Economic growth and economic development 536

Introduction to Modern Economic Growth
firm i ∈ [0, 1] is
(11.34)

Yi (t) = F (Ki (t) , A (t) Li (t)) ,

where Ki (t) and Li (t) are capital and labor rented by a firm i. Notice that A (t) is
not indexed by i, since it is technology common to all firms. Let us normalize the
measure of final good producers to 1, so that we have the following market clearing
conditions:

Z

1

Ki (t) di = K (t)

0

and

Z

1

Li (t) di = L,

0

where L is the constant level of labor (supplied inelastically) in this economy. Firms
are competitive in all markets, which implies that they will all hire the same capital

to effective labor ratio, and moreover, factor prices will be given by their marginal
products, thus
∂F (K (t) , A (t) L)
∂L
∂F (K (t) , A (t) L)
.
R (t) =
∂K (t)
The key assumption of Romer (1986) is that although firms take A (t) as given,
w (t) =

this stock of technology (knowledge) advances endogenously for the economy as a
whole. In particular, Romer assumes that this takes place because of spillovers
across firms, and attributes spillovers to physical capital. Lucas (1988) develops a
similar model in which the structure is identical, but spillovers work through human
capital (i.e., while Romer has physical capital externalities, Lucas has human capital
externalities).
The idea of externalities is not uncommon to economists, but both Romer and
Lucas make an extreme assumption of sufficiently strong externalities such that A (t)
can grow continuously at the economy level. In particular, Romer assumes
(11.35)

A (t) = BK (t) ,

i.e., the knowledge stock of the economy is proportional to the capital stock of
the economy. This can be motivated by “learning-by-doing” whereby, greater investments in certain sectors increases the experience (of firms, workers, managers)
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