Econ 191 2
nd
LE Reviewer
The Solow Growth Model (Robert Solow, 1956): A Contribution to the Theory of Economic Growth
Assumptions
o
Continuous time (t)
o
Single good (
Y
)
o
Constant technology (
A
)
o
No government; no international trade
o
Full employment of all factors (
K, L
)
o
Labor force grows at a constant rate,
η
o
Initial values of
K
and
L
are given at
K
0
and
L
0
Production Function
1.
Y(t) = Y[K(t), L(t)] = AK(t)αL(t)(1-α)
Where: A>0; 0 <α <1
Simplifying, by suppressing t:
2.
Y = AK(α)L(1-α)
Exhibits CRS: γ = α + (1-α) = 1
Inputs are Essential:
3.
Y(0,0) = Y(K,0) = Y(0,L) = 0
Positive Marginal Products
4.
MPK = aAKα-1L(1-α) > 0
5.
MPL = (1-a)AKαL(1-α)-1 > 0
Exhibit diminishing MPs
6.
ΔMPK/ΔK = (a-1)aAKα-2L(1-α) < 0
7.
ΔMPL/ΔL = -a(1-a)AKαL(1-α)-2 < 0

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The Per Worker Terms
o
Define:
y = Y/L - GDP per 'capita'
L grows at the 'natural' rate of the population at η
Growth behavior of y:
If Y grows at a faster rate than η, then y increases;
If Y grows at a slower rate than η, then y decreases;
If Y grows at the same rate as η, then y remains constant (does not grow)
o
Let
k = K/L - Capital per worker (capital intensity)
L grows at the 'natural' rate of the population at η
Growth behavior of k:
If K grows at a faster rate than η, then k increases;
If K grows at a slower rate than η, then k decreases;
If K grows at the same rate as η, then k remains constant.
The per Worker Production Function
Y = AKαL(1-α)
o
Y/L = y = [AKαL(1-α)]/L =
AKα /Lα = A(K /L)α
y(k) = Akα
o
Where 0 < α < 1
Capital-intensity positively contributes to growth per capita
Δy/Δk = MPk =
αAkα-1 > 0
y(k) exhibits diminishing marginal productivity in k.
ΔMPk/Δk = (α-1) αAkα-2 < 0

The Significance of Capital-Intensity (k = K/L) in Output per Capita (y)
o
Given the same amount of labor input (L), investing in higher amounts of capital (K) for the
given L to work with will make them (L) more productive.
o
Not only total output (Y) will increase; output per capita will also increase (y).
The essence of increasing
productivity
of L.
Capital Accumulation (K)
1.
Simple Closed-Economy Model
Income Side:
a.
Y = C + S
b.
C = C(Y) = cY - Consumption function
0 < c < 1 - the marginal propensity to consume (MPC)
c.
S = S(Y) = sY - Savings function
0 < s < 1 - the marginal propensity to save (MPS)
Total income from economic activity goes either to Consumption (C) or to Savings (S)
o
The level of Consumption is always proportional to the level of Income
E.g., C = 0.8Y
o
The level of Savings is always proportional to the level of Income
E.g., S = 0.2Y

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Expenditure Side:
d.
Y = C + I
Where: I – autonomous Investment expenditures
Economy Equilibrium: Income = Expenditure
e.
C + S = Y = C + I
S = Y - C = I
f.
S(Y) = I - Savings = Investment condition
All of GDP is either Consumed (C) by households or put into Investments (I) by the
business sector.

- Fall '19