ECO102 Tutorial 04

ECO102 - Week 03.pdf

• 1
  • $C=10+0.8(Y-5-0.25Y)$
  • $T=5$
  • $t=0.25$
  • $I=3$
  • $G=40$
  • $NX=1-0.1Y$
  • Provide diagrams for $\frac{AE}{45}$ and Budget balance
  • $AE=C+I+G+NX$
  • $AE=(10+0.8(Y-5-0.25Y))+(3)+(40)+(1-0.1Y)$
  • $AE=0.5Y+50.0$
    • $Y=0.5Y+50$
    • $Y=100.0$
  • $B=T-G$
  • $B=5+0.25Y-40$
  • $B=0.25Y-35$
    • $0=0.25Y-35$
    • $Y=140.0$
    • $5+0.25(100)-40=-10.0$
    • Currently in deficit.

        left=-4; right=150;
        top=150; bottom=-4;
        ---
        y=0.5x+50
        y=0.5x+30
        y=x
        (100,100)
        (60,60)
        x=100|dotted
    

        left=-4; right=150;
        top=10; bottom=-40;
        ---
        y=0.25x-35
        y=0.25x-15
        (140,0)
        (60,0)
        x=100|dotted
    

  • a
    • To reduce budget balance to $b=0$
    • What should $G$ be?
    • They can do quantitative easing, bonds, etc to fund themselves, but this model doesn't include any of that. Only through tax revenues.
    • Can we use the multiplier?
      • To affect a $10$ decrease we need to have a $20$ dollar decrease in $G$
      • $0=5+0.25(100)-G$
        • $G=30.0$
        • This suggests it's 1:1.
        • But this is wrong.
      • Multiplier Increase
        • $G=40\downarrow 20⟹G=20$
        • Test
        • $AE=(10+0.8(Y-5-0.25Y))+(3)+(20)+(1-0.1Y)$
        • $AE=0.5Y+30.0$
        • $Y=0.5Y+30.0$
        • $Y=60.0$
        • $5+0.25(60)-(20)=0$
        • This works
      • $G=5+0.25Y$
      • Fake AE Approach
        • $AE=C+I+G+NX$
        • $AE=(10+0.8(Y-5-0.25Y))+(3)+(5+0.25Y)+(1-0.1Y)$
        • $AE=0.75Y+15.0$
        • $Y=0.75Y+15$
        • $Y=60.0$
        • Reverse engineer the $G$ spend.
        • $G=5+0.25(60)=20.0$
        • This matches the AE Multiplier approach I thought of too.
        • Real AE corrected
        • $AE=(10+0.8(Y-5-0.25Y))+(3)+(20)+(1-0.1Y)$
        • $AE=0.5Y+30.0$
      • New Budget
        • $B=T+Yt-G$
        • $B=5+0.25Y-20=0.25Y-15.0$
  • b
    • Graphs above
  • c
    • Spending multiplier
    • $\text{mult.}=\frac{1}{1-(MPC(1-t)-MPI)}$
    • $\text{mult.}=\frac{1}{1-(0.8(1-0.25)-0.1)}=2.0$
  • $\mathrm{\Delta }y=\text{mult.}\cdot \mathrm{\Delta }G⟹2\mathrm{\Delta }G$
  • $\mathrm{\Delta }b=\mathrm{\Delta }T+t(\mathrm{\Delta }Y)-\mathrm{\Delta }G$
  • $-10=0+t(2\mathrm{\Delta }G)-\mathrm{\Delta }G$
  • $-10=0.5\mathrm{\Delta }G-\mathrm{\Delta }G⟹\mathrm{\Delta }G=20$
• 2
  • AE model
  • $\text{mult.}=2$
  • $t=0.25$
  • $G=120$
  • To eliminate a budget deficit of $20$
  • $B=-20$ we need that $G=120\to 120-(20\cdot 2)=80$

  ---

  • $B=T+tY-G$
  • $\mathrm{\Delta }Y=\text{mult.}\cdot \mathrm{\Delta }G$
  • $-20=0+0.25(\mathrm{\Delta }Y)-\mathrm{\Delta }G$
    • We know $\mathrm{\Delta }Y=2\mathrm{\Delta }G$ based on the multiplier
  • $-20=0.25(2\mathrm{\Delta }G)-\mathrm{\Delta }G$
  • $\mathrm{\Delta }G=40.0$
  • $\mathrm{\Delta }G=G_1-\hat{G}$
  • $40=120-\hat{G}$
  • $\hat{G}=80$
• 3
  • $MPC=0.8$
  • $MPI=0.4$
  • No taxes directly
  • When govt increases spending by $42$, real gdp will grow by $x$
  • $\text{mult.}=\frac{1}{1-(MPC(1-t)-MPI)}$
  • $\text{mult.}=\frac{1}{1-(\frac{4}{5}(1-0)-\frac{2}{5})}=\frac{5}{3}$
  • $G\uparrow 42⟹Y\uparrow 42\cdot \frac{5}{3}=70$

  ---

  • $\mathrm{\Delta }G=42$
  • $\text{mult.}=\frac{1}{1-(MPC(1-t)-MPI)}$
  • $\text{mult.}=\frac{1}{1-(\frac{4}{5}(1-0)-\frac{2}{5})}=\frac{5}{3}$
  • $\mathrm{\Delta }Y=\frac{5}{3}\cdot 42$
  • $\mathrm{\Delta }Y=70$
• 4
  • $C=60+0.8(Y-0.25Y-50)$
  • $I=70$
  • $G=100$
  • $NX=10-0.1Y$
  • Budget balance?
  • $AE=C+I+G+NX$
  • $AE=(60+0.8(Y-0.25Y-50))+(70)+(100)+(10-0.1Y)$
  • $AE=0.5Y+200.0$
  • $Y=0.5Y+200$
  • $Y=400.0$
  • $B=T+Yt-G$
  • $B=50+0.25Y-100$
  • $B=0.25Y-50$
  • $B|{}_{Y=400}=50$
  • So it's in surplus
• 5
  • When AE is horizontal the multiplier is $0$
  • Because the aggregate Marginal Propensity of X,Y,Z is $0$