Solow Growth Model Flashcards
Week 1
Provide the case study of the difference between South Korea and the Philippenes
- 1960: Both nations had the same GDP per capita of the US [~10%]
- South Korea had 6% growth rate whilst the Philippenes only experienced 2.5% of growth rates.
- This led to South Korea reaching 75% of the US, whilst the Philippenes stagnated
- The question becomes why is this the case? The answer is investment and capital accumulation
- SK: peak of 50%, PN: peak of 20%
- Link between GDP formula and investment
What is the Cobb-Douglas production function? What do the variables mean?
- Y = A(Kt^α)(Lt^1-α)
- α = 1/3
- A(Bar) = TFP
- A(Bar) is exogenous and therefore not reliant on t
What is the income resource constraint? What are some assumptions
- Yt = Ct + It
- Assuming 0 G, 0 X and 0 M
What is the Capital Accumulation equation? What do the variables mean?
- K’ = I + (1-δ)K
- OR K’ = K + I - δK
- δ = depreciation (6%+/- 2)
- K’ = Next Year Capital, K = This Year Capital, I = Investment
- Since focus is on capital, Lt = L(bar)
What is the Investment Model?
- It = sYt [s is a % of Y invested]
- Yt - Ct = sYt; Ct = (1-s)Yt
- Ct + It = sYt + (1-s)Yt
What are the difference between flows and stock concepts?
- Stock: A quantitiy that can be measured at time t (CAPITAL)
- Flow: A quantity that is measured over time (INVESTMENT)
How can you solve the Solow growth model? (so you only have K, K’, δ, A, s)
- Must be solved graphically, algebraically is technically impossible due to powers
- K’ = sYt - δK
- Yt = A(Kt^α)(Lt^1-α)
- K’ = sA(Kt^α)(Lt^1-α) - δK
What is the Steady-State Point? What happens if you’re not at the Steady State?
-K* = Steady state
- sA(Kt^α)(Lt^1-α) = δK
- To the left of K, I>δ, NINV > 0 , K’>K, Increase in K until you reach K
- To the right of K, I<δ, NINV < 0 , K’<K, Decrease in K until you reach K
- This means that they always end up at K, transition dynamics always occur to reach K
How do you solve for K*?
- sA(K^α)(L^1-α) = δK
- K*^(1-α) = sA(L^1-α) / δ
- K* =L [sA / δ]^ {1/1-α}
How do you solve the steady state of capital per person?
- k* = K* / L*
- k* = [sA / δ]^ {1/1-α}
What happens when you plug k* into Y*?
- Y* = A[L [sA / δ]^ {1/1-α}] ^ α (L^1-α)
- This means that Y* = [A^1/1-α] [(s/δ)^α/1-α] (L)
What happens when investment rates or TFP increases?
- Y* increases
What happens when depreciation increases?
- Y* decreases
How can you find the steady state level of output per person (y*)? How can this increase?
- y* = Y*/L
- y* = [A^1/1-α] [(s/δ)^α/1-α]
- As 1/1-α > 1, Increases in TFP increases K and therefore increases in y*
- There are additional affects due to capital accumulation
Briefly outline why some countries are rich and some countries are poor?
- To examine this, we must take ratios of y*
- y1/y2 = [(A1/A2)^1/1-α] [(s1/s2)^α/1-α] [(δ1/δ2)^α/1-α]
- Differenet levels of A, s and δ in different natuons
- Solow model states TFP is more important than s and δ due to the multiplier
- α/1-α < 1/1-α as 0<α<1
What are some of the Long run Implications of the Solow Model?
- There is no long-run growth in Solow Model
- In the steady state, growth stops; Y, k, y, c are all constant
- However, we see that there are contradictions- UK GDP grows at around 1%
- Key assumptions of Solow-> Capital accumulation drives economic growth in the SR, not LR due to DMR
What happens when variables change?
- If s increases (suddenly/permenantly), s’Y increases sY in steepness reaching a new steady state
- K’* is higher K, so Y increases to Y’*
What is the Ratio Scale?
- The slope of the line means a higher growth rate
What are transition dynamics?
- If K<K, countries will grow; if K>K, countries will shrink
- Output changes more rapidly if you are further from K* [South Korea was further away from K* than the Philippenes]
What are the statistics on cross-country growth rates?
- Yt and GDP growth are negatively correlated in the OECD; meaning that transition dynamics hold
- Yt and GDP growth rates are not correlated for all nations
- Poor growth isn’t becuase K<K, BUT deep rooted issues (K isn’t the same)
What are some growth rate facts?
- Gxt =δXt+1 / Xt
- If growth of x,y,z are gx,gy,gz, then:
- z = x/y; gz = gx - gy
- z = xy; gz = gx + gy
- z = x^a; gz = agx
What happens when the population increases within the Solow Model?
- Assume n = δLt+1 / Lt and kt = Kt / Lt
- Kt growth = s (Yt/Kt) - δ - n
- This means that Kt growth = s(Yt) - (δ + n)Kt
Briefly expand the idea of Solow model population increase
- Adding population growth results in no long-run change in GDP per capita as economy tends to K*
- If population growth increases, GDP per capital falls becuase of some capital investment is diverted to equipping new people not increases in K per person
- LR aggregatee GDP growth rate = population growth rate
What are some strengths and weaknesses of the Solow Model?
- STRENGTHS: Allows theory to determine how rich a country is and allows theory to understand different growth rates
- WEAKNESSES: Focusing on I & K doesn’t explain TFP and the model doesn’t explain why nations differ with productivity
