Economic growth and economic development 667

Introduction to Modern Economic Growth
Exercise 14.25. * Consider a steady-state equilibrium in the model of Section 14.3.
Suppose that we have κ = 0 and
G0 (0) <
Let
∗

0−1

z ≡G
and suppose also that
G0 (0) <

1


à

1


ả

z (1 ) / + G (z ∗ )
.
ρ + z∗

(1) Show that in this case the steady state equilibrium has zero growth.
(2) Show that κ > 0 will lead to a positive growth rate. Interpret this result and
contrast it to the negative effects of relaxing the protection of intellectual
property rights in the baseline model of competitive innovations.

Exercise 14.26. * Modify the model presented in Section 14.3 such that followers
can now use the innovation of the technological leader and immediately leapfrog the
leader, but in this case they have to pay a license fee of ζ to the leader.
(1) Characterize the growth rate of a steady-state equilibrium in this case
(2) Write the value functions.
(3) Explain why licensing can increase the growth rate of the economy in this
case, and contrast this result with the one in Exercise 12.9, where licensing
was never used in equilibrium. What is the source of the difference between
the two sets of results?
Exercise 14.27.

(1) What is the effect of competition on the rate of growth

of the economy in a standard product variety model of endogenous growth?
What about the quality-ladder model? Explain the intuition.
(2) Now consider the following one-period model. There are two Bertrand
duopolists, producing a homogeneous good. At the beginning of each period, duopolist 1’s marginal cost of production is determined as a draw from
the uniform distribution [0, c¯1 ] and the marginal cost of the second duopolist
is determined as an independent draw from [0, c¯2 ]. Both cost realizations
are observed and then prices are set. Demand is given by Q = A − P .
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