Lecture IV Flashcards
Define the variables in the Solow Model.
Y = output
K = capital stock
N = labor
A = effectiveness of labour. This is basically a variable that encompasses all factors that determine how effective labor is, such as knowledge, technology, etc. Often this is just simplified to technology only.
AN = effective unit of labor
y = Y
AN : This is defined as output per unit of effective labor.
k = K
AN : This is a similar measure of capital per unit of effective labor.
Y = F (K, AN )
What is the equation in the Solow Model of growth?
To make this a model of growth, we must introduce time into the model.
Specifically, all of our variables in the original production function (for total
output Y) are functions of time (t):
Y = [K(t)]α[A(t)N (t)]1−α
What are the first two assumptions in the Solow Model?
- Assumption 1: The labor force N grows at a constant, exogenously
given rate n. - Assumption 2: The level of effectiveness of labor A grows at a constant,
exogenously given rate g.
What is the third assumption in the Solow Model?
- Assumption 3: Investment in each period is some fraction of output.
We can assume that investment is equal to the fraction of output that
is saved, e.g. all savings are channelled to investment (like in the
classical loanable funds theory with a balanced government budget).
This can be expressed as I(t) = sY (t). Therefore, the amount invested
each period is determined by the savings rate s, where 0 ≤ s ≤ 1. The
savings rate s is also assumed to be constant and given exogenously.
What is the fourth assumption in the Solow Model?
Assumption 4: Finally, we must indicate how the (total) capital stock
K changes over time, i.e. the value of ̇K. It is assumed that the rate
of change of the capital stock is a function of the level of investment
(from assumption three) and the depreciation of the existing capital
stock. This can be given by ̇K(t) = sY (t) − δK(t) Therefore, the rate of change of the capital stock over time is the
level of investment minus the amount of depreciation, δ. Note that
0 ≤ δ ≤ 1. It is also taken exogenously.
What is the formula for the Solow Model?
The key to the Solow
model lies with the time derivative of k (capital per unit of effective labor).
Specifically, this is given by
k(t) = skα − (n + g + δ)k
Where n,g, and delta are constant.
What does the curved line (skα) in the Solow Model Represent?
The curved line, skα, is the actual level of investment. Since we assumed that all savings are chaneled into investment, the fraction s of output that is saved must
be the level of investment by definition.
What does the straight line (n +
g + δ)k represent in the Solow Model?
The straight line, given by (n +
g + δ)k is what is called break-even investment.
It is the level of investment
needed simply to maintain k at its current level.
What does that mean?
Well, suppose initially that there are 5 units of capital K and 5 units of
effective labour AN . Therefore, k is equal to 1. Now suppose that you have
population growth n. Specifically, suppose that now AN = 6 due to this
increase in N . In order to maintain k = 1, you must invest in one more
unit of K to make K also equal to 6.
What is the relationship between k and k* (intersection of straight and curved lines)?
If k is greater than k∗, then actual investment is below break even investment, and k is getting smaller; from the Solow equation, the second term is larger than the
first term and the rate of change of k is negative. The model thus implies
that k converges to k∗, and k will be constant at that point.
What is “The Steady State?”
In the steady state, all of the variables are growing at a constant rate. The implication is that regardless of its initial starting
position, the economy will move to a long-run steady state, with constant
growth.
What are some of the primary tenets of the Steady State?
The most interesting conclusion is that output Y is growing at a constant
rate n + g. This indicates that in the steady state, the growth rate of
output depends on the growth rate of population and labour effectiveness.
Furthermore, the growth rate of output per worker Y /N depends only on
the growth rate of labour effectiveness A.
Once the new k∗ is attained, is the rate
of change of k is again zero?
We know from the Solow diagram that capital per unit of effective labour,
k, increases to the new steady state. Once the new k∗ is attained, the rate
of change of k is again zero
What happens to output per unit of labor (Y/N) in the Steady State?
The effects of the increase in savings on the natural logarithm of Y /N
can now be seen. Output per unit of labour climbs until the new steady
state is reached, when it becomes parallel to the original growth path, once
again growing at a rate of g.
