Chapter 10: AD part 1. The Keynesian Cross. Elements of the Keynesian Cross. the IS curve. the LM curve

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1 Chapte 10: AD pat 1 the IS cuve the LM cuve how the IS-LM model detemines and when P is fixed slide 0 The Keynesian Coss A simple closed economy model in which income is detemined by expenditue. (due to J.M. Keynes) Notation: I = planned investment = C + I + G = planned expenditue = eal GDP = actual expenditue Diffeence between actual & planned expenditue: unplanned inventoy investment slide 1 lements of the Keynesian Coss consumption function: govt policy vaiables: investment is exogenous: C = C( T ) G = G, T = T I = I planned expenditue: quilibium: Actual expenditue = = = C( T ) + I + G Planned expenditue slide 2 1

2 The equilibium value of income planned expenditue = =C +I +G 45º quilibium income income, output, slide 3 An incease in G = =C +I +G 2 =C +I +G 1 ΔG 1 = 1 Δ 2 = 2 slide 4 Solving fo Δ = C + I + G Δ = Δ C + Δ I + ΔG = Δ C + ΔG = MPC Δ + ΔG equilibium condition in changes because I exogenous because ΔC = MPC Δ Solve fo Δ : 1 Δ = ΔG 1 MPC The govenment puchases multiplie slide 5 2

3 The govenment puchases multiplie xample: MPC = 0.8 Δ = 1 ΔG 1 MPC = 1 1 Δ G = Δ G = ΔG The incease in G causes income to incease by 5 times as much! slide 6 Why the multiplie is geate than 1 Initially, the incease in G causes an equal incease in : Δ = ΔG. But C futhe futhe C futhe So the final impact on income is much bigge than the initial ΔG. slide 7 The IS cuve def: a gaph of all combinations of and that esult in goods maket equilibium, i.e. actual expenditue (output) = planned expenditue The equation fo the IS cuve is: = C ( T) + I( ) + G slide 8 3

4 Deiving the IS cuve = =C +I ( 2 )+G I =C +I ( 1 )+G ΔI Negatively sloped IS slide 9 The Algeba of the IS cuve Suppose C = C 0 + c ( T ) And I = I 0 b Then = C + I + G = C 0 + I 0 + G + c ( T ) b C 0 + I 0 + G c T b 1 c 1 c slide 10 The slope of the IS cuve Hold eveything except and fixed Then Δ = [- b / (1-c) ] Δ Δ / Δ = [ (c 1) / b ] < 0 Thus IS elatively flat if eithe (i) b is vey lage (ii) c is close to 1 slide 11 4

5 Shifting the IS cuve: ΔG At any value of, G so IS shifts ight. = =C +I ( 1 )+G 2 =C +I ( 1 )+G 1 Hoizontal IS shift : 1 Δ = ΔG 1 MPC Δ IS IS 2 slide 12 Tax financed change in G Suppose ΔG = ΔT. Then at fixed : ΔG cδt Δ = = ΔG 1 c The balanced budget multiplie is equal to 1 Why? Δ = ΔG + c ΔG + c 2 ΔG + c ΔT c 2 ΔT = ΔG slide 13 The LM cuve Begins with liquidity pefeence theoy: a simple theoy in which the inteest ate is detemined by money supply and money demand. LM cuve descibes equilibium in the money maket slide 14 5

6 Money Supply The supply of eal money balances is fixed: ( M P ) s = M P inteest ate ( M P ) s M P M/P eal money balances slide 15 Money Demand and equilibium Demand fo eal money balances: (M/P) d = L(,) inteest ate ( M P ) s The inteest ate equates the supply and demand fo money. M P L (, ) M/P eal money balances slide 16 The LM cuve LM cuve : gaph of all combinations of and that equate the supply and demand fo eal money balances. The equation fo the LM cuve is: M P = L(, ) slide 17 6

7 Deiving the LM cuve (a) The maket fo eal money balances (b) The LM cuve LM 2 2 L (, 2 ) 1 1 L (, 1 ) M 1 P M/P 1 2 slide 18 The Algeba of the LM cuve M/P = m 0 + k h Fix M and P 0 = k Δ h Δ Slope of LM cuve : Δ / Δ = k / h > 0 LM flat if (i) k small (ii)h lage ( liquidity tap ) Intuition: An incease in income aises money demand by k Δ Since M/P fixed excess demand in the money maket must ise by k Δ/h to estoe equilibium slide 19 How ΔM shifts the LM cuve (a) The maket fo eal money balances (b) The LM cuve LM LM 1 1 L (, 1 ) 1 M 2 P M 1 P M/P 1 slide 20 7

8 Shifting the LM cuve: change in M Hoizontal shift : keep constant ΔM / P = k Δ Δ / ΔM = 1 / Pk Vetical shift : keep constant ΔM / P = - h Δ Δ / ΔM = - 1 / Ph slide 21 The shot-un un equilibium Fom: = C ( T) + I( ) + G M P = L(, ) LM Can solve fo and as a function of all exogenous vaiables! R IS slide 22 M P Solving fo C0 + I0 + G ct b = 1 c 1 c = m + k h 0 C0 + I0 = + G ct bm0 / h + bm / hp 1 c + bk / h slide 23 8

9 The Big Pictue Keynesian Coss Theoy of Liquidity Pefeence IS cuve LM cuve IS-LM model xplanation of shot-un fluctuations Agg. demand cuve Agg. supply cuve Model of Agg. Demand and Agg. Supply slide 24 9