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Chapter 9
The Cutting Edge of Technology
Note: Special icons in the margin identify problems requiring a computer or calculator and those
requiring calculus .
◼ Solutions to Problems
1. The annual growth rate of productivity is given by the following equation:
ˆˆ
ˆ.A y L
=+
We are given a value of 1/3 for
and 0 for
ˆ,y
leaving the growth rate of the population,
ˆ,L
as the only
unknown. To solve for
ˆ,L
we use the standard growth equation with the initial population as 4 million
and the final population after 10,000 years as 170 million. The equation is:
2. For the relative prices, note that the high rate of productivity in the farming sector will create a fall in
the real price of wheat; whereas, the lack of significant change in productivity in the hair-cutting sector
will maintain the real price for haircuts. Thus, the fall in the price of wheat implies that the relative
price of hair cuts has risen, and the relative price of wheat has, of course, fallen.
The improvement in technology for growing wheat raises the marginal productivity of labor for
farmers, and because workers are always paid their marginal products, the real wage for farmers will
38 Weil • Economic Growth, Second Edition
3. Technological progress in the production of a good will reduce the price of that good. Moreover, the
reduction in price of the good will change the quantity demand for that good. The resulting change in
4. a. In any given year, the production of bread must equal the production of cheese in this
economy. That is,
,
bc
YY=
always. Knowing that the productivity of each good is equal at this
point in time, we can solve for the quantity of labor devoted to each sector as follows.
b. To calculate the growth rate of total output, we first calculate the growth rates of each sector by
taking the natural log of both sides and differentiating with respect to time. For the bread sector:
We know the value for the growth rate of productivity in both sectors. Furthermore, in our answer
to Part (a), we found that labor is currently equally divided among the two sectors. Thus, the
growth of labor in one sector must be offset by the growth of labor in the other—
ˆˆ
( ).
bc
LL=−
We substitute in these values and get,
Chapter 9 The Cutting Edge of Technology 39
c. The figure below depicts the growth rate of output over time. From Part (b), we know that the
growth rate of output is equal to 1.5 percent. But, productivity in the bread sector rises by a greater
percent than in the cheese sector. Bread production would rise faster than cheese production and
