policymakers demonstrate

32 Philippe Aghion and Ufuk Akcigit
to think that diminishing returns will drag its marginal product down to zero,
because part of that accumulation is the very technological progress needed to
counteract diminishing returns. According to the AK paradigm, the way to sustain
high growth rates is to save a large fraction of GDP, some of which will
find its way into financing a higher rate of technological progress and will thus
result in faster growth.
Formally, the AK model is the neoclassical model without diminishing
returns. The theory starts with an aggregate production function that is linear
homogeneous in the stock of capital:
Y = AK
with A a constant. If capital accumulates according to the same equation:
˙K = sY − δK
as before, then the economy’s long-run (and short-run) growth rate is
g = sA − δ.
which is increasing in the saving rate s.
AK theory presents a ‘one size fits all’ view of the growth process. It applies
equally to countries that are at the leading edge of the world technology frontier
and to countries that are far behind. Like the neoclassical model, it postulates
a growth process that is independent of developments in the rest of the world,
except insofar as international trade changes the conditions for capital accumulation.
Yet, it is a useful tool for many purposes when the distinction between
innovation and accumulation is of secondary importance.
1.2.3 The Product-Variety Model
The second wave of endogenous growth theory consists of so-called
‘innovation-based’ growth models, which themselves belong to two parallel
branches. A first branch within this new class of endogenous growth models is
the product variety model of Romer (1990), in which innovation causes productivity
growth by creating new, but not necessarily improved, varieties of
products. This paradigm grew out of the new theory of international trade, and
emphasizes the role of technology spillovers.
It starts from a Dixit and Stiglitz (1977) production function of the form:
∑N t
Y t = Kit α di
0
in which there are N t different varieties of intermediate product, each produced
using K it units of capital. By symmetry, the aggregate capital stock K t will be