Economic growth and economic development 586

Introduction to Modern Economic Growth
13.1. The Lab Equipment Model of Growth with Product Varieties
We start with a particular version of the growth model with expanding varieties
of inputs and an R&D technology such that only output is used in order to undertake
research. This is sometimes referred to as the lab equipment model, since all that
is required for research is investment in equipment or in laboratories–rather than
the employment of skilled or unskilled workers or scientists.
13.1.1. Demographics, Preferences and Technology. Imagine an infinitehorizon economy in continuous time admitting a representative household with preferences
(13.1)

Z∞
0

C (t)1−θ − 1
dt.
exp (−ρt)
1−θ

There is no population growth, and the total population of workers, L supplies labor
inelastically throughout. We also assume, as discussed in the previous chapter, that
the representative household owns a balanced portfolio of all the firms in the economy. Alternatively, we can think of the economy as consisting of many households
with the same preferences as the representative household in each household holding
a balanced portfolio of all the firms.
The unique consumption good of the economy is produced with the following
aggregate production function:
(13.2)

1
Y (t) =
1−β

"Z

0

N(t)
1−β

x(ν, t)

#

dν Lβ ,

where L is the aggregate labor input, N (t) denotes the different number of varieties
of inputs (machines) available to be used in the production process at time t, and
x (ν, t) is the total amount of input (machine) type ν used at time t. We assume that
x’s depreciate fully after use, thus they can be can be interpreted as generic inputs,
as intermediate goods, as machines, or even as capital as long as we are comfortable
with the assumption that there is immediate depreciation. The assumption that
the inputs or machines are “used up” in production or depreciate immediately after
being used makes sure that the amounts of inputs used in the past do not become
additional state variables, and simplifies the exposition of the model (though the
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