### Flowcharts

**Q71.** Consider this little bit of logic that describes a tourist's thinking process (taken from the title of a 1970s movie): “if it’s Tuesday, this must be Belgium. Otherwise, I have no idea where we are.” Sketch a flowchart that represents this flow of thought.

**Q75.** Sketch a flowchart that represents this bit of logic: “If you can get a direct flight for under $1500 take it unless it leaves from SFO before 9 am. Otherwise, see if anything is available on frequent flier miles no matter what the routing. If you can’t find anything, use Expedia to find the cheapest flight out of OAK.”

**Q83.** Weimer & Vining (1989) characterize policy problems in terms of market failure and government failure. Any given problem, they suggest, can be placed in one of four categories: (1) market AND government failure; (2) government works (policy corrects for market failure); (3) market works; (4) government failure to correct for market failure. Their suggested strategy is to start by asking whether there is a market failure and then whether there is government failure. Using the two conditionals, "Is there evidence of market failure?" and "Is there evidence of government failure?" construct a flowchart that would permit you to classify any given situation into one of the four aforementioned categories.

### Decision Models

**Q93.** A new device at your favorite big box store costs $200. It has a one year guarantee from the manufacturer. The cashier offers you a special deal on a three year replacement warranty (assume it's good, will be honored, etc.) — $40. You estimate that the chances of the device failing during second and third years is 25% and that the price of replacement by then will be $150. Should you buy the service plan? What are the parameters of this decision model?

**Q104.** House gets another case. There's this funny rash. We won't say where it appears, but it's a funny rash. In 1% of the cases, it means something really, really bad — anxoreisis. Fortunately, there's a test. Unfortunately, it's not a perfect test. Fortunately, it's a pretty good test. Unfortunately, it is wrong 2% of the time. Work it out.

**Q105.** Following on problem 104, suppose the test is not painless or without its own risks. Suppose the "cost" of the test is 5. And suppose the treatment is also not so nice and the cost of the treatment is 15. But if you have the disease and you are not treated, the results are nasty : 50. Do we have enough information to recommend a course of action? What should we do?

### Stock and Flow Models (system dynamics)

**Q113.** Sketch a causal loop diagram for this system (be sure to label each link and the overall loop). Comment on the long term equilibrium of this system.

- Being happy…
- …makes you to smile…
- …makes people approach you…
- …makes you feel social…
- …makes you happy…

**Q128.** Consider the act of filling up a bathtub for a baby (or yourself!). You have a faucet that you can turn more towards hot or toward cold. List out the flows, the stocks, the sources of information, the "valves," and the rules that govern the valves in this system.

**Q129.** Draw a stock and flow diagram for filling up a bathtub for a baby (or yourself!). You have a faucet that you can turn more towards hot or toward cold. Be sure to show the flows, the stocks, the sources of information, the "valves," and the rules that govern the valves in this system.

### Difference Equations

**Q107.** Our neighborhood association has a ten member board. Each year it plans to add four members. Write the difference equations that describe the size of the board (S) each year.

**Q110.** Each year the feral cat population grows by 3%. Let C_{n} be the number of cats n years from now. Assume there are presently 350. Suppose that each year we catch and euthanize or place in homes 20 cats. Write the equations for this situation.

**Q111.** Let's say we have a 2 year graduate program. The first year class is growing at a rapid rate 5% per year. Between the first and second years, 25% of the students change their minds or get jobs and leave the program. Among the second years, 10% leave before graduation. The program currently has 20 first year and 12 second year. Write difference equations to describe population in future years.

### Markov Models

**Q151.** A cinema has a marquee with lots and lots of light bulbs. In any given week 1% of the light bulbs burn out. Unfortunately, between being busy and being sloppy, replacement is a little bit sporadic. Of all the bulbs that are burnt out, about 95% get replaced each week. Draw the state diagram for this system.

**Q153.** A criminologist and an activist decide to collaborate on a project designed to reduce prison population. In the spirit of starting simple, they identify 4 states in which people can find themselves: never imprisoned; incarcerated; on parole; post-parole. The period of time in their analysis will be one year. Suppose 70% of the population has never been incarcerated. Each year 2% of these people are imprisoned. Of those currently incarcerated, 20% are released each year onto parole. Average parole is 5 years so that a person on parole has a 20% chance of finishing parole. Those on parole have a 10% chance of finding themselves back in prison in any given year. Individuals who are post parole have a 4% chance of returning to prison in any given year. Draw a state diagram and matrix representing this information.

**Q155.** Suppose 25% of the mortgages written in the first years of this century were subprime (meaning the borrowers were not very credit-worthy) and all were 5 year adjustable such that after the fifth year the monthly payments would go way up. In the market in question there is approximately 5% turnover housing each year. The housing stock in the market consists of one million units. Research has shown that 33 1/3% of subprime adjustable mortgages go into default under current conditions when they go past their five year mark (and these conditions are expected to continue for some time) when they adjust.

### Sorting and Peer Effects

**Q173.** Consider this data on the thresholds in a population. Draw a frequency histogram and cumulative frequency diagram. If news reports suggest participation will be at 20 people, how many people's threshold is met or exceeded? How about if the number is 70?

**Q174.** Consider this data on the thresholds in a population. Draw a frequency histogram and cumulative frequency diagram. How does this system behave when the expected number is 10? 20? 50? 60? 90?

**Q178.** Which of the cumulative frequency distributions below corresponds to this frequency distribution

A. | B. | C. |

D. | E. |

### Aggregation & Cellular Automata

**Q166.**Consider a one dimensional cellular automata that looks like this:

Generation 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Generation 2 |

Show what the next few generations would look like subject to "rule 93":

Rule 93 | ||||||||||||||||||||||||||||||

0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 |

**Q167.** Suppose we have a diffusion process in which all susceptibles who are in contact with an infected in a given time period become infected in the next time period. On the grids below color in squares to indicate what happens over the first six time periods beginning with one infected. Then fill in the table and chart the data.

**Q169.** Consider the 12 block neighborhood bounded by parks on the north and south and major thoroughfares on the east and west. Green houses are supporting Obama, purple houses Romney.

Using the facing blocks delineated by the red dashed lines as units (it yields 15 of them), calculate the index of dissimilarity.