Lecture 6 - Solow Growth Model Flashcards
The Solow growth model builds on the production model by adding a theory of …?
capital accumulation
In the Solow growth model, is capital stock exogenous or endogenous?
endogenous
List 4 differences between the Solow model and the basic classical model
- supply of K is no longer fixed (investment causes it to grow, depreciation causes it to shrink)
- supply of L is no longer fixed (population growth causes it to grow)
- no G or T in the Solow model
- Model is dynamic (production model is static)
List 4 assumptions of the neoclassical growth model, in terms of firms’ behaviour, the type of output, technology/production, and if production factors change over time?
- competitive firms maximise profit
- produce homogenous output (Y) using Neoclassical production function
- technology/productivity assumed exogenous
- production factors (K, L) may grow over time
List 3 assumptions of the basic Neoclassical growth model, in relation to labour and productivity
- the population is the same as the labour force
- labour is assumed to be fixed in supply, L = L̅
- assume that productivity does not change over time, and that 1 = A̅
Derive: y = f(k) where f(k) = F(k,1), let L̅ mean L is fixed
- in aggregate terms: Y = F(K,L̅)
- y = Y/L̅ = output per worker
- k = K/L̅ = capital per worker
- assume constant returns to scale: λY = F(λK, λL̅) for λ>0
- pick λ = 1/L̅
- Y/L̅ = F(K/L̅, 1)
- y = F(k,1)
- y = f(k) where f(k) = F(k, 1)
For a graph of y against k, would f(k) be concave or convex, why?
- concave
- as it exhibits diminishing MPK
What is the national income identity for the Solow model, in per worker terms? Why?
- Y = C + I + G + NX
- closed economy: NX = 0
- no government: G = 0
- Y = C + I
- in per worker terms: (c = C/L, i = I/L)
- y = c + i
What does s represent in this model?
s = the saving rate (the fraction of income that is saved)
Is s an exogenous or endogenous parameter?
s is an exogenous parameter
What is the consumption function?
- c = (1 - s)y
- (per worker)
What does saving per worker equal in this model?
- saving (per worker) = y - c
- = y - (1 - s)y
- = sy
Show, using the equations formed, how investment = savings
- y = c + i
- c = y - i
- c = (1 - s)y
- y - i = (1 - s)y
- i = sy (= sf(k))
What is the equation that links change in capital stock (Δk), investment (i), and depreciation (𝛿k)?
- Δk = i - 𝛿k
- as i = sf(k)
- Δk = sf(k) - 𝛿k (fundamental equation of the Solow model)
Δk = sf(k) - 𝛿k determines the behaviour of capital over time, which in turn determines the behaviour of all the other endogenous variables because they all depend on k. For instance… (3 examples)
- income per person: y = f(k)
- consumption per person: c = (1 - s)f(k)
- investment per person: i = sf(k)
