Economic growth and economic development 389
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Introduction to Modern Economic Growth
in the model without growth, discounted utility is finite. When there is growth, we
will strengthen this assumption and introduce Assumption 4.
We start with an economy without any technological progress. Factor and product markets are competitive, and the production possibilities set of the economy is
represented by the aggregate production function
Y (t) = F [K (t) , L (t)] ,
which is a simplified version of the production function (2.1) used in the Solow
growth model in Chapter 2. In particular, there is now no technology term (laboraugmenting technological change will be introduced below). As in the Solow model,
we impose the standard constant returns to scale and Inada assumptions embedded
in Assumptions 1 and 2. The constant returns to scale feature enables us to work
with the per capita production function f (·) such that, output per capita is given
by
Y (t)
L (t)
∙
¸
K (t)
= F
,1
L (t)
≡ f (k (t)) ,
y (t) ≡
where, as before,
(8.4)
k (t) ≡
K (t)
.
L (t)
Competitive factor markets then imply that, at all points in time, the rental rate
of capital and the wage rate are given by:
(8.5)
R (t) = FK [K(t), L(t)] = f 0 (k(t)).
and
(8.6)
w (t) = FL [K(t), L(t)] = f (k (t)) − k (t) f 0 (k(t)).
The household optimization side is more complicated, since each household will
solve a continuous time optimization problem in deciding how to use their assets and
allocate consumption over time. To prepare for this, let us denote the asset holdings
375
