1 Exercises: Models

Exercise 1. 1 Many people experience the symptoms of a housing shortage: splitting up apartments to accomodate roommate groups; financial stress due (in part) to high rents; deferring life decisions such as having children; living in deteriorating, aging buildings, and so on.

We’re used to thinking about people in terms of lifespan, but it is also useful to think about buildings that way. City and local governments keep detailed information about the housing stock, largely for tax purposes. Services like <zillow.com> have data readily available to the public.

Question: What about the houses listed on Zillow might presented a view biased to houses in better condition?

A life-cycle assessment of a sample of US houses and apartments by Aktas and Bilic (2012) produced the following graphic about how long houses and apartments remain habitable.

Figure E1. 1: “Lifetime distribution of residential buildings calculated from multiple American Housing Survey microdata,” from Aktas and Bilic 2012.

Question: Is the graph consistent with the claim that 7% of US housing stock was built before 1920?

Question: Speculate on what might account for the rightward shift of the curve over the ten year period considered. Consider these two hypotheses:

  1. house building techniques have been improving. (When would they have had to improve to produce the curve shift?)
  2. the current housing shortage has resulted in buildings being used after the time that they would have been replaced were there no housing shortage?

File ID: hamster-hurt-lamp

Exercise 1. 2 Consider this simple, made-up mortality table that might be representative of a bird species, e.g. robins.

Age Mortality Starting Population
0 1000
1 0.50 500
2 0.50 250
3 1.00 125
4 0

Calculate the life expectancy for these birds. Give a number, but also explain you reasoning in words. (Hint: It’s not a long calculation.)

File ID: pig-forgive-saw

Exercise 1. 3 Short classroom discussion about the SIR model graphic including:

  • a quick demonstration (narrated by the students) of the patterns seen for different settings of the parameters.
  • speculate on how to operationalize “social distance.”
  • reason why the isolation parameter only goes up to 50%: the behavior doesn’t change much for higher isolations. Explain that % for isolation means the fraction of the infectives who isolate or, equivalently, how much of the time infectives isolate.

File ID: panda-spend-pen

Exercise 1. 4 Using the SIR model in the text: (NOTE: Some students have experienced problems getting the SIR model to load. If you are among these, work with a colleague whose SIR model is functional. Sorry for the inconvenience.)

  1. Describe the behavior of the number of infected persons with time in cases of the following policy options:
    1. Social Distancing = 9’; Isolation = 10%
    2. Social Distancing = 3’; Isolation = 40%
  1. How many people ultimately are infected under each of these policies?
  1. Which of these is preferable to the other, and why?

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