 IS1 Y Y1 Y2 Y3 more interest elastic investment, flatter IS

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**Slope of LM & Income elasticity of Mt**

Y↑, Mt↑, more income elastic Mt, larger ↑in Mt, largerΔr more income elastic Mt, steeper LM r Less income elastic Mt, r1 flatter LM LM1 LM2 Y Y1 Y2 more income elastic Mt, steeper LM

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**Slope of LM & Interest elasticity of Ma**

Y↑, Mt↑, Md > Ms, r↑to ↓Ma, less r elastic Ma, largerΔr less interest elastic Ma, steeper LM r more interest elastic Ma, r1 flatter LM LM1 LM2 Y Y1 Y2 less interest elastic Ma, steeper LM

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**Fiscal Policy - ↑G IS2 AF =ΔG x IS1 LM r B r2 A F r1**

Crowding-out effect Y1 Y2 Y

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**The crowding-out effect**

The crowding-out effect refers to the reduction in income resulting from an increase in interest rate. G E E >Y Y Mt Md > Ms r r I Y (crowding-out effect)

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**The crowding-out effect**

IS2 AF =ΔG x r IS1 LM B r2 A F r1 Crowding-out effect Y1 Y2 Y

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**Factors affecting the crowding-out effect**

condition of employment (unemployment, ? crowding-out effect) (full employment, ? Crowding-out effect) interest elasticity of demand for money, more interest elastic, smaller change in r, crowding-out effect ? interest elasticity of investment, less interest elastic, when r , smaller in I, crowding-out effect ? . smaller larger smaller smaller

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**Fiscal Policy - ↑Tax LM LM IS1 IS1 IS2 IS2 Lump sum tax ↑,**

r LM r LM A A r1 r1 B B r2 r2 IS1 IS1 IS2 IS2 Y2 Y1 Y Y2 Y1 Y Lump sum tax ↑, IS shifts left Tax rate↑, IS steeper

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**Fiscal Policy - Equal↑in G & T**

AF =ΔG = ΔT r IS1 LM B r2 A F r1 Crowding-out effect Y1 Y2 Y

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Monetary Policy - ↑Ms r LM1 LM2 A r1 B r2 IS Y1 Y2 Y

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**Fiscal & Monetary Policies - ↑Ms + ↑G**

B r1 A IS2 IS1 Y1 Y2 Y

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**Effectiveness of Monetary Policy & slope of IS**

Ms ↑→r↓→I↑, LM →right , more interest elastic (flatter IS), larger ↑I, larger↑Y smaller MPS (flatter Y), larger ↑Y r LM1 LM2 A r0 B r1 r2 C IS1 IS2 Y0 Y2 Y1 Y Monetary Policy is more effective if IS is flatter

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**Effectiveness of Fiscal Policy & slope of LM**

r↑smaller, crowding-out smaller G↑, IS →right , Y↑ → Mt↑, Mt less income elastic, Ma more interest elastic, r LM2 C r3 LM1 B r2 A r1 IS2 Crowding-out effect IS1 Y1 Y3 Y2 Y Fiscal Policy is more effective if LM is flatter

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**The LM Curve with liquidity trap**

Ma – perfectly interest elastic Horizontal LM LM r1 Ma Y1 Y2 Y Ma Mt Mt H Mt T1 Y Ma O K

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**The LM Curve with Ma perfectly interest inelastic**

vertical LM r2 Ma r1 Y1 Y Ma Mt Mt H Mt Y Ma O K

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**The IS Curve with perfectly interest inelastic I r r**

Investment perfectly interest elastic IS IS vertical r1 r2 I1 Y1 Y I S S 45 S S1 I Y

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**Horizontal LM G↑ Ms↑ IS2 IS1 IS1 LM Fiscal Policy effective**

B r1 r1 LM LM Y1 Y2 Y Y1 Y Fiscal Policy effective Monetary Policy ineffective

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**Vertical LM G↑ Ms↑ LM1 LM2 IS2 IS1 IS1 Fiscal Policy ineffective**

B IS2 A r1 r1 A B r2 IS1 IS1 Y1 Y Y1 Y2 Y Fiscal Policy ineffective Monetary Policy effective

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**Vertical IS G↑ Ms↑ LM1 IS1 IS2 LM2 IS Fiscal Policy effective**

B r2 r1 r1 B r2 A Y1 Y2 Y Y1 Y Fiscal Policy effective Monetary Policy ineffective

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**Horizontal IS G↑ Ms↑ LM1 LM2 IS Fiscal Policy ineffective**

B Y1 Y2 Y1 Y Y Fiscal Policy ineffective Monetary Policy effective

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