The government purchases multiplier Definition the increase in income resulting from a $1 increase in G. In this model, the g multiplier equals △y △G1-MPC In the example with MPC =0.8, △y 5 △G1-08 CHAPTER 10 Aggregate Demand I slide 11
CHAPTER 10 Aggregate Demand I slide 11 The government purchases multiplier In the example with MPC = 0.8, Definition: the increase in income resulting from a $1 increase in G. In this model, the G multiplier equals 1 1 MPC Y G = − 1 5 1 0.8 Y G = = −
Why the multiplier is greater than 1 Initially, the increase in G causes an equal increase in y△y=△G. But↑y→↑c → further个y → further个c → further个y So the final impact on income is much bigger than the initial AG. CHAPTER 10 Aggregate Demand I slide 12
CHAPTER 10 Aggregate Demand I slide 12 Why the multiplier is greater than 1 ▪ Initially, the increase in G causes an equal increase in Y: Y = G. ▪ But Y C further Y further C further Y ▪ So the final impact on income is much bigger than the initial G
An increase in taxes Initially, the tax increase reduces E=C+I+G consumption, and E=C+I+G therefore e △C=-MPC△T At y. there is now an unplanned inventory buildup so tirms reduce output and income falls toward a new B= Y △y equilibrium E1=y1 CHAPTER 10 Aggregate Demand I slide 13
CHAPTER 10 Aggregate Demand I slide 13 An increase in taxes Y E E =C2 +I +G E2 = Y2 E =C1 +I +G E1 = Y1 Y At Y1 , there is now an unplanned inventory buildup… …so firms reduce output, and income falls toward a new equilibrium C = −MPC T Initially, the tax increase reduces consumption, and therefore E:
Solving for△Y △》=AC+△+△G eq m condition in changes △C I and G exogenous MPC×(△y-△7) Solving for△y:(1-MP)×△y=-MPC×△7 Final result MPC △y △7 1- MPC CHAPTER 10 Aggregate Demand I slide 14
CHAPTER 10 Aggregate Demand I slide 14 Solving for Y = + + Y C I G = − MPC ( Y T ) = C (1 MPC) MPC − = − Y T eq’m condition in changes I and G exogenous Solving for Y : MPC 1 MPC Y T − = − Final result:
The Tax Multiplier def the change in income resulting from a $1 increase in T △y MPC △71-MPC If MPC=0.8 then the tax multiplier equals △y 08 0.8 △71-080.2 CHAPTER 10 Aggregate Demand I slide 15
CHAPTER 10 Aggregate Demand I slide 15 The Tax Multiplier def: the change in income resulting from a $1 increase in T : MPC 1 MPC Y T − = − 0 8 0 8 4 1 0 8 0 2 . . . . Y T − − = = = − − If MPC = 0.8, then the tax multiplier equals