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AFX3355 Property Investment
Tutorial 3 – Solution guidelines
GM Chapter 3:
Q’s 3.1 – 3.14
Q 3.1
What is the “rank/size rule” (or Zipf’s Law)? What is the implication of this
rule for patterns of city size in an economy?
Answer:
Zipf’s Law rank cities from 1, 2, 3, …, with the largest city being ranked
number 1, the next largest number 2, etc.
The population for any city may
then be predicted by dividing the largest city’s size by the rank of that city.
Q 3.2
In 2000, the Census Bureau’s estimate of the population of New York City
Consolidated Metropolitan Statistical Area (CMSA) was 21,199,865. For
Boston, it was 5,819,100. According to the rank/size rule and the rank of
Boston as indicated in Exhibit 3-1b, what should the population of Boston
have been?
Answer:
According to the simple version of the rank/size rule given in the text,
Boston’s population should have been 21,199,865/7 = 3,028,552. This is only
about half of Boston’s actual population of 5,819,100. This shows that the
simple version of the rank/size rule given in the text does not quite fit the U.S.
system of cities. In particular, the cities tend to be a bit larger than what is
predicted by the simple rule. The more general statement of Zipf’s Law is as
follows:
j
K
N
j
β
=
where N j is the population of the jth rank city, K is an unspecified constant,
and the exponent
β
is a constant whose value is ‘‘near one.’’ For the top 30
U.S. cities shown in Exhibit 3-1b, statistical regression analysis indicates that
K is a bit larger than the population of New York (about 24 million instead of
20 million), and
β
is about 0.8.
Q 3.3
While the rank/size rule generally describes the distribution of city sizes
remarkably well, it does tend to over predict the number of small cities in an
economy; there are fewer small towns than predicted by the rank/size rule.
What explanation, based on volatility of growth, has been proposed to explain
this discrepancy? [Hint: See the text box “What causes the Rank/Size Rule?”]
Answer:
The rank/size rule is most applicable within a system of cities, that is, the
cities within a geographically integrated economy. Economic integration
within Europe is a relatively recent development, and at the end of the
twentieth century was still less economically integrated into a single economy
than is the case of the United States. A regression of the 11 European cities
shown in Exhibit 3-6 indicates a
β
exponent of only 0.55 (Zipf’s Law suggests
this should be close to 1).