•
On an individual
f
rm level, production can certainly be subject to scale economies
or scale diseconomies, for the economy as a whole, we do not think that either
assumption is plausible. If aggregate production is indeed subject to increasing
returns to scale, there should be higher labor productivities in more populous
countries. Think of two countries
i
and
j
,andthat
j
is two times the size of
i
in that
K
j
=2
K
i
and
N
j
=2
N
i
. Labor productivity in
i
is
y
i
≡
Y
i
N
i
=
AF
(
K
i
,N
i
)
N
i
.
Labor productivity in
j
is
y
j
≡
Y
j
N
j
=
AF
(
K
j
,N
j
)
N
j
=
AF
(2
K
i
,
2
N
i
)
2
N
i
>
2
AF
(
K
i
,N
i
)
2
N
i
=
y
i
.
Conversely, if aggregate production should be subject to decreasing returns to
scale
y
j
≡
Y
j
N
j
=
AF
(
K
j
,N
j
)
N
j
=
AF
(2
K
i
,
2
N
i
)
2
N
i
<
2
AF
(
K
i
,N
i
)
2
N
i
=
y
i
.
But there does not seem to be any systematic relation between country size
and living standard. The U.S. is a few times larger than Germany; yet the
two countries have just about the same living standard. Such considerations
suggest that it is most reasonable to assume that aggregate production is subject
to constant returns to scale, meaning that
AF
([1 +
x
]
K,
[1 +
x
]
N
)=[1+
x
]
AF
(
K,N
)
,
(1)
whereby an increase in the two factor inputs by
x
percent results in aggregate
output rising by just the same
x
percent.
•
An important consequence from assuming constant returns to scale is that a
country’s labor productivity depends only on the country’s capital—labor ratio
K/N
, but not on the levels of
K
and
N.
To see this, let
[1 +
x
]=1
/N
in
(1) ;
then the condition becomes
AF
μ
K
×
1
N
,N
×
1
N
¶
=
1
N
×
AF
(
K,N
);
i.e.,
y
=
AF
μ
K
N
,
1
¶
≡
Af
(
k
)
,
where