Economic growth and economic development 591

Introduction to Modern Economic Growth
research may be very unprofitable and there may be zero R&D effort, in which case
ηV (ν, t) could be strictly less than 1. Nevertheless, for the relevant parameter values
there will be positive entry and economic growth (and technological progress), so
we often simplify the exposition by writing the free-and the condition as
ηV (ν, t) = 1.
Note also that since each monopolist ν ∈ [0, N (t)] produces machines given

by (13.10), and there are a total of N (t) monopolists, the total expenditure on
machines is
(13.15)

X (t) = N (t) L.

Finally, the representative household’s problem is standard and implies the usual
Euler equation:
1
C˙ (t)
= (r (t) − ρ)
C (t)
θ
and the transversality condition

à Z t
ả
á
(13.17)
lim exp
r (s) ds N (t) V (t) = 0,
(13.16)

t→∞

0

which is written in the “market value” form and requires the value of the total
wealth of the representative household, which is equal to the value of corporate
assets, N (t) V (t), not to grow faster than the discount rate (see Exercise 13.3).
In light of the previous equations, we can now define an equilibrium more for-

mally as time paths of consumption, expenditures, R&D decisions and total number
of varieties, [C (t) , X (t) , Z (t) , N (t)]∞
t=0 , such that (13.3), (13.15), (13.16), (13.17)
and (13.14) are satisfied; time paths of prices and quantities of each machine and the
net present discounted value of profits from that machine, [χ (ν, t) , x (ν, t)]∞
ν∈N(t),t=0
that satisfy (13.9) and (13.10), time paths of interest rate and wages such that
[r (t) , w (t)]∞
t=0 (13.13) and (13.16), hold.
We define a balanced growth path equilibrium in this case to be one in which
C (t) , X (t) , Z (t) and N (t) grow at a constant rate. Such an equilibrium can alternatively be referred to as a “steady state”, since it is a steady state in transformed
variables (even though the original variables grow at a constant rate). This is a
feature of all the growth models and we will throughout use the terms steady state
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