ECO102 Tutorial 08

• #tk probably a lot of multiple choice on the test.
• ECO102 - Week 08.pdf
• 1
  • $y_0=y^{\ast }=100$
  • #tk hardest question in the course.
  • #tk however never shown up in the past, so maybe not on the test. But still study it.
  • $B=-15$
  • $AS=2p+100-w$
  • $w_0=100$
  • $t=0.5$
  • $MPC=0.8$
  • $MPI=0$
  • $\frac{AS}{AD}SM=1.25$
  • Govt wants to increase $T$ so that at $y_2$ the deficit is gone.
  • Bundle A:
    • $AS=2p+100-w$
    • $AS=2p+100-100=2p$
    • $y=y^{\ast }=100$ we know this from the question.
    • $100=2p$
    • $p=50|w=100,y=100$
    • Indirect taxes affect real gdp in a convoluted way. It's complicated to solve. But we can.
    • $\mathrm{\Delta }y=(SM)(\mathrm{\Delta }G)$
    • $\mathrm{\Delta }y=\left(\frac{AS}{AD}\right)(-MPC)(\mathrm{\Delta }T)$
    • $\mathrm{\Delta }y=(SM)(-MPC)(\mathrm{\Delta }T)$
    • Both above are equivalent
    • $-MPC$ because $C=30+0.8(Y-0.2Y-\underset{T}{\underbrace{10}})$
    • So it affects $Y$ by $-MPC\times T$ as laid out above due to disposable income formula.
    • $\mathrm{\Delta }b=\mathrm{\Delta }T+t\mathrm{\Delta }y$ we don't have $G$ so we can't add it there.
    • So we need to increase it by $15$
    • $15=\mathrm{\Delta }T+t\mathrm{\Delta }y$
    • $15=\mathrm{\Delta }T+0.25\mathrm{\Delta }y$
    • $15=\mathrm{\Delta }T+0.25\left(\frac{AS}{AD}\right)(-MPC)(\mathrm{\Delta }T)$
    • $15=\mathrm{\Delta }T+(0.25)(1.25)(-0.8)(\mathrm{\Delta }T)$
    • $15=\mathrm{\Delta }T(1+(0.25)(1.25)(-0.8))$
    • $15=0.75\mathrm{\Delta }T$
    • $20=\mathrm{\Delta }T$
    • We need to increase indirect taxes by $20$ to eliminate the deficit.
  • We need to find long run budget balance.
    • $-15=0+0.25(100-G)$
    • $G=40$ in the long run.
    • $B_{LR}=20+0.25(100)-40=5$
  • Find the long run wages
  • Bundle C:
    • $\mathrm{\Delta }y=\left(\frac{AS}{AD}\right)(-MPC)(\mathrm{\Delta }T)$
    • $\mathrm{\Delta }y=(1.25)(-0.8)(20)$
    • $\mathrm{\Delta }y=-20$
    • $y_2=100+(-20)=80$
    • Plug back into $AS$
    • $80=2p+100-w|w_0=100$
    • $80=2p⟹p=40$
    • $y=80$
  • Bundle B:
    • We can't use the same steps as $C$
    • $A$ has the same prices as $B$
    • $SM=\frac{1}{1-MPC(1-t)+MPI}=\frac{1}{1-0.8(1-0.25)}=\frac{1}{0.4}=2.5$
    • $\mathrm{\Delta }y=(2.5)(-0.8)(20)=-40$
    • $y_1=100-40=60$
    • $y=60⟹p=50$
    • $p=50$ because bundle b is using bundle A price because we have sticky price.
    • $B_1=20+0.25(60)-40=-5$
  • Bundle D:
    • $y=mx+b$
    • We'll use this to solve for $AD$
    • $y=100$
    • $p=50$
    • $100=a-m(50)$
    • $m=\frac{y_2-y_1}{p_2-p_1}$
    • Bundle C - Bundle B
    • $m=\frac{80-60}{40-50}=-2$
    • $100=x-2(50)$
    • $x=200$
    • $AD=200-2p$
    • $B_2=20+0.25(100)-40=5$
  • Bundle B,C,D:
    • Let's use Bundle C's values, $y_2$
    • $y=80,p=40$
    • $A{D}_1=x-2p$
      • We keep the same slope because we didn't change MPI, MPC, etc, just indirect tax. Constant values.
    • $80=x-(2)(40)$
      • $x=160$
    • $A{D}_1=160-2p$
  • Solve for Bundle D's values:
    • $y^{\ast }=y_0=100$
    • $100=160-2p$
    • $p=30$
    • Solve for wages.
    • $AS=2p+100-w$
    • $100=(2)(30)+100-w$
    • $w=60$
  • Second AS curve:
    • $A{S}_1=2p+100-60$
    • $A{S}_1=2p+40$
  • $p=30,y=100$
  • Budget Balances:
    • $B_0=0+0.25\cdot y-40$ we know it's $-15$ from the question.
      • A
    • $B_1=20+0.25\cdot y-40$
      • C -> $5$
      • B -> $-5$
      • D -> $5$

left=-5; right=120;
top=220; bottom=-5;
---
y=2p
y=200-2p
y=160-2p
(50,100)
x=50
(50,150)|label:LRAS=y*=100
(40,80)
(30,100)
x=30|dashed|0<=y<=100
x=40|dashed|0<=y<=80
y=100|dashed|0<=x<=50
y=2p-40

left=-5; right=120;
top=50; bottom=-50;
---
x=30|dashed
x=40|dashed
x=50|dashed
y=0.5p-40
y=0.5p-20
(50,-15)|label:A
(30,-5)|label:B
(40,0)|label:C
(50,5)|label:D

• Multiple choice:
  • D
  • A
  • C
  • C
  • A