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AFX3355_TuteEx3_Soln - -1 AFX3355 Property Investment GM...

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- 1 - 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).
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- 2 - Q 3.4 Look at the rank/size chart of cities in the European Union (EU) shown in Exhibit 3-6. Do European cities’ rank/sizes appear to conform to the exponential shape predicted by Zipf’s Law as well as US cities seems to do? Why do you suppose the rank/size rule may not apply as well for Europe?
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AFX3355_TuteEx3_Soln - -1 AFX3355 Property Investment GM...

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