Chapter 10
Efficiency
Note: Special icons in the margin identify problems requiring a computer or calculator and those
requiring calculus .
◼ Solutions to Problems
1. Denoting each country by the appropriate subscript, we are given that,
2
X
Z
A
A=
and
4.
X
Z
T
T=
2. The level of productivity in Country X, relative to the United States is given as
U.S.
1.
2
X
A
A=
Chapter 10 Efficiency 41
Since, productivity is defined as T E, we can divide the productivity level of Country X by the
productivity level of the United States to obtain the ratio of efficiency in both countries.
3. Assuming that and that the growth rate of productivity is
0.66%, we write the functional productivity equation of each country in ratio form and substitute in
the necessary values to obtain:
4. Brief examples of real-world inefficiencies for each category are given below.
Unproductive Activities: In addition to theft and political lobby activities, wars are generally extremely
unproductive. Other examples are black market activities such as drug use, drug dealing, and so forth.
42 Weil • Economic Growth, Second Edition
6. The figure below depicts an inefficient allocation of labor between the urban and rural sector. An
efficient allocation is given by Point A, the point where the marginal productivity of labor equalizes
in both sectors. However, with a minimum wage of the urban sector set above the optimal wage
7. The marginal product of Sector 1 is found by differentiating the production function of Sector 1.
That is,
Chapter 10 Efficiency 43
In equilibrium, the wage of both sectors must be equal, as workers are free to move between sectors.
Therefore, we set to solve for the number of workers in each sector.
The figure below depicts, graphically, the scenario above with the assumption that L = 10. As predicted,
the intersection of wage curves intersect where two workers are employed in Sector 1, where marginal
products are paid, and four times that number of workers (eight workers) are employed in Sector 2,
where average products are paid.