of the SolowSwan model.
To incorporate the Romer model into the SolowSwan model we
recall that in the SolowSwan model all persons were engaged in
production and all "percapita" terms such as
Y
/
L
and
K
/
L
were
implicitly "per production worker". Thus, the substitution
L
(
t
)
→
(
1

γ
)
L
(
t
)
(
35
)
recasts the SolowSwan model in Romer form. After this substitu
tion we have the same capital accumulation equation for
κ
shown in
Eq. (
10
) and the same expression for
κ
*
, but with
κ
now given by
κ
=
K
E
(
1

γ
)
L
.
(
36
)
Carrying this substitution through to the expression for percapita
income results in income per production worker
Y
(
t
)
(
1

γ
)
L
(
t
)
=
κ
(
t
)
α
E
(
t
)
.
(
37
)
Multiplying both sides of this expression by
(
1

γ
)
yields
Y
(
t
)
L
(
t
)
= (
1

γ
)
κ
(
t
)
α
E
(
t
)
(
38
)
which is percapita income including both those in production
and
R&D.
the solow

swan and romer models
9
E
ndogenizing
g
E
with the
R
omer model
provides more eco
nomic variables whose shocks can change the evolution of the econ
omy. Let’s consider each in turn.
If the efficiency of R&D,
χ
, increases there is an immediate in
crease in
g
E
which causes
κ
*
to drop but has no immediate effect on
κ
(
t
)
: the economy is now above the new steady state. The righthand
side of the capital accumulation equation will now be negative and
the associated dynamics will slow the growth of the economy ini
tially. The economic shock will dissipate faster since the halflife of
the recovery will be smaller. Once steadystate as been reestablished
the economy will grow at the new higher
g
E
.
If the fraction of the labor force engaged in R&D,
γ
, increases there
will be an immediate drop in
Y
/
L
because of the associated decrease
in the number of people working in production. With more capital
than production labor (the capital used in production by those now
in R&D is now not being used in production) the economy will be
above steady state and the growth rate will slow until the economy is
once again on the balancedgrowth path. Mathematically, the
(
1

γ
)
prefactor together with the same factor in the denominator of
κ
α
will result in a factor of
(
1

γ
)
1

α
which gets smaller. This shock
will cause
κ
to increase because
(
1

γ
)
in the denominator will
have decreased and cause
κ
*
to decrease because
g
E
has increased.
By increasing
κ
and decreasing
κ
*
this shock moves the economy
above steady state. The righthand side of the capital accumulation
equation will now be negative and and contribute a growth drag to
the new
g
E
. As before the economic shock will dissipate faster since
the halflife of the recovery will be smaller, and once steadystate as
been reestablished the economy will grow at the new higher
g
E
.
If the labor force
L
increases there will be an immediate decrease
in
κ
(
t
)
and
Y
/
L
and an immediate increase in
g
E
that will result
in an associated decrease both of
κ
*
and of the halflife
t
1
/
2
. If the
resulting sign of the capital accumulation equation is negative the
economy will be above steady state and the associated negative
g
κ
will slow economic growth during the transition phase. If, on the
other hand, the sign is positive, then the economy will be below
steady state and, like Germany following WWII,
g
κ
will enhance