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明海大学マクロ経済学:影山純二(学生用)

8.6 補足資料

IS曲線の導出:CIN XGTを均衡式に代入し整理すると、IS曲線の式が求められる

Y = 1

1 − b + m[a − b ¯T+ i + ¯G+ g − (d + n)R]

• Rの前の符号が“−”なので、IS曲線は右下がり

• Rについて解くと、他の解き方で導出したIS曲線の式と同じ

LM曲線の導出:LMsを均衡式に代入し整理すると、LM曲線の式が求められる R=k

hY − 1 h

M¯ P

• Y の前の符号が“+”なので、LM曲線は右上がり 財市場と貨幣市場の均衡式が同時に満たされる点:IS-LMの交点

! Y =1−b+m1 [a − b ¯T+ i + ¯G+ g − (d + n)R] R=hkY −1h

¯ M P

均衡GDP: 下の式を上の式に代入し、Y について解く

Y = 1

1 − b + m +(d+n)kh

"

a−b ¯T+ i + ¯G+ g +d+ n h

M¯ P

#

均衡利子率: 上で求めたY をLM曲線に代入し、Rについて解く R=k

h

$ 1

1 − b + m +(d+n)kh

"

a − b ¯T+ i + ¯G+ g −d+ n h

M¯ P

#%

− 1 h

M¯ P

49

参照

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