Economics 200
Macroeconomic Theory
Problem Set 4
Due at the beginning of class on October 9, 2007.
1
.
Consider an economy with a technology described by the aggregate production function
2
.
]œ OP
"
33
2
Suppose that there is no population growth or technical progress and that the depreciation rate is 5% (
).
$
œÞ!&
(a) Show that the per capita production function is
2
.
Cœ 5
"
3
(b) Suppose that the saving rate is 10% (
, find the steadystate levels of capital, income and
=œÞ"Ñ
consumption per person.
(c) Find the golden rule levels of capital and income per person.
2
,
.
Note that, for
Cœ 5 QT œ 5
"#
$
3
5
#
$
(d) What is the golden rule saving rate?
(e) Find the golden rule level of consumption per person.
(f) Suppose that this economy had reached the steady state with
and then the saving rate rose to
=œÞ"
the golden rule level and stayed there forever.
Draw a graph showing the paths of income, consumption, and
gross investment prior to the change in
and for at least 50 years during the transition to the new steady state.
=
How many years does it take for consumption per person to exceed its value at the original steady state?
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This note was uploaded on 04/26/2010 for the course ECON 101 taught by Professor Staff during the Spring '08 term at Vassar.
 Spring '08
 Staff
 Economics, Microeconomics

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