Question 1
k
max
is the maximum sustainable capital to labor ratio in the economy. This
will occur where the cost of maintaining that level of capital stock is equal to the
output that level of capital produces.
k
max
is the solution to the following equation.
Ak
α
max
= (
n
+
d
)
k
max
3
k
0
.
4
= 0
.
15
k
→
k
max
= 147
.
36
The Golden Rule capital stock is the level of
k
that allows the maximum pos
sible consumption. This occurs where the production function is tangent to the
depreciationpopulation growth line. The slope of the production funtion is given
by 1
.
2
k

0
.
6
, and the slope of the depreciationpopulation growth line is a constant
0.15. The derivative of the production function is
αAk
α

1
, and the depreciation
population growth line has slope
n
+
d
. So,
k
gr
is deﬁned by the following equation:
αAk
α

1
gr
= (
n
+
d
)
1
.
2
k

0
.
6
= 0
.
15
→
k
gr
= 32
The steady state capital labor ratio is given by the intersection of the savings
curve with the depreciation population growth line.
(0
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 Spring '07
 MBIEKOP
 Economics, Macroeconomics, Derivative, Inflation, Stock and flow, MD

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