ECO102 Lecture 08

Pre-Lecture

ECO102 Lecture 08 Pre-Lecture

Lecture

ECO102 - Week 08.pdf

• Basic Model

  • GDP per capita: $y=\frac{Y}{L}$
  • Equilibrium level of $y^{\ast }=5$
  • Suppose $L=20$, $20$ workers.
  • Then $y^{\ast }=5\cdot 20=100$ as potential GDP. [COMPLETED]
  • Long-Run Aggregate Supply (LRAS)
  • The Solow Model determines the Equilibrium output per worker. [COMPLETED]
  • If the number of workers is known, then the LRAS curve is vertical at $y^{\ast }$. [COMPLETED]
    • #tk flashcard this and line above
  • If Aggregate Demand ($AD$) shifts right, that could be because government spending ($G$) increases ($G\uparrow$). [COMPLETED]
    • The multiplier in spend (if the price level is fixed), we use $\frac{1}{1-(1-t)b+m}$
    • If the price level is not fixed, we move to point C on the graph. [COMPLETED]
    • As the prices go up, Net Exports ($NX$) decrease ($NX\downarrow$). [COMPLETED]
    • Now the effective multiplier is smaller, and we end up with $y_2$
    • $y_2>y^{\ast }$, which exceeds potential output. [COMPLETED]
      • This creates upward pressure on wages.
      • Everyone's working full time.
      • As nominal wages ($w$) increase ($w\uparrow$), then Short-Run Aggregate Supply ($AS$) decreases ($AS\downarrow$). [COMPLETED]
      • Firms pay more to workers, so firms supply less. [COMPLETED]
    • This entire scenario is called an Inflationary Gap. [COMPLETED]
      • Prices and wages rise in order to restore the long-run Equilibrium. [COMPLETED]
  • If $AD$ shifts left, that could be because $G\downarrow$
    • The multiplier in spend (if price is fixed), we use $\frac{1}{1-(1-t)b+m}$
    • If the price level is not fixed, we move to point C on the graph. [COMPLETED]
    • As the prices go down, $NX\uparrow$
    • Now our multiplier is smaller, we end up with $y_2$
    • $y_2<y^{\ast }$, which is below potential output. [COMPLETED]
      • This creates downward pressure on wages.
      • As $w\downarrow$ then $AS\uparrow$
      • Firms pay less to workers, so firms supply more. [COMPLETED]
    • This entire scenario is called a Recessionary Gap. [COMPLETED]
      • Prices and wages fall in order to restore the long-run Equilibrium. [COMPLETED]
  • An Inflationary Gap can be caused by a right shift in $AS$
    • There is no equilibrium $B$ in a supply shock.
    • Since $y_2>y^{\ast }$
    • $w\uparrow$, so $AS$ shifts back left to the exact same starting spot. [COMPLETED]
    • This adjustment is different from a demand shift, meaning the long-run price goes up in a demand shift. [COMPLETED]
    • From an $AS$ supply shift, the long-run price level remains the same. [COMPLETED]
  • A Recessionary Gap can be caused by a left shift in $AS$
    • There is no equilibrium $B$ in a supply shock.
    • Since $y_2<y^{\ast }$
    • $w\downarrow$, so $AS$ shifts back right to the exact same starting spot. [COMPLETED]
    • This adjustment is different from a demand shift, meaning the long-run price goes down in a demand shift. [COMPLETED]
    • From an $AS$ supply shift, the long-run price level remains the same. [COMPLETED]
  • Recessionary gaps close slowly, while inflationary gaps close quickly. [COMPLETED]
    • Because wages are sticky downwards, but not sticky upwards. [COMPLETED]
    • If the economy experiences a recession, firms do not want to cut wages, so firms lay off workers instead. [COMPLETED]
    • If the economy experiences inflation, firms can just raise wages and keep everyone working. [COMPLETED]
      • It is easy to close an inflationary gap because both employers and workers agree on wage increases. [COMPLETED]
  • Long-run (LR) never happens argument.
    • The economy is always getting shocked. There is a left shift in $AD$ when tariffs are imposed. [COMPLETED]
    • There is a change in supply when wars occur, etc. [COMPLETED]
    • The Output Gap Adjustment Process moves the economy back to $y^{\ast }$. By the time the economy moves back to $y^{\ast }$, it gets shocked again. So the economy never actually reaches $y^{\ast }$. [COMPLETED]
    • The return to potential output is asymptotic. [COMPLETED]

• Fiscal Policy:

  • We're initially in long run Equilibrium

  • $y^{\ast }=y_0$

  • $AS=2p+20-2w$

    • $w_0=10$

  • $A{S}_0=2p$

  • $C=36+0.8(Y-20-0.25Y)$

  • $I=10$

  • $G_0=20$

  • $G_1=40$

  • $NX=10-p-0.1Y$

  • $AE=C+I+G+NX$

  • $A{E}_0=36+0.8(Y-20-0.25Y)+10+20+10-p-0.1Y$

  • $A{E}_0=0.5Y-p+60.0$

  • $A{E}_1=0.5Y-p+80.0$

  • $Y=A{E}_0$

    • $Y=0.5Y-p+60.0$
    • $0.5Y=60.0-p$ [COMPLETED]
    • $Y=120.0-2.0p$
    • $p=120-2p$ (Setting $Y=AS=2p$ for equilibrium) [COMPLETED]
    • $3p=120⟹p=40$ [COMPLETED]

  • $Y=A{E}_1$

    • $Y=0.5Y-p+80.0$
    • $0.5Y=80.0-p$ [COMPLETED]
    • $Y=160.0-2.0p$
    • $2p=160.0-2.0p$ (Setting $AS=AD$) [COMPLETED]
    • $4p=160.0⟹p=40$ (Short-run fixed price calculation) [COMPLETED]
    • Wait, if solving $AD=AS$: $2p=160-2p⟹4p=160⟹p=40$. The notes say $p=53.33$, which comes from $3p=160⟹p=53.33$. [AMBIGUOUS]: The algebraic step $p=160-2.0p$ appears to incorrectly drop the $2$ coefficient from $AS=2p$.
    • $Y=160-(2)(40)$
    • $Y=80$
    • $40=160-2p$
    • $2p=120⟹p=60$ [COMPLETED]

    left=-5; right=200;
    top=100; bottom=-5;
    ---
    x=120-2y
    x=160-2y
    y=x
    (40,40)|label:A
    (53.3333333333333,53.3333333333333)|label:B
    (80,40)|label:C
    x=40|dashed|
    (40,60)|label:D
    x=2y-40|hidden
    y=2x-20
    

  • Simple Multiplier (SM): $SM=2=\frac{40}{20}$ (Change in Y / Change in G at fixed price) [COMPLETED]

  • AS/AD Multiplier: $SM=1=\frac{20}{20}$ (Wait, $53.33-40=13.33$ change in Y. The notes say $SM=1$, which implies a $20$ change in $Y$ for a $20$ change in $G$). [AMBIGUOUS]: The multiplier derivation here contradicts the algebraic solution for point B.

  • This is an Inflationary Gap since $80>60$

  • $w\uparrow$ which means $AS$ shifts left. [COMPLETED]

  • $AD=160-2p=60$ (Setting long run $Y$ back to $60$) [COMPLETED]

  • So $2p=100⟹p^{\ast }=50$ [COMPLETED]

  • $AS=2(50)+20-2w=60$ means $120-2w=60⟹2w=60⟹w=30$. [COMPLETED]

  • $AS=2p-40$

  • So Fiscal Policy is not effective in the long run, because it just causes prices to go up, but real output is the same. [COMPLETED]

  • #tk fix the graph, professors notes on the graph are not good and nonsensical curve which don't match the points.

  • Budget Balance ($B$): $B=T-G=20+0.25Y-G$. [COMPLETED]

  • Initial $B=20+0.25Y-20=0.25Y$. [COMPLETED]

  • After $G\uparrow$: $B=20+0.25Y-40=0.25Y-20$. [COMPLETED]

    left=-5; right=200;
    top=30; bottom=-30;
    ---
    x=40|dashed|
    x=80|dashed|
    y=0.25x
    y=0.25x-20
    (80,0)|label:B
    (40,10)|label:A
    

  • Net exports, nothing directly affected it

  • $N{X}_2=10-p-0.1Y$

  • #tk graph below

  desmos-graph left=-5; right=200; top=30; bottom=-30; --- x=40|dashed| x=80|dashed|
  - Savings
  - $S_0=S_1=S_2=S^{\ast }$
  - #tk graph below

  desmos-graph left=-5; right=200; top=30; bottom=-30; --- x=40|dashed| x=80|dashed|

  - #tk graph below
  - What do I do with the $-p$ in $AE=80+0.5Y-P$?
  - $AE=80+0.5Y-p$
  - $A{E}_2=80+0.5Y-p$
  - $A{E}^{\ast }=A{E}_0=60+0.5Y-p$
  -

  desmos-graph left=-5; right=200; top=200; bottom=-30; --- x=40|dashed| x=80|dashed| Y=80+0.5X Y=60+0.5X

• Foreign Shocks

  • $y^{\ast }=y_0$

  • $AS=2p+80-2w$

  • $w_0=40$

  • $C=36+0.8(Y-20-0.2Y)$

  • $I=10$

  • $G=30$

  • $N{X}_0=40-p-0.1Y$

  • $N{X}_1=20-p-0.1Y$ (Negative export shock, e.g., tariffs). [COMPLETED]

  • $A{E}_0=100+0.5Y-p$

  • $A{D}_0=200-2p$ (Derived from $Y=A{E}_0⟹0.5Y=100-p$). [COMPLETED]

  • $A{S}_0=2p$ (Since $w_0=40$, $AS=2p+80-80=2p$). [COMPLETED]

  • $A{D}_0=A{S}_0$

    • $200-2p=2p$
    • $4p=200⟹p=50$ [COMPLETED]
    • $y_0=2(50)=100$ [COMPLETED]

  • $A{E}_1=80+0.5Y-p$ (After $NX$ drops by $20$). [COMPLETED]

  • $A{D}_1=160-2p$ (Derived from $Y=A{E}_1⟹0.5Y=80-p$). [COMPLETED]

    left=-5; right=200;
    top=100; bottom=-5;
    ---
    x=200-2y
    x=160-2y
    y=x
    x=100|dashed|
    y=50|dashed|
    x=60|dashed|
    

  • Solving short-run equilibrium: $A{S}_0=A{D}_1⟹2p=160-2p⟹4p=160⟹p=40$. The note says $100=160-2p⟹p=30$, which calculates the price level if output remained at $100$. [AMBIGUOUS]: The arithmetic progression here is mixed up between fixed output and equilibrium output.

  • Long-run adjustment: $Y$ returns to $100$.

  • $100=160-2p⟹2p=60⟹p=30$. [COMPLETED]

  • $AS=2p+80-2w$

    • $100=2(30)+80-2w⟹100=140-2w$. [COMPLETED]
    • $2w=40⟹w=20=w^{\ast }$

  • $AS=2p+80-(2)(20)$

  • $AS=2p+40$

  • The simple multiplier is initially $2$; a $20$ change in $NX$ results in a $40$ change in GDP at a fixed price level. [COMPLETED]

  • After the price level adjusts in the short run, the effective multiplier is $1$; a $20$ change in $NX$ results in a $20$ change in GDP. [COMPLETED]

  • In the long run, the effective multiplier is $0$; a $20$ change in $NX$ results in a $0$ change in GDP. [COMPLETED]

  • Tariffs will cause Canadian wage rates to fall. Therefore, real GDP will fall in the short run, but in the long run, it will return to the potential level. Thus, tariffs are not effective at changing output in the long run. [COMPLETED]

  • Because the tariff causes an $AD$ shift left, $p$ falls as well. [COMPLETED]

  • Initial $N{X}_0=40-0.1Y-p$

  • $Y_0=100$ and $P_0=50$

  • $N{X}_0=40-0.1(100)-50=-20$. The note says $-10-0.1Y$, which simplifies the constant terms: $40-p=40-50=-10$. [COMPLETED]

  • Tariffs shift $N{X}_1=20-0.1Y-p$

  • Because the price level is the same initially ($p=50$):

  • We have $-30$ as the intercept ($20-50=-30$). [COMPLETED]

  • But then output falls to $Y_1=60$.

  • $N{X}_1=-30-0.1Y$

    • $-30-(0.10)(60)=-36.0$

  • In the short run equilibrium, $Y_2=80$ means $P_1=40$

  • #tk go to office hours tomorrow

  • $N{X}_2=20-0.1Y-p$

    • $N{X}_2=20-0.1(80)-40=20-8-40=-28$. [COMPLETED]

  • At long-run equilibrium $D$, $Y=100$ and $P^{\ast }=30$. The note says $P^{\ast }=50$ which contradicts the previous derivation of $P=30$. [AMBIGUOUS]

  • $NX$ at long run: $NX=20-0.1(100)-30=20-10-30=-20$. [COMPLETED]

  • Equilibrium $A=D$

    left=-5; right=200;
    top=200; bottom=-5;
    ---
    y=x
    y=100-50+0.5x
    y=90-50+0.5x
    y=80-50+0.5x
    y=30+0.5x
    (100,100)|label:A
    (60,60)|label:B
    (80,80)|label:C
    

    • $AE=80+0.5Y-p$
    • If $p^{\ast }=50$ (from earlier ambiguity):
    • $AE=80+0.5Y-50$
    • $AE=0.5Y+30$

• Example: Aggregate Supply Shock

  • If the $AS$ shifts left, the economy goes from equilibrium A directly to C; there is no fixed-price bundle B. [COMPLETED]
  • This creates a Recessionary Gap, because $y_2<y^{\ast }$. [COMPLETED]
  • If $w\downarrow$, then $AS$ keeps shifting right until the economy returns to the original $AS$ curve, so we end up at A again. [COMPLETED]
  • The price level and real GDP do not change in the long run. The nominal wage ($w$) is the only variable that permanently changes. [COMPLETED]
  • $y^{\ast }=y_0$
  • $A{S}_0=2p+80-2w$
  • $w_0=40$
  • $C=36+0.8(y-20-0.25Y)$
  • $I=10$
  • $G=30$
  • $NX=40-p-0.1Y$
  • $AS=2p+40-2w$ (Supply shock equation). [COMPLETED]
    • $AE=36+(0.8)(Y-20-0.25Y)+10+30+40-p-0.1Y$
    • $AE=0.5Y-p+100.0$
  • $A{D}_0=200-2p$
    • #tk how do we get this
    • (Derived by setting $Y=AE⟹Y=0.5Y-p+100⟹0.5Y=100-p⟹Y=200-2p$) [COMPLETED]
  • $p^{\ast }=50$
  • $Y=100$
  • $AS=2p+80-2w$
  • $w_0=40$
  • There is no fixed-price equilibrium $B$ in a supply shock, because the price level immediately changes along with output. [COMPLETED]
  • As the price level rises, $NX$ decreases, which causes a smaller multiplier effect along the $AD$ curve, leading to $y_2$. [COMPLETED]
  • The decrease in $NX$ pulls the $AE$ curve down. [COMPLETED]
  • Since $y_2<y^{\ast }$, the economy experiences a recessionary gap, which puts downward pressure on wages. As wages fall, $AS$ shifts right until it reaches the original $AS$ curve, restoring equilibrium at point A. [COMPLETED]
  • Long-run $y=100$
  • Long-run $p=50$
  • Given the shocked equation $AS=2p+40-2w$:
  • $100=2(50)+40-2w⟹100=140-2w⟹2w=40$. [COMPLETED]
  • $w=20$
  • $AS=2p+40-2(20)=2p+40-40=2p$. [COMPLETED]
  • Which equals $A{S}_0$
  • The only variable that permanently changed was $w\downarrow$. At initial point $A$ and final point $D$, the price level and real GDP remain exactly the same. [COMPLETED]
  • $NX$ also returns to the exact same position because output and prices returned to their initial levels. [COMPLETED]
  • With an aggregate supply shock, the nominal wage ($w$) is the only thing that permanently changes. [COMPLETED]
    • #tk flashcard this

• Example: AS Curve Rotation

  • $A{S}_0=2p+80-2w$
  • $w_0=40$
  • $C=36+(0.8)(Y-20-0.25Y)$
  • $I=10$
  • $G=30$
  • $NX=40-p-0.1Y$
  • $A{S}_1=3p+80-2w$ (Slope change/rotation). [COMPLETED]
  • $AE=100+0.5Y-p$
  • $AD=200-2p$
  • $A{S}_0=2p$
  • $A{S}_1=3p+80-(2)(40)$
  • $A{S}_1=3p$
  • This represents a rotation of the AS curve. [COMPLETED]
  • If $A{S}_0=2p$, then $A{S}_1=3p$ represents a steeper curve when graphed with price on the y-axis. [COMPLETED]
  • #tk exam question
  • Then we graph the inverse function ($P=\frac{1}{3}Y$ vs $P=\frac{1}{2}Y$). [COMPLETED]
  • So at a given price level, $A{S}_1$ yields higher output than $A{S}_0$? Wait, $3p>2p$, so $A{S}_1>A{S}_0$. [AMBIGUOUS]: The note says $A{S}_1<A{S}_0$. If $A{S}_1=3p$, output at any given price is higher, meaning a rightward rotation.
  • If $y_2>y^{\ast }$, the economy is in an inflationary gap, causing upward pressure on wages. Therefore $w\uparrow$. [COMPLETED]
  • We shift $A{S}_1$ up (left) to meet the long-run equilibrium on the $AD$ curve at $y^{\ast }$. [COMPLETED]
  • $Y_0=100$ [COMPLETED]
  • $p^{\ast }=50$ (From $100=200-2p$) [COMPLETED]
  • Same price level we originally had. [COMPLETED]
  • Then $p^{\ast }=p_0$
  • Using the new function $AS=3p+80-2w$:
  • $100=(3)(50)+80-(2)(w)⟹100=150+80-2w⟹100=230-2w$. [COMPLETED]
  • $2w=130⟹w=65$. [COMPLETED]
  • $A{S}^{\ast }=3p+80-(2)(65)⟹A{S}^{\ast }=3p+80-130$. [COMPLETED]
  • $A{S}^{\ast }=3p-50$
  • The AS rotation shock causes a permanent $\mathrm{\Delta }w$ but no permanent $\mathrm{\Delta }p$ in the long run. [COMPLETED]