Economics | Annuity | Assignment

Running head: BUSINESS 1
economics
[Author Name(s), First M. Last, Omit Titles and Degrees]
[Institutional Affiliation(s)]

BUSINESS 2
Question 2
We are asked to Start from the law of motion for the aggregate capital stock to come up with the
Solow model. For every step we will provide a brief description of the formulas and equation
used. We have n as the population growth rate, d the depreciation rate, s the saving
rate and z as the TFP. The Cobb-Douglas production function Y =Z K
1
2 N
1
2 is given. The aim of
this part is to obtain the equation that describes the equilibrium output per person.
As part of the data, we use GDP (constant $US 2010), population growth rate, population, gross
savings (% of GDP) data for 2018.
using the description above we are task with calculating:
•For both Australia and Tunisia, we need to get the model generated output per person (Since the
Solow model assumes z is the same across countries, we are given that z = 1 for both countries.
Also, d = 0.1 for both countries).
• for both Australia and Tunisia, we need to obtain the data generated output per person.
Lastly, we will compare the model generated outcomes and the data generated outcomes and
scrutinize and critique for the Solow model.
Solution
To understand Solow growth model, a short description is necessary. The production function in
this model is Y =f ( K , L ) and can also be formulated in reference to output per worker as y=f ( k )
. Take for instance a dispute leading to war occurs, the labor force is reduced when killings
happen. This results to fall in L but capital to labor ratio given by k = K
L increases. The
production function expounds that total output reduces because of lesser workers. The result here
is increase in output per worker because each worker gains more wages.
The aggregate production function:
Y (t )= AF(K (t ), N (t )),

BUSINESS 3
Cobb-Douglas production function Y =Z K
1
2 N
1
2 ,
Applying law of motion for the stock of capital considering discrete time we obtain:
Kt +1=I t +(1−δ)Kt
The dynamics of capital over the time interval t is expressed as
K (t +∆)=I (t ) ∆−(1−δ ∆) K (t)
where the flow-variables are the ones multiplied by the span of the interval. Dividing both sides
by ∆ and taking the limit as ∆ → 0, we obtain that
K (t )=I (t)−δK (t )
The savings/investment function. It is presumed to be of a Keynesian nature, i.e. savings (and
investment in a closed economy) equals a constant fraction s of total income
Y (t), or S(t )=I (t)=d Y ¿t)
Let’s also assume that population growth rate is n.
We begin by converting the model from income per capita:
y (t )=Y (t) N (t)=z K
1
2 N
1
2 =z ( K
N )1
2 =z kα
But z=1. Substituting in the equation we get
y ( t ) =( K
N ) 1
2 =k
1
2
Next, the law of motion for capital ·
̇K
N = I
N −δ K
N ⇒ ̇K
N =i−δk
Consider:
̇k = ∂ k
∂ t =
∂ ( K
N )
∂t = ( ̇K N − ̇N K )
N2 = K
N − ̇N K
NN