1
Economics 102
Problem Set #2
Due in SmartSite on Monday, April 19 by 10 p.m.
Department of Economics
Professor Siegler
UC Davis
Spring 2010
Instructions:
Please turn in a Word document summarizing all of your answers for all questions,
with calculations and explanations where appropriate.
Also turn in an Excel file for any
questions which required you to use Excel.
Be sure that both files are wellformatted.
1.
Growth Accounting
Economists model the production process by using a production function, which
transforms the factors of production(such as capital and labor) into final goods and
services (GDP).
Consider the following CobbDouglas production function that
approximates the U.S. production function:
ܻ
௧
ൌ ܣ
௧
ܭ
௧
ଵ/ଷ
ܮ
௧
ଶ/ଷ
ܻ
௧
is real GDP in time t,
ܭ
௧
is the amount of physical capital in time t (factories,
computers, tools, etc. that are used to produce goods and services), and
ܮ
௧
is the
aggregate number of labor hours in an economy in time t.
The exponent on capital (1/3)
is the proportion of total output that is paid to owners of capital, while the exponent on
labor (2/3) is the proportion of total output that is paid to workers.
That is, workers
receive 2/3 of what is produced while owners of capital receive the remaining third.
Finally, “
ܣ
௧
” is called total factor productivity in time t or the “Solow residual” since it
cannot be directly measured.
It is called the “Solow residual” after Robert Solow who
developed growth accounting in 1957.
1
If an economy can produce more real GDP with
the same amount of capital and labor, then its factors of production (labor and capital)
must have gotten more productive.
The primary determinant that causes “A” to increase
is new technology.
Suppose that over the next 50 years, the average annual growth rate of real GDP and
physical capital is 3 percent per year while the average annual growth rate of labor hours
is 1 percent per year.
Using the growth rate approximation rules:
A.
What is the average annual growth rate of total factor productivity
ሺ݃
ሻ
?
Be sure
to show your work.
B.
Labor productivity is defined as
ܻ
௧
ܮ
௧
⁄
.
That is, labor productivity is the amount
of output produced per hour of work.
Given the assumptions above, what is the
1
Solow, Robert (1957).
“Technical Change and the Aggregate Production Function,”
Review of Economics and
Statistics
39, pp. 312320.
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 Spring '11
 PARMAN
 Economics, Normal Distribution, Standard Deviation, Annual growth rate, average annual growth

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