Final Exam °Econ 4010
17 December 2007
Department of Economics
York University
Section A: do all three problems
1. The Ramsey model [10 marks]
Consider the Ramsey model.
It can be shown that the dynamics of consumption,
c
, are given by the
socalled Euler equation:
°
c
c
=
r
°
°
°
±g
±
,
where
r
=
f
0
(
k
)
is the real interest rate. (We assume that depreciation is zero.) The dynamics of
k
are given
by
°
k
=
f
(
k
)
°
c
°
(
n
+
g
)
k
.
We assume that
f
0
(
k
)
>
0
and
f
00
(
k
)
<
0
.
(a) Draw the (
°
k
= 0
)locus in a phase diagram with
c
on the vertical axis and
k
on the horizontal. Explain
why it is shaped the way it is. [5 marks]
(b) Find an expression for the steadystate level of
r
, denoted
r
±
, in terms of exogenous parameters. [5
marks]
2. Endogenous growth [10 marks]
Consider an endogenous growth model. We can write the growth rate of capital,
K
(
t
)
, as
g
K
(
t
)
±
°
K
(
t
)
K
(
t
)
=
s²
°
A
(
t
)
K
(
t
)
±
1
²
°
.
where
³
is the capital share of output,
A
(
t
)
the level of technology,
s
the rate of saving, and
²
a constant
which depends on exogenous parameters. (The labor force is also constant and set to
1
.)
The growth rate of technology can be written as
g
A
(
t
)
±
°
A
(
t
)
A
(
t
)
=
!
°
K
(
t
)
A
(
t
)
±
±
,
where
´
is a parameter in the production function for technology (i.e., new ideas), and
!
is constant and
depends on exogenous parameters.
The growth rates of
A
(
t
)
and
K
(
t
)
are constant on the balanced growth path. We denote these by
g
±
A
and
g
±
K
, respectively.
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 Spring '09
 ZAFARKAYANI
 Economics, Inflation, Endogenous growth theory, Exogenous growth model, exogenous parameters

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