ECO2543 - Theorie Macroeconomics

Running head: ECONOMICS 1
ECO2543-Theorie Macroeconomics 2
Name
Institution

ECONOMICS 2
Solution
Q1
Population is a determinant of different phenomena including age structure of a country’s
population, economic inequality, and the labor market of a country. As a result, effects of these
factors lead to a general national effect on the economic growth and developments (Zhang,
2018). Using the basic Solow model, even though investment leads to an increased capital stock,
it is still affected by the depreciation rate thus leading to change in the rate of capital per worker
which results in a fall of workforce (Heijdra, 2017). We therefore assume that the number of
workers will grow over a given time at the rate “n” per period leading to change in capital stock
per worker which is represented through the following function;
Δk = i – (δ + n)k
The above equation shows that increase in investment rate leads to an increased capital
stock (k) while depreciation (δ k) and population growth (n) results in a decrease in stock
accumulation. As a result, these factors together influences the rate of capital per worker since
once an economy reaches its steady state, its investment will serve two purposes (Fontana &
Setterfield, 2016). These includes a portion of investment will be used to replace the depreciation
rate, denoted as (δk*) while the balance, nk* is used to provide the workers with the steady state
amount of the required capital. As a result, the phenomenon that the model cannot explain
includes income differences among countries, steady state, and efficiency in labor demand and
supply, and the technological progress within and among nations.

ECONOMICS 3
Q2
a. From the Cobb-Douglas equation given above i.e. F (Kt, L) = Kt 1-αLα, we can note that
the marginal product of labor which is gotten as;
MPL = Δ Y
Δ L = α Kt 1-αLα-1
= α ( K t
L )^1-α
Letting the components of capital to be positive, the Kt is regarded as the capital per
capita at the start of the year, at t. It will then be;
kt+1 = kt(1 − δ) + it showing that the capital stock changes over time where δ is the rate of
the physical depreciation between year t and year t+1. As a result, δkt (1-p)units of
capital were lost from the depreciation (Elbers et al., 2015). However, since savings is
equal to investment, we can relate investment to the available capital i.e. it = sAf(kt).
As a result the capital evaluation equation can then be written as;
kt+1 = kt(1 − δ) + sAf(kt).
Steady state rule is a state of capital stock whereby if an economy accumulates, then it
remains at that level and it is denoted as k*. As a result, the steady state solve the
equations of k* = k*(1 − δ) + sAf(k*). At the steady state, the lost capital through
depreciation will be offset by the exact amount of saving thus leading to zero investment

ECONOMICS 4
at the steady state. On the other hand, if current capital stock is below k*, then the
economy is said to be accumulating capital where kt+1 > kt
The law of motion for capital is given as;
Kt = (1 − δ)kt-1 + It.
Algebraically,
kt
kt−1 = ( 1−δ ) +1+ SKt
( 1+Ʋ ) (1+ y) represents the capital per unit labor, and consumption per unit of
work will be c*= (1-s)f(k*) showing that consumption decreases with an increase in
saving.
b. An increase in the population recycle rate will lead to an increase in the capital stock per
worker. Thus as a result, if the economy is at the steady state initially before the recycling
state of the population, then after the recycling state, the economy shall have enough
capital stock than in the steady state level. This can be shown graphically as follows;