Solow Growth Model Flashcards

1
Q

What does Growth achieve?

A
  • Creates jobs and lowers unemployment
  • Increases income and improves SoL
  • Reduces poverty and creates opportunities for income generation and wealth accumulation
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2
Q

What is Growth Theory? What can it help with?

A
  • Shows how growth is affected by shocks
  • Helps understand why countries are poor
  • Allows us to design policy to aid growth
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3
Q

What is the Solow Model?

A
  • Shows how the capital stock, the labour force and advancements in technology affect GDP growth
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4
Q

What does Constant Returns to Scale assume?

A
  • zY = F(zK,zL)
  • If you need to check if the powers of K and L add together, it is CRS
  • CRS allows us to analyse per capita if z = 1/L
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5
Q

How can you use per capita output to help us?

A
  • Y/L = F(K/L, L/L) ; F(K/L,1)
  • This means that if y = Y/L and k = K/L
  • y = f(k)
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6
Q

What is the Marginal Product of Capital?

A
  • MPK = the increase in output when k is increased by one unit
  • f(k+1) - f(k) or the slope of the production function
  • f exhibits diminishing MPK
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7
Q

How do you obtain per capita worker functions?

A
  • Assume closed economy: Y = C + I
  • So, divide through by L to get per worker terms; y = c + i
  • Workers can save s amount and consume (1-s) amount
  • To affect c, governments affect s; c = (1-s)y
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8
Q

What is the investment per worker function ( in terms of f(k))?

A
  • Savings per worker = y - c
  • As c = (1-s)y and y = c + i; i= y - (1-s) y
  • Expanding gives us, i = sy = sf(k)
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9
Q

How does the depreciation of capital fit into the Solow Model?

A
  • δk = the fraction of capital that wears out each period (0<δ<1)
  • Change in capital = investment - depreciation of capital
  • Δk = i - δk, or Δk = sf(k) - δk
  • Shows behaviour of k over time
  • All endogenous variables are dependent on k (y,c and i have k in them)
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10
Q

What is the steady star of capital?

A
  • Δk = 0 ; Meaning sf(k) = δk
  • Steady-state: sf(k) = δk
  • Difference between sf(k) and δk is Δk
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11
Q

What does an increase in the savings ratio do to the sf(k) curve?

A
  • Shifts sf(k) curve upwards
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12
Q

What is the relationship between Fiscal Policy and Savings?

A
  • Persistent budget deficit reduces national savings
  • This crowds out investment, reducing the purchasing power of capital, lower per person output
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13
Q

How does the Solow Model contradict itself?

A
  • Suggests that higher s, higher k, and higher y, hence higher c
  • But higher s would reduce c
  • This means that to maximise y, c = 0
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14
Q

Prove the Golden Rule Steady State (referring to consumption maximisation)

A
  • sf(k) = δk
  • c* = f(k) - δk
  • As k* increases, f(k) increases and -δk decreases
  • The question is; what maximised c*?
  • k*gold will achieve this ; where Mᵗᵃⁿᵍᵉⁿᵗ = Mδᵏ
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15
Q

How do you achieve k*gold?

A
  • Economy doesn’t naturally rest at k*gold
  • Hence, Government policy has to adjust s to cause a new steady state with higher consumption
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16
Q

What happens in the case where k=k>kgold

A
  • Government will reduce the savings rate
  • For y, i reduces and c increases since y = c + i
  • i < δk, Δk = i - δk (< 0) and k reduces
  • Since y = f(k), y, i and c all fall until k=k*gold
17
Q

What is satisfied when k = kgold ( k>k*gold )

A
  • k = kgold < k; cgold > c; ygold < y and igold < i
18
Q

What happens in the case where k=k<kgold

A
  • Government will increase the savings rate
  • For y, i increases and c falls since y = c + i
  • i > δk, Δk = i - δk (> 0) and k increases
  • Since y = f(k), y, i and c all rise until k=k*gold
19
Q

What is satisfied when k = kgold ( k<k*gold )

A
  • k = kgold > k; cgold < c; ygold > y and igold > i
20
Q

How do technological advances impact the Solow Model?

A
  • Without technological progress, Increases in S will increase output and growth temporarily, not at a steady state
  • That is dependent on exogenous variables