Economic growth and economic development 563
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Introduction to Modern Economic Growth
12.3.3. Innovation and Ex Post Monopoly. Let us now return to the same
environment as above, and suppose that if firm 1 undertakes a successful innovation
it can obtain a fully-enforced patent. Once this happens, firm 1 will have better
technology than the rest of the firms, and will possess ex post monopoly power. This
monopoly power will enable the firm to earn profits from the innovation, potentially
encouraging its research activity in the first place. This is the basis of the claim
by Schumpeter, Arrow, Romer and others that there is an intimate link between ex
post monopoly power and innovation.
Let us now analyze this situation in a little more detail. It is useful to separate
two cases:
(1) Drastic innovation: a drastic innovation corresponds to a sufficiently high
value of λ such that firm 1 becomes an effective monopolist after the innovation. To determine which values of λ will lead to a situation of this
sort, let us first suppose that firm 1 does indeed act like a monopolist. This
implies that it will choose its price to maximize
¡
¢
π I1 = D (p) p − λ−1 ψ .
The first-order condition of this maximization is
¡
¢
D0 (p) p − λ−1 ψ + D (p) = 0.
Clearly the solution to this equation gives the standard monopoly pricing
formula (see Exercise 12.1):
(12.2)
pM ≡
λ−1 ψ
.
1 − εD (p)−1
We say that the innovation is drastic if pM ≤ ψ. In this case, firm 1 can
set its unconstrained monopoly price, pM , and capture the entire market.
(2) Limit pricing: when the innovation is not drastic, so that pM > ψ, the
equilibrium will involve limit pricing, where firm 1 sets the price
p1 = ψ,
so as to make sure that it still captures the entire market (since in this case
if it were to set p1 = pM , other firms can profitably undercut firm 1). This
type of limit pricing arises in many situations. In the case we have just
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