Background
- You have been playing the Hazards Game for a few weeks now, and many players (?) still do not seem to have a clear strategy on how to play, or even a clear understanding of how to determine whether you can expect to gain or lose money in a region. In this problem set, you will solve this second aspect.
- Basically, we need to graph both the income and expected losses in a region as a function of Rate and Nhouses. Then you'll be able to see where you want to go in terms of rates & Nhouses (though getting there is up to you!).
- The key graph is Nhouses versus Rate, and I've included this basic graph below. You'll need to print this out, then draw various curves and lines on it -- or, you can construct your own graph of Nhouses vs. Rate from your favorite spreadsheet program (keep the axes the same). The only advantage of the below graph is that it also plots the data from our game: it shows Nhouses vs. Rate for 28 players after Step #6.
The Problem (in ten parts)
Income
1. Income: Write down the simple equation that gives income, I, as a function of Nhouses, N, and Rate, R. 2. Now, rearrange that equation to give N as a function of R and I. 3. You will now plot "contours" of equal-income values on the N vs R graph. Plot at least 5 contours: I=$100,000; I=$75,000; I=$50,000; I=$25,000; and I=$10,000.Expected Losses: We will go through the calculation for the NE region.
4. First, calculate the average annual total loss of houses in the NE region due to tornados. 5. To calculate the fraction losses per year, divide your number from above by the total number of houses in the NE region. (you can also quote this as a percentage loss). 6. Now, lets say that a player has 1,000 houses in the NE region. Calculate the expected $ loss per year (recall that each house is covered for $10,000). 7. Draw the "contour" for an expected loss of $100,000 across the above graph. 8. Now add the expected loss contours for: $75,000; $50,000; $25,000; and $10,000. 9. Indicate the region of the N vs. R graph where income exceeds losses. 10. But, you also need to pay back money to the bank each year. Lets suppose that you want to generate an "extra" $25,000 each year from the NE region as a 1/4 contribution toward the $100,000. Now, identify the sector of the N vs R graph that provides a profit above and beyond this $25,000.You should now have a better idea of where you want to be in the N vs R graph.
The next steps, entirely up to you, are to repeat this process for the other regions, and then to change your rates to try and get to where you want to be.
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