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Chapter 8
The Role of Technology in Growth
Note: Special icons in the margin identify problems requiring a computer or calculator .
◼ Solutions to Problems
1. a. Nonrival. Nonexcludable. One’s consumption of National Defense does not diminish
c. Non-Rival. Excludable. My authorized use of a website does not diminish another’s use of the
2. The advantage to having patent laws in the creation of life-saving prescription drugs is that the resulting
monopoly pricing will actually provide an incentive for companies to undertake that the research and
3. With no change in the fraction of workers devoted to research and development, productivity and
output per worker would continue to grow indefinitely at the previous rate. That is,
ˆ
ˆ,
L
yA
==
Because the change in
to
is temporary, at the time
2,t
that
returns to the original fraction
,
the process will reverse itself. Output per worker will jump up to a new level as workers move out of
Because the change in
is the same and
A
A, we know that the absolute difference in the jump up
is greater than the jump down. The level of
A
is dependent on the length of the temporary increase in
4. The given parameters of the model are, L = 1,
= 5, and
= 0.5. To calculate the growth rate of
output per worker, we substitute in these values into the following equation and solve to get:
In this case, output per worker grows at 15 percent a year. However, the level of output per worker
has dropped. The level before the drop can be found by substituting the previous parameter values
into the production function to get:
Therefore, the original level of output per worker is A(0.5), and we need to find how long it will
take to reach this level, starting from a level of A(0.25) with a growth rate of 15 percent. We use the
standard growth equation, substitute and solve.
34 Weil • Economic Growth, Second Edition
5. In the diagram below, the increase in the fraction of labor devoted to R&D in Country 1 will create
a drop in the level of output per worker but an increase in the growth rate of productivity as well as
output per worker. Country 1 behaves in accordance with the one-country model. However, the
Chapter 8 The Role of Technology in Growth 35
6. We are given a scenario where the follower, Country 2, raises the fraction of the labor force devoted
to R&D beyond the fraction in the leader, Country 1. The implication in the long run is for Country 2
to become the technological leader. The process by which this occurs is illustrated in the diagrams
of the growth rates of productivity and output per worker below. The initial rise in the fraction of
36 Weil • Economic Growth, Second Edition
7. a. In the steady state,
12
ˆˆ
.AA=
Therefore,
Rearranging and solving for
,
c
we get,
Rearranging, we find out solution to be:
b. If we assume
1/2,
=
=10,
i
=
,1 0.2,
A
and
=
,2 0.1,
A
we can solve the previous equation
to get:
