ECO102 Tutorial 12

ECO102 - Week 11.pdf

• Study tip:
  • Watch john ron annihilate the field!!11!1
  • Bryson will choke !!111!!
  • Get 100 on exam
• Review session.
• Likely chained CPI RGDP.
  • (ECO102 - Week 11, p.6)
  • Suppose that an economy produces only three goods. The prices and quantities produced within the economy for three years is given by the data below. Using 2018 as base year, calculate Laspeyres Chained Real GDP for 2020. Using 2018 as the base year, calculate Laspeyres Chained Real GDP for 2020.
  • RGDP
    • First find GDP
      • $GD{P}_{2018}=(10)(100)+(2)(50)+(5)(100)=1600$
      • $GD{P}_{2019}=(11)(120)+(2.3)(60)+(7)(110)=2228.0$
      • $GD{P}_{2020}=(12)(110)+(2.5)(60)+(6)(80)=1950.0$
    • Last First Price
      • $L{Q}_t=p_{t-1}\cdot q_t$
      • $L{Q}_{2018}=1$
      • $L{Q}_{2019}=(10)(120)+(2)(60)+(5)(110)=1870$
      • $L{Q}_{2020}=(11)(110)+(2.3)(60)+(7)(80)=1908.0$
      • Keep quantities at this year, price at last year.
    • Index
      • ${\text{Index}}_{2018}=1$
      • ${\mathrm{Index}}_t={\displaystyle \frac{L{Q}_t}{GD{P}_{t-1}}}$
      • ${\mathrm{Index}}_{2019}=\frac{1870}{1600}=\frac{187}{160}=1.16875$
      • ${\mathrm{Index}}_{2020}=\frac{1908}{2228}=\frac{477}{557}=0.856373429084381$
    • RGDP
      • $RGD{P}_{2018}=GD{P}_{2018}\cdot {\mathrm{Index}}_{2018}$
        • $RGD{P}_{2018}=1600\cdot 1=1600$
      • $RGD{P}_{2019}=RGD{P}_{2018}\cdot {\mathrm{Index}}_{2019}$
        • $RGD{P}_{2019}=1600\cdot 1.16875=1870.0$
      • $RGD{P}_{2020}=RGD{P}_{2019}\cdot {\mathrm{Index}}_{2020}$
    • $RGD{P}_{2020}=1870.0\cdot 0.856373429084381=1601.41831238779$
  • CPI
    • GDP
      • Already have it
    • Last First Quantity
      • $L{P}_t=p_t\cdot q_{t-1}$
      • $L{P}_{2018}=1$
      • $L{P}_{2019}=(11)(100)+(2.3)(50)+(7)(100)=1915.0$
      • $L{P}_{2020}=(12)(120)+(2.5)(60)+(6)(110)=2250.0$
    • Index
      • ${\mathrm{Index}}_{2018}=1$
      • ${\mathrm{Index}}_t={\displaystyle \frac{L{P}_t}{GD{P}_{t-1}}}$
      • ${\mathrm{Index}}_{2019}=\frac{1915}{1600}=\frac{383}{320}=1.196875$
      • ${\mathrm{Index}}_{2020}=\frac{2250}{2228}=\frac{1125}{1114}=1.00987432675045$
    • Chained CPI
      • $CP{I}_{2018}=100$
      • $CP{I}_{2019}=CP{I}_{2018}\cdot {\mathrm{Index}}_{2019}$
        • $CP{I}_{2019}=100\cdot 1.196875=119.6875$
      • $CP{I}_{2020}=CP{I}_{2019}\cdot {\mathrm{Index}}_{2020}$
        • $CP{I}_{2020}=119.6875\cdot 1.00987432675045=120.869333482944$
• Simple multipliers
• Aggregate expenditure with tax rate
• Bonds
• Aggregate expenditure with NX
• IRP
  • Question 13
  • Chained RGDP and CPI will be on exam #tk
  • #tk expect IRP on exam too.
  • $C=14+0.9(Y-0.1Y-10)$
  • $I=15-r$
  • $G_0=5$
  • $MD=0.1Y-r$
  • $MS=5$
  • $e=10-r$
  • $NX=15-0.01Y-02.P+e$
  • $AS=2P$
  • $G_1=8$
  • Preliminary steps
    • $MD=MS$
      • $0.1Y-r=5$
      • $Y=10.0r+50.0$
      • $r=0.1Y-5.0$
    • $AS=2P⟹P=\frac{Y}{2}$
    • Put in investments
      • $I=15-r$
      • $I=15-0.1Y+5$
      • $I=20-0.1Y$
    • $e$ in terms of $Y$
      • $e=10-0.1Y+5$
      • $e=15-0.1Y$
    • $NX$ in terms of $Y$
      • $NX=15-0.01Y-0.2P+e$
      • $NX=15-0.01Y-0.2P+15-0.1Y$
      • $NX=-0.2P-0.11Y+30$
      • $P=\frac{Y}{2}$
      • $NX=-0.2\cdot \frac{Y}{2}-0.11Y+30$
      • $NX=30-0.21Y$
  • A:
    • Fake AE:
      • $AE=C+I+G_0+NX$
      • $AE=14+0.9(Y-0.1Y-10)+20-0.1Y+5-0.2P-0.11Y+30$
      • $AE=-0.2P+0.6Y+60.0$
      • Sub in $P$
        • $AE=-0.2\cdot \frac{Y}{2}+0.6Y+60.0$
        • $AE=0.5Y+60.0$
      • $\frac{AE}{45}$
        • $Y=0.5Y+60$
        • $Y=120.0$
        • $P=\frac{Y}{2}⟹P=60$
      • Figure out prelims based on this
        • $r=0.1Y-5$
          • $r=0.1(120)-5=7.0$
        • $I=15-r$
          • $I=15-7=8$
        • $e=10-r$
          • $e=10-7=3$
        • $NX=15-0.01Y-0.2P+e$
          • $NX=15-0.01(120)-0.2(60)+3=4.8$
    • Real AE:
      • $AE=C+I+G_0+NX$
      • $AE=14+0.9(Y-0.1Y-10)+8+5+15-0.01Y-0.2P+3=-0.2P+0.8Y+36.0$
      • $AE=-0.2P+0.8Y+36.0$
      • $AD$
        • $Y=-0.2P+0.8Y+36$
        • $Y=180.0-P$
      • $AD=AS$
        • $2P=180-P$
        • $P=60$
        • $60=\frac{Y}{2}$
        • $Y=120$
      • To get $AE$ use $P=60$
        • $AE=-0.2P+0.8Y+36.0$
        • $AE=-0.2(60)+0.8Y+36.0$
        • $AE=0.8Y+24.0$
  • C:
    • Sticky everything.
    • $AE=5+0.81Y+8+8+15-0.01Y-0.2P+3$
    • $AE=-0.2P+0.8Y+39$
    • $AD$
      • $Y=-0.2P+0.8Y+39$
      • $Y=195-P$
    • $AS=AD$
      • $2P=195-P$
      • $P=65$
      • $65=\frac{Y}{2}$
      • $Y=130$
    • $AE$
      • $AE=-0.2P+0.8Y+39$
      • $AE=-0.2(65)+0.8Y+39$
      • $AE=0.8Y+26.0$
  • B:
    • Prices are constant.
    • $P=60$
    • $AE=5+0.81Y+8+8+15-0.01Y-0.2P+3$
    • $AE=-0.2P+0.8Y+39$
    • $AE=-0.2(60)+0.8Y+39$
    • $AE=0.8Y+27.0$
    • $AD$
      • $Y=-0.2P+0.8Y+39$
      • $Y=195-P$
      • $Y=195-60=135$
      • $P=60,Y=135$
    • The only thing you actually need to do is $AD$ with the constant price and $AE$ with the constant price.
  • Two more
  • E:
    • flexible exchange rate
    • $e=10-r$
    • $AE=5+0.81Y+20-0.1Y+8+30-0.21Y$
    • $AE=0.5Y+63$
    • $AD$
      • $Y=0.5Y+63$
      • $Y=126.0$
    • Prelims
      • $r=0.1Y-5$
      • $r=0.1(126)-5=7.6$
      • $I=15-r$
      • $I=15-7.6=7.4$
      • $e=10-r$
      • $e=10-7.6=2.4$
      • $NX=15-0.01Y-0.2P+e$
      • $NX=15-0.01(126)-0.2(63)+2.4=3.54$
    • $AE=5+0.81Y+7.4+8+15-0.01Y-0.2P+2.4=-0.2P+0.8Y+37.8$
    • $AE=-0.2P+0.8Y+37.8$
    • $AD$
      • $Y=-0.2P+0.8Y+37.8$
      • $Y=189-P$
    • $AS=AD$
      • $2P=189-P$
      • $P=63$
      • $63=\frac{Y}{2}$
      • $Y=126$
  • $F$ is $C$ because you fix the exchange rate to the same as $C$.
• Solow Growth Model