Econ 204
Instructor: J. Li
1
QUIZ 2 ANSWERS, SPRING 2011
Given: production function:
(a)
Find: per worker production function.
f
(
k
) =
F
(
K
,
L
) /
L
(+0.25)
=
K
α
L
1
α
/
L
= (
K
/
L
)
α
=
k
α
+0.25
(b)
Given: rate population growth =
n
.
Find: The SS capital per worker, output per worker, and consumption per worker as
a function of savings, depreciation and α.
+0.25
The SS value of capital per worker
k
* is defined as the value of
k
at which capital per
worker is constant; that is,
Δ
k
= 0
sf
(
k
)
–
(
δ
+
n
)
k
= 0.
+0.25
Or
+0.25
Solving for
we get:
Or
+0.25
Substituting
k
* into perworker production function yields
y
*:
y
=
k
α
+0.25
Similarly solve for
c
*:
c
= (1
–
s
)
y
*
+0.25
(c)
Demonstrate: The steady state solution in a diagram.
+0.5
(d)
(i)
Define: The Golden Rule level of capital.
The Golden Rule level of capital is the steady state value of
k*
that
maximizes consumption.
+0.25
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Econ 204
Instructor: J. Li
2
(ii)
Find: The condition of Gold Rule:
MPK
=
δ
+
n
.
+0.5
(iii)
In a diagram:
+0.25 for clear labeling; +0.25 for indicating at
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 Spring '11
 Beryl Li
 Economics, Macroeconomics, Steady State

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