Solow Growth Model Flashcards
What does Growth achieve?
- Creates jobs and lowers unemployment
- Increases income and improves SoL
- Reduces poverty and creates opportunities for income generation and wealth accumulation
What is Growth Theory? What can it help with?
- Shows how growth is affected by shocks
- Helps understand why countries are poor
- Allows us to design policy to aid growth
What is the Solow Model?
- Shows how the capital stock, the labour force and advancements in technology affect GDP growth
What does Constant Returns to Scale assume?
- 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
How can you use per capita output to help us?
- 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)
What is the Marginal Product of Capital?
- 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
How do you obtain per capita worker functions?
- 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
What is the investment per worker function ( in terms of f(k))?
- 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)
How does the depreciation of capital fit into the Solow Model?
- 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)
What is the steady star of capital?
- Δk = 0 ; Meaning sf(k) = δk
- Steady-state: sf(k) = δk
- Difference between sf(k) and δk is Δk
What does an increase in the savings ratio do to the sf(k) curve?
- Shifts sf(k) curve upwards
What is the relationship between Fiscal Policy and Savings?
- Persistent budget deficit reduces national savings
- This crowds out investment, reducing the purchasing power of capital, lower per person output
How does the Solow Model contradict itself?
- 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
Prove the Golden Rule Steady State (referring to consumption maximisation)
- 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
How do you achieve k*gold?
- Economy doesn’t naturally rest at k*gold
- Hence, Government policy has to adjust s to cause a new steady state with higher consumption