WEEK 4 - Economic Growth I (Basic Solow model) Flashcards
(36 cards)
What is the importance of growth for poor countries?
-Standard of living
(Daily caloric intake 1/3 lower than in richest fifth)
-the infant mortality rate is 200 per 1000 births, compared to 4 per 1000 births in the richest fifth
What does the Solow Model look at?
The determinants of econ growth and standards of living in LR
What are some elements of Solow’s model that differ from traditional growth models?
- K no longer fixed
(Depreciation shrinks it, Investment causes it to grow) - L no longer fixed
(Pop growth causes it to grow) - Consumption function simpler
- No G or T
What is the basic Solow production function?
Y = F(K,L)
Where:
y = Y/L = Output per worker
k = K/L = Capital per worker
How do we derive a production function that expresses output per worker as a function of capital pr worker?
- Assume constant returns to scale (noted as z):
zY = F(zK,zL) for any z>0 - Put z = 1/L then,
Y/L = F(K/L, 1)
y = F (k,1)
y = f (k) (per worker production function)
SEE GRAPH IN NOTES
What is the national income identity in the Solow Model?
Y = C+I
In per worker terms:
y = c + i
Where:
c = C/L and i = I/L
How do we define the savings rate?
As the fraction of income that’s saved (s)
What is the Solow Consumption function (per worker)?
c = (1 - s)y
How do we find the savings and investment function for the Solow Model?
- Savings (per worker) = y - c
= y - (1-s)y
= sy - National income identity is y = c + i
Rearrange to get: i = y - c = sy
Which gives us:
i = sy = sf(k)
Output, Consumption and Investment graph
SEE IN NOTES
How do we identify depreciation?
δ = The rate of depreciation
= The fraction of the capital stock that wears out each period
(capital stock = Physical Capital Stock)
SEE GRAPH IN NOTES
What alters the level of capital stock?
Investment increases it
Depreciation decreases it
How do you identify the change in capital stock /capital accumulation?
ΔK = i - δ
(Change in capital stock = investment - depreciation)
Since i = sf(k) this becomes,
ΔK = sf(k) - δk
What is known as the law of motion of k (central equation of Solow)?
ΔK = sf(k) - δk
(Determines behaviour of capital over time)
So, it determines behaviour of all other endogenous variables because they all depend on k
What is known as the steady state?
ΔK = sf(k) - δk
If investment is just enough to cover depreciation
(sf(k) = δk) then capital per worker will remain constant
SEE GRAPH IN NOTES
What do we denote the steady state by?
k* - called the steady state capital stock
How does an economy move towards the steady state?
SEE NOTES
What is the overall statement about moving towards the steady state?
As long as k
How do you numerically identify the steady state?
- Production function (aggergate):
Y = F(K,L) = Sq root of KxL = K1/2 L1/2 - To derive per worker production function, divide through by L:
Y/L = K1/2 L1/2 / L = (K/L)1/2 - Then sub y=Y/L and k = K/L to get:
y = f(k) = k 1/2
How do you calculate for the steady state?
Use equation of motion (ΔK = sf(k) - δk )
e.g. s = 0.3 δ = 0.1 y= k1/2
- Set ΔK to 0
leaving us with just sf(k) - δk - Using assumed values
0.3 Sq root K = 0.1k
3 = k/Sq root K = Sq root of k
Giving us k* = 9 and y* = Sq root k* = 3
Finally, c=(1-s)y = 0.7 x 3 = 2.1
What does an increase in the savings rate do?
Raises investment since in the model all that isn’t consumed is saved and what is saved is then invested.
Causing k to grow toward a new steady state
What does the Solow Model predict?
Higher s = Higher k*
and since y = f(k)
higher k* = Higher y*
Thus, solow model predicts that countries with higher rates of saving and investment will have higher lvls of capital and income per worker in LR
What is the golden rule of capital stock?
The steady state value of k that maximises consumption
How do we find the golden rule of capital stock?
K*gold
- Express c* in terms of k*
c* = y* - i*
= f(k) - i
= f(k) - δk
Because in general i = ΔK + δk
In steady state i* = δk because ΔK = 0
SEE GRAPH IN NOTES
