Problem Set 1
Prof. Nordhaus and Staff
Econ 122a: Fall 2013
Due: In class, Wednesday, September 11
Problem Set 1 (required but ungraded)
General Instructions: The best procedure is to solve the problems first and then prepare a
neat answer sheet based on your solutions. You should show all the essentials, but your
responses should be concise.
Please read the rules on “Rules on problem set joint work” on the web page.
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1. There are three major statistical agencies of the US government: the Bureau of
Economic Analysis, the Bureau of Labor Statistics, and the Census Bureau. This
question is designed to help familiarize you with some of these data sources.
a. Go to the BEA website (www.bea.gov), and click the following links: “Gross
Domestic Product”, “Interactive NIPA Tables”, and “Begin using the data…”. Take a
moment to examine the data that are available through this page. Look at table 1.1.1
(“Percent Change From Preceding Period in Real Gross Domestic Product”). In which
quarters since 2007 did the US experience a decline in Real GDP?
b. Recessions are sometimes defined as periods in which real GDP decline in two or
more consecutive quarters. Using this definition, identify the recessions since 1960.
c. Go to the BLS website (www.bls.gov), and click “Subject Areas”. Take a moment to
look at the data available from this page. Click “Consumer Price Index”, and under
“CPI databases”, click the “Top Picks” for “All Urban Consumers”. First, retrieve data
from “U.S. All Items”, and format the data to be shown as annual percent changes. In
which years since 1960 did the US economy experience deflation (that is, negative
percent changes in the annual inflation series), according the CPI?
d. One criticism of the CPI is that it includes items whose prices that are highly volatile,
such as the prices for food and energy, and including such items may cause the index
to be unnecessarily volatile. Therefore, economists also look at “All Items Less Food
and Energy”, which is also known as “Core CPI”. In which years since 1960 did the US
economy experience deflation according to this measure?
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2. Consider the following actual data on computer and non-computer prices and
quantities (from slide 14 of the lecture notes on measurement):
Sector
Computers
Non computers
Output (billions 2005$)
1960
2012
0.0000337
87.94
3,105.8
15,382.8
Computers
Non computers
Price (2005 = 1)
1960
2012
5,935.7
0.9006
0.1749
1.0560
Calculate the Laspeyres, Paasche, and Fisher indexes for output growth between the two
periods. Report the result as an average annual growth rate. (Extra non-credit: do the
same using the Törnqvist index.)
3.
Consider a Cobb-Douglas production function with three inputs. K is capital (number
of machines), L is the number of workers, and H is human capital (the average number
of years of education per worker). The production function is:
𝑌 = 𝐾𝐿𝐻
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a. Derive an expression for the marginal product of workers. How does an increase in
the quantity of human capital affect the marginal product of workers?
b. Derive an expression for the marginal product of human capital. How does an
increase in the quantity of human capital affect the marginal product of human capital?
c. In the national income accounts of this economy, what is the income share of labor?
d. Does the above production function exhibit constant returns to the number of workers
and the quantity of capital? Explain your answer both mathematically and intuitively.
e. Assume that initial values of K, L, and H are 100, 1, and 10. In the second period,
capital grew by 10%, workers were constant, and the amount of education increased by
12 years. Show the formula for the logarithmic growth in output as a function of the
logarithmic growth in inputs, and calculate the growth of output.
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