ECO102 Tutorial 07

• 1

  • #tk put money on this polymarket it's on test.
  • To approach the solow growth model:
    • Get rid of of the greek terms.
    • $\delta =$ depreciation rate
    • $\sigma =s=$ savings rate
    • $n=$ population growth rate
    • …
  • Essentially three steps
  • $Y=\sqrt{K}\sqrt{AL}$
  • $\delta =0.02$
  • $LFG=0.02$
  • $\text{Tech progress}=0.01$
  • Steady state equilibrium
    • GDP per worker growth is $0.01$
    • GDP growth:
      • $\mathrm{\Delta }\text{LFG}+\mathrm{\Delta }\text{Tech Progress}$
      • $0.03$
    • #tk
      • This is a very important question. Make flashcards on this. Make sure you understand how to do this.

• 2

  • $Y=\sqrt{K}\sqrt{AL}$
  • $\delta =0.1$
  • $\sigma =0.6$
  • $\text{LFG}=0.2$
  • $\text{TP}=0.3$
  • Provide a diagram showing eq A and B if $TP\to 0$
  • Solow Model:

    • Two equations getting equal to each other.

    • Savings line = Break even line

    • $(\text{Savings})K^{\alpha }=(\text{Depreciation}+\text{Tech Progress}+\text{LFG})K$

    • Savings should cover costs.

    • In this example, $y=x$ is break even

    • $y=8\sqrt{x}$ is the savings

    • At $x=64$ we can only grow with $TP$ or $LFG$.

    • Can't add capital at equilibrium.

      left=-5; right=100;
      top=100; bottom=-5;
      ---
      y=x
      y=8\sqrt{x}
      (64,64)
      (75,75)|label:"Break Even Line"
      (64,64)|label:"Equilibrium"
      (20,35.77708764)|label:"Savings Line"
      

    • A

      • $\sigma K^{\frac{1}{2}}$
      • $0.6\sqrt{K}=(0.1+0.3+0.2)K$
      • $K=1$
      • Output per effective worker:
        • $y=\sqrt{K}$
        • $y=\sqrt{1}$
        • $y=1$
      • Savings amount:
        • $s=0.6\sqrt{K}$
        • $s=0.6\sqrt{1}$
        • $s=0.6$

    • B

      • What is $TP\to 0$
      • $0.6\sqrt{K}=(0.1+0.2)K$
      • $K=4.0$
        • You need more capital to get the same growth.
      • Output per effective worker:
        • $y=\sqrt{K}$
        • $y=\sqrt{4}$
        • $y=2$
      • Savings amount:
        • $s=0.6\sqrt{K}$
        • $s=0.6\sqrt{4}=1.2$

    • Graph

      left=-0.5; right=5;
      top=5; bottom=-0.5;
      ---
      y=0.6x
      (1,0.6)|label:"A"
      (4,2.0)|label:"B"
      y=\sqrt{x}
      y=0.6\sqrt{x}
      (4,0)|label:"K"
      (0,4)|label:"Y"
      y=0.6|0<=x<=1|dashed
      x=1|0<=y<=0.6|dashed
      

      left=-0.5; right=5;
      top=3; bottom=-0.5;
      ---
      y=0.3x	
      y=0.6\sqrt{x}
      y=\sqrt{x}
      (4,1.2)|label:"B"
      (4,2)|label:"B"
      (4,0)|label:"K"
      (0,4)|label:"Y"
      

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• Multiple choice questions:

  • Rising levels in output per capita:
    • Higher depreciation rate
    • Lower savings rate
    • Low investment
    • Higher savings rate
      • Correct answer. Higher savings rate means more investment in capital, which can lead to higher output per capita.
  • Increase in labour force $x$ the total output and $x$ the output per worker
    • Increase decrease
      • Law of dimiishing returns. As you increase the labour force, the output per worker decreases because there is less capital available per worker.
  • 3
    • d
  • 4
    • a
    • Lower depreciation means flatter break even line. Higher savings means steeper savings line.
  • 5
    • a